From d72dd0b2e4c59cb21af9dcb338a5e48baddf7824 Mon Sep 17 00:00:00 2001
From: Markus Pfeiffer <markus.pfeiffer@morphism.de>
Date: Fri, 5 Feb 2016 12:35:43 +0000
Subject: [PATCH] Pretty print json

---
 gap/gaptypes.json | 353306 ++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 353305 insertions(+), 1 deletion(-)

diff --git a/gap/gaptypes.json b/gap/gaptypes.json
index f3b7017..c125bbd 100644
--- a/gap/gaptypes.json
+++ b/gap/gaptypes.json
@@ -1 +1,353305 @@
-[{"name" : "IsObject","type" : "GAP_Category","implied" : []},{"name" : "IsMutable","type" : "GAP_Category","implied" : ["IsMutable","IsCopyable"]},{"name" : "IsCopyable","type" : "GAP_Category","implied" : ["IsCopyable"]},{"name" : "IsFunction","type" : "GAP_Category","implied" : ["IsFunction"]},{"name" : "IsOperation","type" : "GAP_Category","implied" : ["IsFunction","IsOperation"]},{"name" : "IsInt","type" : "GAP_Category","implied" : ["IsInt","IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},{"name" : "IsRat","type" : "GAP_Category","implied" : ["IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},{"name" : "IsCyc","type" : "GAP_Category","implied" : ["IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},{"name" : "Tester(CONDUCTOR)","type" : "GAP_Attribute","filters" : ["Tester(CONDUCTOR)"]},{"name" : "IsFFE","type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement"]},{"name" : "IsPerm","type" : "GAP_Category","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement"]},{"name" : "IsTransformation","type" : "GAP_Category","implied" : ["IsTransformation","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement"]},{"name" : "IsPartialPerm","type" : "GAP_Category","implied" : ["IsPartialPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement"]},{"name" : "IsBool","type" : "GAP_Category","implied" : ["IsBool"]},{"name" : "IsRecord","type" : "GAP_Category","implied" : ["IsRecord"]},{"name" : "IsList","type" : "GAP_Category","implied" : ["IsList","IsListOrCollection"]},{"name" : "IsDenseList","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsListOrCollection"]},{"name" : "IsHomogeneousList","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection"]},{"name" : "IsTable","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection"]},{"name" : "Tester(LENGTH)","type" : "GAP_Attribute","filters" : ["Tester(LENGTH)"]},{"name" : "IsSSortedList","type" : "GAP_Property","filters" : ["IsSSortedList","Tester(IS_SSORT_LIST)","IsSortedList","Tester(IsSortedList)"]},{"name" : "Tester(IS_SSORT_LIST)","type" : "GAP_TrueProperty","implied" : ["Tester(IS_SSORT_LIST)"]},{"name" : "IsNSortedList","type" : "GAP_Property","filters" : ["IsNSortedList","Tester(IS_NSORT_LIST)"]},{"name" : "Tester(IS_NSORT_LIST)","type" : "GAP_TrueProperty","implied" : ["Tester(IS_NSORT_LIST)"]},{"name" : "IsPositionsList","type" : "GAP_Property","filters" : ["IsPositionsList","Tester(IS_POSS_LIST)"]},{"name" : "Tester(IS_POSS_LIST)","type" : "GAP_TrueProperty","implied" : ["Tester(IS_POSS_LIST)"]},{"name" : "IsPlistRep","type" : "GAP_Representation","implied" : ["Tester(LENGTH)","IsPlistRep","IsInternalRep"]},{"name" : "IsBlist","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsBlist","IsListOrCollection"]},{"name" : "IsBlistRep","type" : "GAP_Representation","implied" : ["IsBlistRep","IsInternalRep"]},{"name" : "IsRange","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsRange","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsCyclotomic)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "IsRangeRep","type" : "GAP_Representation","implied" : ["IsRangeRep","IsInternalRep"]},{"name" : "IsString","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsString","IsListOrCollection"]},{"name" : "IsStringRep","type" : "GAP_Representation","implied" : ["IsStringRep","IsInternalRep"]},{"name" : "IsWeakPointerObject","type" : "GAP_Category","implied" : ["IsList","IsWeakPointerObject","IsListOrCollection","IsFinite","Tester(IsFinite)","IsSmallList","Tester(IsSmallList)"]},{"name" : "IsNoImmediateMethodsObject","type" : "GAP_Filter","implied" : ["IsNoImmediateMethodsObject"]},{"name" : "IsInternalRep","type" : "GAP_Representation","implied" : ["IsInternalRep"]},{"name" : "IsPositionalObjectRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep"]},{"name" : "IsComponentObjectRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep"]},{"name" : "IsDataObjectRep","type" : "GAP_Representation","implied" : ["IsDataObjectRep"]},{"name" : "IsNonAtomicComponentObjectRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsNonAtomicComponentObjectRep"]},{"name" : "IsReadOnlyPositionalObjectRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsReadOnlyPositionalObjectRep"]},{"name" : "IsAtomicPositionalObjectRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsAtomicPositionalObjectRep"]},{"name" : "IsAttributeStoringRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep"]},{"name" : "IsFamily","type" : "GAP_Category","implied" : ["IsFamily"]},{"name" : "IsType","type" : "GAP_Category","implied" : ["IsType"]},{"name" : "IsFamilyOfFamilies","type" : "GAP_Category","implied" : ["IsFamily","IsFamilyOfFamilies"]},{"name" : "IsFamilyOfTypes","type" : "GAP_Category","implied" : ["IsFamily","IsFamilyOfTypes"]},{"name" : "IsFamilyDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsFamilyDefaultRep"]},{"name" : "IsTypeDefaultRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsTypeDefaultRep"]},{"name" : "Tester(Name)","type" : "GAP_Attribute","filters" : ["Tester(Name)"]},{"name" : "Tester(InfoText)","type" : "GAP_Attribute","filters" : ["Tester(InfoText)"]},{"name" : "Tester(String)","type" : "GAP_Attribute","filters" : ["Tester(String)"]},{"name" : "Tester(IsImpossible)","type" : "GAP_Attribute","filters" : ["Tester(IsImpossible)"]},{"name" : "IsPackedElementDefaultRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsPackedElementDefaultRep"]},{"name" : "IsToBeDefinedObj","type" : "GAP_Category","implied" : ["IsToBeDefinedObj"]},{"name" : "IsLVarsBag","type" : "GAP_Category","implied" : ["IsLVarsBag"]},{"name" : "IsListOrCollection","type" : "GAP_Category","implied" : ["IsListOrCollection"]},{"name" : "IsCollection","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection"]},{"name" : "Tester(CollectionsFamily)","type" : "GAP_Attribute","filters" : ["Tester(CollectionsFamily)"]},{"name" : "CategoryFamily(IsCollection)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsCollection)"]},{"name" : "Tester(ElementsFamily)","type" : "GAP_Attribute","filters" : ["Tester(ElementsFamily)"]},{"name" : "IsStandardIterator","type" : "GAP_Filter","implied" : ["IsStandardIterator"]},{"name" : "IsIterator","type" : "GAP_Category","implied" : ["IsIterator"]},{"name" : "IsEmpty","type" : "GAP_Property","filters" : ["IsEmpty","Tester(IsEmpty)"]},{"name" : "Tester(IsEmpty)","type" : "GAP_TrueProperty","implied" : ["Tester(IsEmpty)"]},{"name" : "IsTrivial","type" : "GAP_Property","filters" : ["IsTrivial","Tester(IsTrivial)","IsFinite","Tester(IsFinite)","CanComputeSize"]},{"name" : "Tester(IsTrivial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTrivial)"]},{"name" : "IsNonTrivial","type" : "GAP_Property","filters" : ["IsNonTrivial","Tester(IsNonTrivial)"]},{"name" : "Tester(IsNonTrivial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNonTrivial)"]},{"name" : "IsFinite","type" : "GAP_Property","filters" : ["IsFinite","Tester(IsFinite)"]},{"name" : "Tester(IsFinite)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFinite)"]},{"name" : "IsWholeFamily","type" : "GAP_Property","filters" : ["IsWholeFamily","Tester(IsWholeFamily)"]},{"name" : "Tester(IsWholeFamily)","type" : "GAP_TrueProperty","implied" : ["Tester(IsWholeFamily)"]},{"name" : "Tester(Size)","type" : "GAP_Attribute","filters" : ["Tester(Size)","CanComputeSize"]},{"name" : "Tester(Representative)","type" : "GAP_Attribute","filters" : ["Tester(Representative)"]},{"name" : "Tester(RepresentativeSmallest)","type" : "GAP_Attribute","filters" : ["Tester(RepresentativeSmallest)"]},{"name" : "Tester(PseudoRandomSeed)","type" : "GAP_Attribute","filters" : ["Tester(PseudoRandomSeed)"]},{"name" : "Tester(Enumerator)","type" : "GAP_Attribute","filters" : ["Tester(Enumerator)"]},{"name" : "Tester(EnumeratorSorted)","type" : "GAP_Attribute","filters" : ["Tester(EnumeratorSorted)"]},{"name" : "Tester(UnderlyingCollection)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingCollection)"]},{"name" : "Tester(AsList)","type" : "GAP_Attribute","filters" : ["Tester(AsList)"]},{"name" : "Tester(AsSortedList)","type" : "GAP_Attribute","filters" : ["Tester(AsSortedList)"]},{"name" : "Tester(AsSSortedList)","type" : "GAP_Attribute","filters" : ["Tester(AsSSortedList)"]},{"name" : "CanEasilyCompareElements","type" : "GAP_Property","filters" : ["CanEasilyCompareElements","Tester(CanEasilyCompareElements)"]},{"name" : "Tester(CanEasilyCompareElements)","type" : "GAP_TrueProperty","implied" : ["Tester(CanEasilyCompareElements)"]},{"name" : "CanEasilySortElements","type" : "GAP_Property","filters" : ["CanEasilyCompareElements","Tester(CanEasilyCompareElements)","CanEasilySortElements","Tester(CanEasilySortElements)"]},{"name" : "Tester(CanEasilySortElements)","type" : "GAP_TrueProperty","implied" : ["Tester(CanEasilySortElements)"]},{"name" : "CanComputeSize","type" : "GAP_Filter","implied" : ["CanComputeSize"]},{"name" : "Tester(RandomizerAttr)","type" : "GAP_Attribute","filters" : ["Tester(RandomizerAttr)"]},{"name" : "Tester(CheapRandomizerAttr)","type" : "GAP_Attribute","filters" : ["Tester(CheapRandomizerAttr)"]},{"name" : "IsConstantTimeAccessList","type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsConstantTimeAccessList"]},{"name" : "IsSmallList","type" : "GAP_Property","filters" : ["IsSmallList","Tester(IsSmallList)"]},{"name" : "Tester(IsSmallList)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSmallList)"]},{"name" : "Tester(ConstantTimeAccessList)","type" : "GAP_Attribute","filters" : ["Tester(ConstantTimeAccessList)"]},{"name" : "IsSortedList","type" : "GAP_Property","filters" : ["IsSortedList","Tester(IsSortedList)"]},{"name" : "Tester(IsSortedList)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSortedList)"]},{"name" : "IsDuplicateFree","type" : "GAP_Property","filters" : ["IsDuplicateFree","Tester(IsDuplicateFree)"]},{"name" : "Tester(IsDuplicateFree)","type" : "GAP_TrueProperty","implied" : ["Tester(IsDuplicateFree)"]},{"name" : "IsQuickPositionList","type" : "GAP_Filter","implied" : ["IsQuickPositionList"]},{"name" : "Tester(AsDuplicateFreeList)","type" : "GAP_Attribute","filters" : ["Tester(AsDuplicateFreeList)"]},{"name" : "Tester(SortingPerm)","type" : "GAP_Attribute","filters" : ["Tester(SortingPerm)"]},{"name" : "IsExtAElement","type" : "GAP_Category","implied" : ["IsExtAElement"]},{"name" : "CategoryCollections(IsExtAElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsExtAElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtAElement))"]},{"name" : "IsNearAdditiveElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement"]},{"name" : "CategoryCollections(IsNearAdditiveElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsNearAdditiveElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))"]},{"name" : "IsNearAdditiveElementWithZero","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero"]},{"name" : "CategoryCollections(IsNearAdditiveElementWithZero)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)"]},{"name" : "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))"]},{"name" : "IsNearAdditiveElementWithInverse","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse"]},{"name" : "CategoryCollections(IsNearAdditiveElementWithInverse)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)"]},{"name" : "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))"]},{"name" : "IsAdditiveElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsAdditiveElement"]},{"name" : "CategoryCollections(IsAdditiveElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsAdditiveElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsAdditiveElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditiveElement))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))"]},{"name" : "IsExtLElement","type" : "GAP_Category","implied" : ["IsExtLElement"]},{"name" : "CategoryCollections(IsExtLElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsExtLElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtLElement))"]},{"name" : "IsExtRElement","type" : "GAP_Category","implied" : ["IsExtRElement"]},{"name" : "CategoryCollections(IsExtRElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtRElement","CategoryCollections(IsExtRElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsExtRElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtRElement))"]},{"name" : "IsMultiplicativeElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement"]},{"name" : "CategoryCollections(IsMultiplicativeElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsMultiplicativeElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))"]},{"name" : "IsMultiplicativeElementWithOne","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne"]},{"name" : "CategoryCollections(IsMultiplicativeElementWithOne)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)"]},{"name" : "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))"]},{"name" : "IsMultiplicativeElementWithInverse","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse"]},{"name" : "CategoryCollections(IsMultiplicativeElementWithInverse)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)"]},{"name" : "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))"]},{"name" : "IsOddAdditiveNestingDepthFamily","type" : "GAP_Filter","implied" : ["IsOddAdditiveNestingDepthFamily"]},{"name" : "IsOddAdditiveNestingDepthObject","type" : "GAP_Filter","implied" : ["IsOddAdditiveNestingDepthObject"]},{"name" : "IsGeneralizedRowVector","type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsGeneralizedRowVector"]},{"name" : "IsMultiplicativeGeneralizedRowVector","type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVector"]},{"name" : "Tester(NestingDepthA)","type" : "GAP_Attribute","filters" : ["Tester(NestingDepthA)"]},{"name" : "Tester(NestingDepthM)","type" : "GAP_Attribute","filters" : ["Tester(NestingDepthM)"]},{"name" : "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))"]},{"name" : "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))"]},{"name" : "IsZDFRE","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE"]},{"name" : "CategoryCollections(IsZDFRE)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)"]},{"name" : "CategoryCollections(CategoryCollections(IsZDFRE))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))"]},{"name" : "CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))"]},{"name" : "IsOrdinaryMatrix","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","IsMultiplicativeElement","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVector","IsOrdinaryMatrix"]},{"name" : "CategoryCollections(IsOrdinaryMatrix)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))","CategoryCollections(IsOrdinaryMatrix)"]},{"name" : "IsLieMatrix","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","IsMultiplicativeElement","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVector","IsLieMatrix"]},{"name" : "IsAssociativeElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement"]},{"name" : "CategoryCollections(IsAssociativeElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "CategoryCollections(CategoryCollections(IsAssociativeElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsAssociativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "IsAdditivelyCommutativeElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsAdditivelyCommutativeElement"]},{"name" : "CategoryCollections(IsAdditivelyCommutativeElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsAdditivelyCommutativeElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))"]},{"name" : "CategoryFamily(IsAdditivelyCommutativeElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsAdditivelyCommutativeElement)"]},{"name" : "IsCommutativeElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsCommutativeElement"]},{"name" : "CategoryCollections(IsCommutativeElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsCommutativeElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsCommutativeElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))"]},{"name" : "IsFiniteOrderElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsFiniteOrderElement"]},{"name" : "CategoryCollections(IsFiniteOrderElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsFiniteOrderElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsFiniteOrderElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsFiniteOrderElement))"]},{"name" : "IsJacobianElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement"]},{"name" : "CategoryCollections(IsJacobianElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsJacobianElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsJacobianElement))"]},{"name" : "IsRestrictedJacobianElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement","IsRestrictedJacobianElement"]},{"name" : "CategoryCollections(IsRestrictedJacobianElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)","CategoryCollections(IsRestrictedJacobianElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsRestrictedJacobianElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsJacobianElement))","CategoryCollections(CategoryCollections(IsRestrictedJacobianElement))"]},{"name" : "IsZeroSquaredElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsZeroSquaredElement"]},{"name" : "CategoryCollections(IsZeroSquaredElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsZeroSquaredElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsZeroSquaredElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsZeroSquaredElement))"]},{"name" : "IsZero","type" : "GAP_Property","filters" : ["IsZero","Tester(IsZero)"]},{"name" : "Tester(IsZero)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZero)"]},{"name" : "IsOne","type" : "GAP_Property","filters" : ["IsOne","Tester(IsOne)"]},{"name" : "Tester(IsOne)","type" : "GAP_TrueProperty","implied" : ["Tester(IsOne)"]},{"name" : "Tester(ZeroImmutable)","type" : "GAP_Attribute","filters" : ["Tester(ZeroImmutable)"]},{"name" : "Tester(AdditiveInverseImmutable)","type" : "GAP_Attribute","filters" : ["Tester(AdditiveInverseImmutable)"]},{"name" : "Tester(OneImmutable)","type" : "GAP_Attribute","filters" : ["Tester(OneImmutable)"]},{"name" : "Tester(InverseImmutable)","type" : "GAP_Attribute","filters" : ["Tester(InverseImmutable)"]},{"name" : "Tester(Int)","type" : "GAP_Attribute","filters" : ["Tester(Int)"]},{"name" : "Tester(Rat)","type" : "GAP_Attribute","filters" : ["Tester(Rat)"]},{"name" : "Tester(Characteristic)","type" : "GAP_Attribute","filters" : ["Tester(Characteristic)"]},{"name" : "Tester(Order)","type" : "GAP_Attribute","filters" : ["Tester(Order)"]},{"name" : "Tester(NormedRowVector)","type" : "GAP_Attribute","filters" : ["Tester(NormedRowVector)"]},{"name" : "IsCommutativeFamily","type" : "GAP_Property","filters" : ["IsCommutativeFamily","Tester(IsCommutativeFamily)"]},{"name" : "Tester(IsCommutativeFamily)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCommutativeFamily)"]},{"name" : "IsSkewFieldFamily","type" : "GAP_Property","filters" : ["IsSkewFieldFamily","Tester(IsSkewFieldFamily)"]},{"name" : "Tester(IsSkewFieldFamily)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSkewFieldFamily)"]},{"name" : "IsUFDFamily","type" : "GAP_Property","filters" : ["IsUFDFamily","Tester(IsUFDFamily)"]},{"name" : "Tester(IsUFDFamily)","type" : "GAP_TrueProperty","implied" : ["Tester(IsUFDFamily)"]},{"name" : "IsAdditiveElementAsMultiplicativeElementRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAdditiveElementAsMultiplicativeElementRep"]},{"name" : "Tester(AdditiveElementsAsMultiplicativeElementsFamily)","type" : "GAP_Attribute","filters" : ["Tester(AdditiveElementsAsMultiplicativeElementsFamily)"]},{"name" : "Tester(AdditiveElementAsMultiplicativeElement)","type" : "GAP_Attribute","filters" : ["Tester(AdditiveElementAsMultiplicativeElement)"]},{"name" : "IsIdempotent","type" : "GAP_Property","filters" : ["IsIdempotent","Tester(IsIdempotent)"]},{"name" : "Tester(IsIdempotent)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIdempotent)"]},{"name" : "CategoryCollections(IsFFE)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsFFE)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "CategoryCollections(CategoryCollections(IsFFE))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]},{"name" : "IsLexOrderedFFE","type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsLexOrderedFFE"]},{"name" : "IsLogOrderedFFE","type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsLogOrderedFFE"]},{"name" : "CategoryFamily(IsFFE)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsAdditivelyCommutativeElement)","CategoryFamily(IsFFE)"]},{"name" : "Tester(DegreeFFE)","type" : "GAP_Attribute","filters" : ["Tester(DegreeFFE)"]},{"name" : "Tester(IntFFE)","type" : "GAP_Attribute","filters" : ["Tester(IntFFE)"]},{"name" : "Tester(IntFFESymm)","type" : "GAP_Attribute","filters" : ["Tester(IntFFESymm)"]},{"name" : "Tester(AsInternalFFE)","type" : "GAP_Attribute","filters" : ["Tester(AsInternalFFE)"]},{"name" : "IsGeneralizedDomain","type" : "GAP_Category","implied" : ["IsGeneralizedDomain"]},{"name" : "Tester(GeneratorsOfDomain)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfDomain)"]},{"name" : "Tester(ParentAttr)","type" : "GAP_Attribute","filters" : ["Tester(ParentAttr)"]},{"name" : "IsChar","type" : "GAP_Category","implied" : ["IsChar"]},{"name" : "CategoryCollections(IsChar)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsChar)"]},{"name" : "IsCyclotomic","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},{"name" : "CategoryCollections(IsCyclotomic)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsCyclotomic)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "CategoryCollections(CategoryCollections(IsCyclotomic))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"]},{"name" : "IsPosRat","type" : "GAP_Category","implied" : ["IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsPosRat"]},{"name" : "IsNegRat","type" : "GAP_Category","implied" : ["IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsNegRat"]},{"name" : "IsZeroCyc","type" : "GAP_Category","implied" : ["IsInt","IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsZero","Tester(IsZero)","IsCyclotomic","IsZeroCyc"]},{"name" : "IsSmallIntRep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsSmallIntRep"]},{"name" : "IsInfinity","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsInfinity"]},{"name" : "IsNegInfinity","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsNegInfinity"]},{"name" : "IsIntegralCyclotomic","type" : "GAP_Property","filters" : ["IsIntegralCyclotomic","Tester(IsIntegralCyclotomic)"]},{"name" : "Tester(IsIntegralCyclotomic)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIntegralCyclotomic)"]},{"name" : "CategoryCollections(IsRecord)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsRecord)"]},{"name" : "CategoryCollections(CategoryCollections(IsRecord))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsRecord))"]},{"name" : "Tester(RecNames)","type" : "GAP_Attribute","filters" : ["Tester(RecNames)"]},{"name" : "IsEnumeratorByFunctionsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsEnumeratorByFunctionsRep"]},{"name" : "IsIteratorByFunctionsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsIteratorByFunctionsRep"]},{"name" : "IsListDefault","type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVector","IsListDefault"]},{"name" : "IsRectangularTable","type" : "GAP_Property","filters" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsRectangularTable","Tester(IsRectangularTable)"]},{"name" : "Tester(IsRectangularTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRectangularTable)"]},{"name" : "CategoryCollections(IsPerm)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsFiniteOrderElement)","CategoryCollections(IsPerm)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)"]},{"name" : "CategoryCollections(CategoryCollections(IsPerm))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsFiniteOrderElement))","CategoryCollections(CategoryCollections(IsPerm))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "Tester(SmallestGeneratorPerm)","type" : "GAP_Attribute","filters" : ["Tester(SmallestGeneratorPerm)"]},{"name" : "Tester(SmallestMovedPoint)","type" : "GAP_Attribute","filters" : ["Tester(SmallestMovedPoint)"]},{"name" : "Tester(LargestMovedPoint)","type" : "GAP_Attribute","filters" : ["Tester(LargestMovedPoint)"]},{"name" : "Tester(NrMovedPoints)","type" : "GAP_Attribute","filters" : ["Tester(NrMovedPoints)"]},{"name" : "Tester(MovedPoints)","type" : "GAP_Attribute","filters" : ["Tester(MovedPoints)"]},{"name" : "Tester(SignPerm)","type" : "GAP_Attribute","filters" : ["Tester(SignPerm)"]},{"name" : "Tester(CycleStructurePerm)","type" : "GAP_Attribute","filters" : ["Tester(CycleStructurePerm)"]},{"name" : "IsPerm2Rep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsPerm2Rep"]},{"name" : "IsPerm4Rep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsPerm4Rep"]},{"name" : "CategoryCollections(IsTransformation)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsTransformation)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "CategoryCollections(CategoryCollections(IsTransformation))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsTransformation))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "IsTrans2Rep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsTrans2Rep"]},{"name" : "IsTrans4Rep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsTrans4Rep"]},{"name" : "CategoryCollections(IsPartialPerm)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsPartialPerm)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsGeneratorsOfInverseSemigroup","Tester(IsGeneratorsOfInverseSemigroup)"]},{"name" : "CategoryCollections(CategoryCollections(IsPartialPerm))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsPartialPerm))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "IsPPerm2Rep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsPPerm2Rep"]},{"name" : "IsPPerm4Rep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsPPerm4Rep"]},{"name" : "IsInfoClass","type" : "GAP_Category","implied" : ["IsInfoClass"]},{"name" : "CategoryCollections(IsInfoClass)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsInfoClass)"]},{"name" : "IsDirectory","type" : "GAP_Category","implied" : ["IsDirectory"]},{"name" : "IsInputTextStringRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputTextStringRep"]},{"name" : "IsClosedStream","type" : "GAP_Category","implied" : ["IsClosedStream"]},{"name" : "IsStream","type" : "GAP_Category","implied" : ["IsStream"]},{"name" : "IsInputStream","type" : "GAP_Category","implied" : ["IsStream","IsInputStream"]},{"name" : "IsInputTextStream","type" : "GAP_Category","implied" : ["IsStream","IsInputStream","IsInputTextStream"]},{"name" : "IsInputTextNone","type" : "GAP_Category","implied" : ["IsStream","IsInputStream","IsInputTextStream","IsInputTextNone"]},{"name" : "IsOutputStream","type" : "GAP_Category","implied" : ["IsStream","IsOutputStream"]},{"name" : "IsOutputTextStream","type" : "GAP_Category","implied" : ["IsStream","IsOutputStream","IsOutputTextStream"]},{"name" : "IsOutputTextNone","type" : "GAP_Category","implied" : ["IsStream","IsOutputStream","IsOutputTextStream","IsOutputTextNone"]},{"name" : "IsInputOutputStream","type" : "GAP_Category","implied" : ["IsStream","IsInputStream","IsOutputStream","IsInputOutputStream"]},{"name" : "IsRowVectorObj","type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj"]},{"name" : "IsMatrixObj","type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj"]},{"name" : "IsRowListMatrix","type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix"]},{"name" : "IsFlatMatrix","type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsFlatMatrix"]},{"name" : "IsGF2VectorRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsDataObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","IsGF2VectorRep"]},{"name" : "IsGF2MatrixRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","IsGF2MatrixRep"]},{"name" : "Is8BitVectorRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsDataObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","Is8BitVectorRep"]},{"name" : "Is8BitMatrixRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","Is8BitMatrixRep"]},{"name" : "IsInfoClassListRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInfoClassListRep"]},{"name" : "IsRandomSource","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource"]},{"name" : "IsGlobalRandomSource","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource","IsGlobalRandomSource"]},{"name" : "IsGAPRandomSource","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource","IsGAPRandomSource"]},{"name" : "IsMersenneTwister","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource","IsMersenneTwister"]},{"name" : "IsObjSet","type" : "GAP_Filter","implied" : ["IsInternalRep","IsObjSet"]},{"name" : "IsObjMap","type" : "GAP_Filter","implied" : ["IsInternalRep","IsObjMap"]},{"name" : "IsFloat","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat"]},{"name" : "IsFloatInterval","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsFloatInterval"]},{"name" : "IsComplexFloat","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsComplexFloat"]},{"name" : "IsComplexFloatInterval","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsFloatInterval","IsComplexFloat","IsComplexFloatInterval"]},{"name" : "CategoryFamily(IsFloat)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsFloat)"]},{"name" : "CategoryCollections(IsFloat)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsFloat)"]},{"name" : "CategoryCollections(CategoryCollections(IsFloat))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFloat))"]},{"name" : "Tester(Cos)","type" : "GAP_Attribute","filters" : ["Tester(Cos)"]},{"name" : "Tester(Sin)","type" : "GAP_Attribute","filters" : ["Tester(Sin)"]},{"name" : "Tester(Tan)","type" : "GAP_Attribute","filters" : ["Tester(Tan)"]},{"name" : "Tester(Sec)","type" : "GAP_Attribute","filters" : ["Tester(Sec)"]},{"name" : "Tester(Csc)","type" : "GAP_Attribute","filters" : ["Tester(Csc)"]},{"name" : "Tester(Cot)","type" : "GAP_Attribute","filters" : ["Tester(Cot)"]},{"name" : "Tester(Asin)","type" : "GAP_Attribute","filters" : ["Tester(Asin)"]},{"name" : "Tester(Acos)","type" : "GAP_Attribute","filters" : ["Tester(Acos)"]},{"name" : "Tester(Atan)","type" : "GAP_Attribute","filters" : ["Tester(Atan)"]},{"name" : "Tester(Cosh)","type" : "GAP_Attribute","filters" : ["Tester(Cosh)"]},{"name" : "Tester(Sinh)","type" : "GAP_Attribute","filters" : ["Tester(Sinh)"]},{"name" : "Tester(Tanh)","type" : "GAP_Attribute","filters" : ["Tester(Tanh)"]},{"name" : "Tester(Sech)","type" : "GAP_Attribute","filters" : ["Tester(Sech)"]},{"name" : "Tester(Csch)","type" : "GAP_Attribute","filters" : ["Tester(Csch)"]},{"name" : "Tester(Coth)","type" : "GAP_Attribute","filters" : ["Tester(Coth)"]},{"name" : "Tester(Asinh)","type" : "GAP_Attribute","filters" : ["Tester(Asinh)"]},{"name" : "Tester(Acosh)","type" : "GAP_Attribute","filters" : ["Tester(Acosh)"]},{"name" : "Tester(Atanh)","type" : "GAP_Attribute","filters" : ["Tester(Atanh)"]},{"name" : "Tester(Log2)","type" : "GAP_Attribute","filters" : ["Tester(Log2)"]},{"name" : "Tester(Log10)","type" : "GAP_Attribute","filters" : ["Tester(Log10)"]},{"name" : "Tester(Log1p)","type" : "GAP_Attribute","filters" : ["Tester(Log1p)"]},{"name" : "Tester(Exp)","type" : "GAP_Attribute","filters" : ["Tester(Exp)"]},{"name" : "Tester(Exp2)","type" : "GAP_Attribute","filters" : ["Tester(Exp2)"]},{"name" : "Tester(Exp10)","type" : "GAP_Attribute","filters" : ["Tester(Exp10)"]},{"name" : "Tester(Expm1)","type" : "GAP_Attribute","filters" : ["Tester(Expm1)"]},{"name" : "Tester(CubeRoot)","type" : "GAP_Attribute","filters" : ["Tester(CubeRoot)"]},{"name" : "Tester(Square)","type" : "GAP_Attribute","filters" : ["Tester(Square)"]},{"name" : "Tester(Ceil)","type" : "GAP_Attribute","filters" : ["Tester(Ceil)"]},{"name" : "Tester(Floor)","type" : "GAP_Attribute","filters" : ["Tester(Floor)"]},{"name" : "Tester(Round)","type" : "GAP_Attribute","filters" : ["Tester(Round)"]},{"name" : "Tester(Trunc)","type" : "GAP_Attribute","filters" : ["Tester(Trunc)"]},{"name" : "Tester(FrExp)","type" : "GAP_Attribute","filters" : ["Tester(FrExp)"]},{"name" : "Tester(Argument)","type" : "GAP_Attribute","filters" : ["Tester(Argument)"]},{"name" : "Tester(AbsoluteValue)","type" : "GAP_Attribute","filters" : ["Tester(AbsoluteValue)"]},{"name" : "Tester(Frac)","type" : "GAP_Attribute","filters" : ["Tester(Frac)"]},{"name" : "Tester(SinCos)","type" : "GAP_Attribute","filters" : ["Tester(SinCos)"]},{"name" : "Tester(Erf)","type" : "GAP_Attribute","filters" : ["Tester(Erf)"]},{"name" : "Tester(Zeta)","type" : "GAP_Attribute","filters" : ["Tester(Zeta)"]},{"name" : "Tester(Gamma)","type" : "GAP_Attribute","filters" : ["Tester(Gamma)"]},{"name" : "Tester(ComplexI)","type" : "GAP_Attribute","filters" : ["Tester(ComplexI)"]},{"name" : "Tester(PrecisionFloat)","type" : "GAP_Attribute","filters" : ["Tester(PrecisionFloat)"]},{"name" : "Tester(SignFloat)","type" : "GAP_Attribute","filters" : ["Tester(SignFloat)"]},{"name" : "Tester(Sup)","type" : "GAP_Attribute","filters" : ["Tester(Sup)"]},{"name" : "Tester(Inf)","type" : "GAP_Attribute","filters" : ["Tester(Inf)"]},{"name" : "Tester(Mid)","type" : "GAP_Attribute","filters" : ["Tester(Mid)"]},{"name" : "Tester(AbsoluteDiameter)","type" : "GAP_Attribute","filters" : ["Tester(AbsoluteDiameter)"]},{"name" : "Tester(RelativeDiameter)","type" : "GAP_Attribute","filters" : ["Tester(RelativeDiameter)"]},{"name" : "IsPInfinity","type" : "GAP_Property","filters" : ["IsPInfinity","Tester(IsPInfinity)"]},{"name" : "Tester(IsPInfinity)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPInfinity)"]},{"name" : "IsNInfinity","type" : "GAP_Property","filters" : ["IsNInfinity","Tester(IsNInfinity)"]},{"name" : "Tester(IsNInfinity)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNInfinity)"]},{"name" : "IsXInfinity","type" : "GAP_Property","filters" : ["IsXInfinity","Tester(IsXInfinity)"]},{"name" : "Tester(IsXInfinity)","type" : "GAP_TrueProperty","implied" : ["Tester(IsXInfinity)"]},{"name" : "IsNaN","type" : "GAP_Property","filters" : ["IsNaN","Tester(IsNaN)"]},{"name" : "Tester(IsNaN)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNaN)"]},{"name" : "IsIEEE754FloatRep","type" : "GAP_Representation","implied" : ["IsInternalRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsIEEE754FloatRep"]},{"name" : "IsDirectoryRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsDirectoryRep"]},{"name" : "IsInputTextFileRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputTextFileRep"]},{"name" : "IsInputTextNoneRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputTextNoneRep"]},{"name" : "IsOutputTextStringRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsOutputTextStringRep"]},{"name" : "IsOutputTextFileRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsOutputTextFileRep"]},{"name" : "IsOutputTextNoneRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsOutputTextNoneRep"]},{"name" : "IsInputOutputStreamByPtyRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputOutputStreamByPtyRep"]},{"name" : "IsDirectProductElement","type" : "GAP_Category","implied" : ["IsCopyable","IsList","IsDenseList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsDirectProductElement"]},{"name" : "CategoryFamily(IsDirectProductElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsDirectProductElement)"]},{"name" : "CategoryCollections(IsDirectProductElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsDirectProductElement)"]},{"name" : "Tester(ComponentsOfDirectProductElementsFamily)","type" : "GAP_Attribute","filters" : ["Tester(ComponentsOfDirectProductElementsFamily)"]},{"name" : "IsDefaultDirectProductElementRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsList","IsDenseList","IsPositionalObjectRep","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsDirectProductElement","IsDefaultDirectProductElementRep"]},{"name" : "Tester(EmptyRowVector)","type" : "GAP_Attribute","filters" : ["Tester(EmptyRowVector)"]},{"name" : "IsExtASet","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet"]},{"name" : "IsAssociativeAOpDSum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpDSum"]},{"name" : "IsAssociativeAOpESum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpESum"]},{"name" : "IsTrivialAOpEZero","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsTrivialAOpEZero"]},{"name" : "Tester(GeneratorsOfExtASet)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfExtASet)"]},{"name" : "Tester(AdditivelyActingDomain)","type" : "GAP_Attribute","filters" : ["Tester(AdditivelyActingDomain)"]},{"name" : "IsExtLSet","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet"]},{"name" : "IsAssociativeLOpDProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd"]},{"name" : "IsAssociativeLOpEProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd"]},{"name" : "IsDistributiveLOpDProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpDProd"]},{"name" : "IsDistributiveLOpDSum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpDSum"]},{"name" : "IsDistributiveLOpEProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpEProd"]},{"name" : "IsDistributiveLOpESum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpESum"]},{"name" : "IsTrivialLOpEOne","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsTrivialLOpEOne"]},{"name" : "IsTrivialLOpEZero","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsTrivialLOpEZero"]},{"name" : "IsLeftActedOnByRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsLeftActedOnByRing"]},{"name" : "IsLeftActedOnByDivisionRing","type" : "GAP_Property","filters" : ["IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)"]},{"name" : "Tester(IsLeftActedOnByDivisionRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLeftActedOnByDivisionRing)"]},{"name" : "IsLeftActedOnBySuperset","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsLeftActedOnBySuperset"]},{"name" : "Tester(GeneratorsOfExtLSet)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfExtLSet)"]},{"name" : "Tester(LeftActingDomain)","type" : "GAP_Attribute","filters" : ["Tester(LeftActingDomain)"]},{"name" : "IsExtRSet","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet"]},{"name" : "IsAssociativeROpDProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsAssociativeROpDProd"]},{"name" : "IsAssociativeROpEProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsAssociativeROpEProd"]},{"name" : "IsDistributiveROpDProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpDProd"]},{"name" : "IsDistributiveROpDSum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpDSum"]},{"name" : "IsDistributiveROpEProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpEProd"]},{"name" : "IsDistributiveROpESum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpESum"]},{"name" : "IsTrivialROpEOne","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsTrivialROpEOne"]},{"name" : "IsTrivialROpEZero","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsTrivialROpEZero"]},{"name" : "IsRightActedOnByRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsRightActedOnByRing"]},{"name" : "IsRightActedOnByDivisionRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsRightActedOnByRing","IsRightActedOnByDivisionRing"]},{"name" : "IsRightActedOnBySuperset","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsRightActedOnBySuperset"]},{"name" : "Tester(GeneratorsOfExtRSet)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfExtRSet)"]},{"name" : "Tester(RightActingDomain)","type" : "GAP_Attribute","filters" : ["Tester(RightActingDomain)"]},{"name" : "IsExtUSet","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet"]},{"name" : "IsAssociativeUOpDProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsAssociativeUOpDProd"]},{"name" : "IsAssociativeUOpEProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsAssociativeUOpEProd"]},{"name" : "IsDistributiveUOpDProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpDProd"]},{"name" : "IsDistributiveUOpDSum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpDSum"]},{"name" : "IsDistributiveUOpEProd","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpEProd"]},{"name" : "IsDistributiveUOpESum","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpESum"]},{"name" : "IsTrivialUOpEOne","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsTrivialUOpEOne"]},{"name" : "IsTrivialUOpEZero","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsTrivialUOpEZero"]},{"name" : "IsUpperActedOnByGroup","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsUpperActedOnByGroup"]},{"name" : "IsUpperActedOnBySuperset","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsUpperActedOnBySuperset"]},{"name" : "Tester(GeneratorsOfExtUSet)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfExtUSet)"]},{"name" : "Tester(UpperActingDomain)","type" : "GAP_Attribute","filters" : ["Tester(UpperActingDomain)"]},{"name" : "IsDictionary","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary"]},{"name" : "IsLookupDictionary","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary"]},{"name" : "IsHash","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsHash"]},{"name" : "IsDictionaryDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDefaultRep"]},{"name" : "IsListDictionary","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDefaultRep","IsListDictionary"]},{"name" : "IsListLookupDictionary","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsDictionaryDefaultRep","IsListDictionary","IsListLookupDictionary"]},{"name" : "IsSortDictionary","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDefaultRep","IsListDictionary","IsSortDictionary"]},{"name" : "IsSortLookupDictionary","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsDictionaryDefaultRep","IsListDictionary","IsListLookupDictionary","IsSortDictionary","IsSortLookupDictionary"]},{"name" : "IsPositionDictionary","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDefaultRep","IsPositionDictionary"]},{"name" : "IsPositionDictionary","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsDictionaryDefaultRep","IsPositionDictionary","IsPositionDictionary"]},{"name" : "TableHasIntKeyFun","type" : "GAP_Filter","implied" : ["TableHasIntKeyFun"]},{"name" : "IsDenseHashRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsHash","IsDenseHashRep"]},{"name" : "IsSparseHashRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsHash","IsSparseHashRep"]},{"name" : "IsGeneralMapping","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping"]},{"name" : "IsSPGeneralMapping","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping"]},{"name" : "IsNonSPGeneralMapping","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping"]},{"name" : "CategoryCollections(IsGeneralMapping)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsGeneralMapping)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "CategoryFamily(IsGeneralMapping)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsGeneralMapping)"]},{"name" : "Tester(FamilyRange)","type" : "GAP_Attribute","filters" : ["Tester(FamilyRange)"]},{"name" : "Tester(FamilySource)","type" : "GAP_Attribute","filters" : ["Tester(FamilySource)"]},{"name" : "Tester(FamiliesOfGeneralMappingsAndRanges)","type" : "GAP_Attribute","filters" : ["Tester(FamiliesOfGeneralMappingsAndRanges)"]},{"name" : "IsConstantTimeAccessGeneralMapping","type" : "GAP_Property","filters" : ["IsConstantTimeAccessGeneralMapping","Tester(IsConstantTimeAccessGeneralMapping)"]},{"name" : "Tester(IsConstantTimeAccessGeneralMapping)","type" : "GAP_TrueProperty","implied" : ["Tester(IsConstantTimeAccessGeneralMapping)"]},{"name" : "IsEndoGeneralMapping","type" : "GAP_Property","filters" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]},{"name" : "Tester(IsEndoGeneralMapping)","type" : "GAP_TrueProperty","implied" : ["Tester(IsEndoGeneralMapping)"]},{"name" : "IsTotal","type" : "GAP_Property","filters" : ["IsTotal","Tester(IsTotal)"]},{"name" : "Tester(IsTotal)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTotal)"]},{"name" : "IsSingleValued","type" : "GAP_Property","filters" : ["IsSingleValued","Tester(IsSingleValued)"]},{"name" : "Tester(IsSingleValued)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSingleValued)"]},{"name" : "IsInjective","type" : "GAP_Property","filters" : ["IsInjective","Tester(IsInjective)"]},{"name" : "Tester(IsInjective)","type" : "GAP_TrueProperty","implied" : ["Tester(IsInjective)"]},{"name" : "IsSurjective","type" : "GAP_Property","filters" : ["IsSurjective","Tester(IsSurjective)"]},{"name" : "Tester(IsSurjective)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSurjective)"]},{"name" : "Tester(Range)","type" : "GAP_Attribute","filters" : ["Tester(Range)"]},{"name" : "Tester(Source)","type" : "GAP_Attribute","filters" : ["Tester(Source)"]},{"name" : "Tester(UnderlyingRelation)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingRelation)"]},{"name" : "Tester(UnderlyingGeneralMapping)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingGeneralMapping)"]},{"name" : "Tester(IdentityMapping)","type" : "GAP_Attribute","filters" : ["Tester(IdentityMapping)"]},{"name" : "Tester(InverseGeneralMapping)","type" : "GAP_Attribute","filters" : ["Tester(InverseGeneralMapping)"]},{"name" : "Tester(ImagesSource)","type" : "GAP_Attribute","filters" : ["Tester(ImagesSource)"]},{"name" : "Tester(PreImagesRange)","type" : "GAP_Attribute","filters" : ["Tester(PreImagesRange)"]},{"name" : "IsCompositionMappingRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsCompositionMappingRep"]},{"name" : "IsGeneralRestrictedMappingRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsGeneralRestrictedMappingRep"]},{"name" : "Tester(MappingGeneratorsImages)","type" : "GAP_Attribute","filters" : ["Tester(MappingGeneratorsImages)"]},{"name" : "RespectsMultiplication","type" : "GAP_Property","filters" : ["RespectsMultiplication","Tester(RespectsMultiplication)"]},{"name" : "Tester(RespectsMultiplication)","type" : "GAP_TrueProperty","implied" : ["Tester(RespectsMultiplication)"]},{"name" : "RespectsOne","type" : "GAP_Property","filters" : ["RespectsOne","Tester(RespectsOne)"]},{"name" : "Tester(RespectsOne)","type" : "GAP_TrueProperty","implied" : ["Tester(RespectsOne)"]},{"name" : "RespectsInverses","type" : "GAP_Property","filters" : ["RespectsInverses","Tester(RespectsInverses)"]},{"name" : "Tester(RespectsInverses)","type" : "GAP_TrueProperty","implied" : ["Tester(RespectsInverses)"]},{"name" : "Tester(KernelOfMultiplicativeGeneralMapping)","type" : "GAP_Attribute","filters" : ["Tester(KernelOfMultiplicativeGeneralMapping)"]},{"name" : "Tester(CoKernelOfMultiplicativeGeneralMapping)","type" : "GAP_Attribute","filters" : ["Tester(CoKernelOfMultiplicativeGeneralMapping)"]},{"name" : "RespectsAddition","type" : "GAP_Property","filters" : ["RespectsAddition","Tester(RespectsAddition)"]},{"name" : "Tester(RespectsAddition)","type" : "GAP_TrueProperty","implied" : ["Tester(RespectsAddition)"]},{"name" : "RespectsZero","type" : "GAP_Property","filters" : ["RespectsZero","Tester(RespectsZero)"]},{"name" : "Tester(RespectsZero)","type" : "GAP_TrueProperty","implied" : ["Tester(RespectsZero)"]},{"name" : "RespectsAdditiveInverses","type" : "GAP_Property","filters" : ["RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]},{"name" : "Tester(RespectsAdditiveInverses)","type" : "GAP_TrueProperty","implied" : ["Tester(RespectsAdditiveInverses)"]},{"name" : "Tester(KernelOfAdditiveGeneralMapping)","type" : "GAP_Attribute","filters" : ["Tester(KernelOfAdditiveGeneralMapping)"]},{"name" : "Tester(CoKernelOfAdditiveGeneralMapping)","type" : "GAP_Attribute","filters" : ["Tester(CoKernelOfAdditiveGeneralMapping)"]},{"name" : "RespectsScalarMultiplication","type" : "GAP_Property","filters" : ["RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]},{"name" : "Tester(RespectsScalarMultiplication)","type" : "GAP_TrueProperty","implied" : ["Tester(RespectsScalarMultiplication)"]},{"name" : "IsFieldHomomorphism","type" : "GAP_Property","filters" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]},{"name" : "Tester(IsFieldHomomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFieldHomomorphism)"]},{"name" : "TransformsMultiplicationIntoAddition","type" : "GAP_Property","filters" : ["TransformsMultiplicationIntoAddition","Tester(TransformsMultiplicationIntoAddition)"]},{"name" : "Tester(TransformsMultiplicationIntoAddition)","type" : "GAP_TrueProperty","implied" : ["Tester(TransformsMultiplicationIntoAddition)"]},{"name" : "TranformsOneIntoZero","type" : "GAP_Property","filters" : ["TranformsOneIntoZero","Tester(TranformsOneIntoZero)"]},{"name" : "Tester(TranformsOneIntoZero)","type" : "GAP_TrueProperty","implied" : ["Tester(TranformsOneIntoZero)"]},{"name" : "TransformsInversesIntoAdditiveInverses","type" : "GAP_Property","filters" : ["TransformsInversesIntoAdditiveInverses","Tester(TransformsInversesIntoAdditiveInverses)"]},{"name" : "Tester(TransformsInversesIntoAdditiveInverses)","type" : "GAP_TrueProperty","implied" : ["Tester(TransformsInversesIntoAdditiveInverses)"]},{"name" : "TransformsAdditionIntoMultiplication","type" : "GAP_Property","filters" : ["TransformsAdditionIntoMultiplication","Tester(TransformsAdditionIntoMultiplication)"]},{"name" : "Tester(TransformsAdditionIntoMultiplication)","type" : "GAP_TrueProperty","implied" : ["Tester(TransformsAdditionIntoMultiplication)"]},{"name" : "TransformsZeroIntoOne","type" : "GAP_Property","filters" : ["TransformsZeroIntoOne","Tester(TransformsZeroIntoOne)"]},{"name" : "Tester(TransformsZeroIntoOne)","type" : "GAP_TrueProperty","implied" : ["Tester(TransformsZeroIntoOne)"]},{"name" : "TransformsAdditiveInversesIntoInverses","type" : "GAP_Property","filters" : ["TransformsAdditiveInversesIntoInverses","Tester(TransformsAdditiveInversesIntoInverses)"]},{"name" : "Tester(TransformsAdditiveInversesIntoInverses)","type" : "GAP_TrueProperty","implied" : ["Tester(TransformsAdditiveInversesIntoInverses)"]},{"name" : "Tester(Successors)","type" : "GAP_Attribute","filters" : ["Tester(Successors)"]},{"name" : "Tester(DegreeOfBinaryRelation)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOfBinaryRelation)"]},{"name" : "IsReflexiveBinaryRelation","type" : "GAP_Property","filters" : ["IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)"]},{"name" : "Tester(IsReflexiveBinaryRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsReflexiveBinaryRelation)"]},{"name" : "IsSymmetricBinaryRelation","type" : "GAP_Property","filters" : ["IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)"]},{"name" : "Tester(IsSymmetricBinaryRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSymmetricBinaryRelation)"]},{"name" : "IsTransitiveBinaryRelation","type" : "GAP_Property","filters" : ["IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)"]},{"name" : "Tester(IsTransitiveBinaryRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTransitiveBinaryRelation)"]},{"name" : "IsAntisymmetricBinaryRelation","type" : "GAP_Property","filters" : ["IsAntisymmetricBinaryRelation","Tester(IsAntisymmetricBinaryRelation)"]},{"name" : "Tester(IsAntisymmetricBinaryRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAntisymmetricBinaryRelation)"]},{"name" : "IsPreOrderBinaryRelation","type" : "GAP_Property","filters" : ["IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)"]},{"name" : "Tester(IsPreOrderBinaryRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPreOrderBinaryRelation)"]},{"name" : "IsPartialOrderBinaryRelation","type" : "GAP_Property","filters" : ["IsPartialOrderBinaryRelation","Tester(IsPartialOrderBinaryRelation)"]},{"name" : "Tester(IsPartialOrderBinaryRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPartialOrderBinaryRelation)"]},{"name" : "IsLatticeOrderBinaryRelation","type" : "GAP_Property","filters" : ["IsPartialOrderBinaryRelation","Tester(IsPartialOrderBinaryRelation)","IsLatticeOrderBinaryRelation","Tester(IsLatticeOrderBinaryRelation)"]},{"name" : "Tester(IsLatticeOrderBinaryRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLatticeOrderBinaryRelation)"]},{"name" : "IsEquivalenceRelation","type" : "GAP_Property","filters" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]},{"name" : "Tester(IsEquivalenceRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsEquivalenceRelation)"]},{"name" : "IsHasseDiagram","type" : "GAP_Property","filters" : ["IsHasseDiagram","Tester(IsHasseDiagram)"]},{"name" : "Tester(IsHasseDiagram)","type" : "GAP_TrueProperty","implied" : ["Tester(IsHasseDiagram)"]},{"name" : "Tester(PartialOrderOfHasseDiagram)","type" : "GAP_Attribute","filters" : ["Tester(PartialOrderOfHasseDiagram)"]},{"name" : "Tester(EquivalenceRelationPartition)","type" : "GAP_Attribute","filters" : ["Tester(EquivalenceRelationPartition)"]},{"name" : "Tester(GeneratorsOfEquivalenceRelationPartition)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfEquivalenceRelationPartition)"]},{"name" : "IsEquivalenceClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass"]},{"name" : "Tester(EquivalenceClassRelation)","type" : "GAP_Attribute","filters" : ["Tester(EquivalenceClassRelation)"]},{"name" : "Tester(EquivalenceClasses)","type" : "GAP_Attribute","filters" : ["Tester(EquivalenceClasses)"]},{"name" : "IsMagma","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma"]},{"name" : "IsMagmaWithOne","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)"]},{"name" : "IsMagmaWithInversesIfNonzero","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","Tester(MultiplicativeNeutralElement)"]},{"name" : "IsMagmaWithInverses","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","Tester(MultiplicativeNeutralElement)"]},{"name" : "Tester(AsMagma)","type" : "GAP_Attribute","filters" : ["Tester(AsMagma)"]},{"name" : "Tester(GeneratorsOfMagma)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfMagma)"]},{"name" : "Tester(GeneratorsOfMagmaWithOne)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfMagmaWithOne)"]},{"name" : "Tester(GeneratorsOfMagmaWithInverses)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfMagmaWithInverses)"]},{"name" : "IsGeneratorsOfMagmaWithInverses","type" : "GAP_Property","filters" : ["IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)"]},{"name" : "Tester(IsGeneratorsOfMagmaWithInverses)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGeneratorsOfMagmaWithInverses)"]},{"name" : "Tester(TrivialSubmagmaWithOne)","type" : "GAP_Attribute","filters" : ["Tester(TrivialSubmagmaWithOne)"]},{"name" : "IsAssociative","type" : "GAP_Property","filters" : ["IsAssociative","Tester(IsAssociative)"]},{"name" : "Tester(IsAssociative)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAssociative)"]},{"name" : "IsCommutative","type" : "GAP_Property","filters" : ["IsCommutative","Tester(IsCommutative)"]},{"name" : "Tester(IsCommutative)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCommutative)"]},{"name" : "Tester(MultiplicativeNeutralElement)","type" : "GAP_Attribute","filters" : ["Tester(MultiplicativeNeutralElement)"]},{"name" : "Tester(Centre)","type" : "GAP_Attribute","filters" : ["Tester(Centre)"]},{"name" : "Tester(Idempotents)","type" : "GAP_Attribute","filters" : ["Tester(Idempotents)"]},{"name" : "Tester(CentralizerInParent)","type" : "GAP_Attribute","filters" : ["Tester(CentralizerInParent)"]},{"name" : "Tester(MagmaGeneratorsOfFamily)","type" : "GAP_Attribute","filters" : ["Tester(MagmaGeneratorsOfFamily)"]},{"name" : "Tester(GeneratorsOfMagmaIdeal)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfMagmaIdeal)"]},{"name" : "IsMultiplicativeElementWithZero","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithZero"]},{"name" : "CategoryCollections(IsMultiplicativeElementWithZero)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithZero)"]},{"name" : "Tester(MultiplicativeZero)","type" : "GAP_Attribute","filters" : ["Tester(MultiplicativeZero)"]},{"name" : "IsMagmaWithZeroAdjoinedElementRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithZero","IsMagmaWithZeroAdjoinedElementRep"]},{"name" : "IsMagmaWithZeroAdjoined","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsMagmaWithZeroAdjoined"]},{"name" : "Tester(InjectionZeroMagma)","type" : "GAP_Attribute","filters" : ["Tester(InjectionZeroMagma)"]},{"name" : "Tester(MagmaWithZeroAdjoined)","type" : "GAP_Attribute","filters" : ["Tester(MagmaWithZeroAdjoined)"]},{"name" : "Tester(UnderlyingInjectionZeroMagma)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingInjectionZeroMagma)"]},{"name" : "IsLeftMagmaCongruence","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsLeftMagmaCongruence"]},{"name" : "Tester(GeneratingPairsOfLeftMagmaCongruence)","type" : "GAP_Attribute","filters" : ["Tester(GeneratingPairsOfLeftMagmaCongruence)"]},{"name" : "Tester(PartialClosureOfCongruence)","type" : "GAP_Attribute","filters" : ["Tester(PartialClosureOfCongruence)"]},{"name" : "IsRightMagmaCongruence","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsRightMagmaCongruence"]},{"name" : "Tester(GeneratingPairsOfRightMagmaCongruence)","type" : "GAP_Attribute","filters" : ["Tester(GeneratingPairsOfRightMagmaCongruence)"]},{"name" : "IsMagmaCongruence","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","RespectsMultiplication","Tester(RespectsMultiplication)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsLeftMagmaCongruence","IsRightMagmaCongruence","IsMagmaCongruence"]},{"name" : "Tester(GeneratingPairsOfMagmaCongruence)","type" : "GAP_Attribute","filters" : ["Tester(GeneratingPairsOfMagmaCongruence)"]},{"name" : "IsCongruenceClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsGeneralizedDomain","IsEquivalenceClass","IsCongruenceClass"]},{"name" : "IsLeftSemigroupCongruence","type" : "GAP_Property","filters" : ["IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)"]},{"name" : "Tester(IsLeftSemigroupCongruence)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLeftSemigroupCongruence)"]},{"name" : "IsRightSemigroupCongruence","type" : "GAP_Property","filters" : ["IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)"]},{"name" : "Tester(IsRightSemigroupCongruence)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRightSemigroupCongruence)"]},{"name" : "IsSemigroupCongruence","type" : "GAP_Property","filters" : ["IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)","IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)","IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]},{"name" : "Tester(IsSemigroupCongruence)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSemigroupCongruence)"]},{"name" : "IsReesCongruence","type" : "GAP_Property","filters" : ["IsReesCongruence","Tester(IsReesCongruence)"]},{"name" : "Tester(IsReesCongruence)","type" : "GAP_TrueProperty","implied" : ["Tester(IsReesCongruence)"]},{"name" : "Tester(AsSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(AsSemigroup)"]},{"name" : "IsGeneratorsOfSemigroup","type" : "GAP_Property","filters" : ["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},{"name" : "Tester(IsGeneratorsOfSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGeneratorsOfSemigroup)"]},{"name" : "Tester(CayleyGraphSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(CayleyGraphSemigroup)"]},{"name" : "Tester(CayleyGraphDualSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(CayleyGraphDualSemigroup)"]},{"name" : "IsZeroGroup","type" : "GAP_Property","filters" : ["IsZeroGroup","Tester(IsZeroGroup)","IsZeroSimpleSemigroup","Tester(IsZeroSimpleSemigroup)"]},{"name" : "Tester(IsZeroGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZeroGroup)"]},{"name" : "IsSimpleSemigroup","type" : "GAP_Property","filters" : ["IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)"]},{"name" : "Tester(IsSimpleSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSimpleSemigroup)"]},{"name" : "IsZeroSimpleSemigroup","type" : "GAP_Property","filters" : ["IsZeroSimpleSemigroup","Tester(IsZeroSimpleSemigroup)"]},{"name" : "Tester(IsZeroSimpleSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZeroSimpleSemigroup)"]},{"name" : "Tester(ANonReesCongruenceOfSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(ANonReesCongruenceOfSemigroup)"]},{"name" : "IsReesCongruenceSemigroup","type" : "GAP_Property","filters" : ["IsReesCongruenceSemigroup","Tester(IsReesCongruenceSemigroup)"]},{"name" : "Tester(IsReesCongruenceSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsReesCongruenceSemigroup)"]},{"name" : "IsRegularSemigroup","type" : "GAP_Property","filters" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)"]},{"name" : "Tester(IsRegularSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRegularSemigroup)"]},{"name" : "IsInverseSemigroup","type" : "GAP_Property","filters" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},{"name" : "Tester(IsInverseSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsInverseSemigroup)"]},{"name" : "Tester(NilpotencyDegree)","type" : "GAP_Attribute","filters" : ["Tester(NilpotencyDegree)"]},{"name" : "IsBand","type" : "GAP_Property","filters" : ["IsBand","Tester(IsBand)"]},{"name" : "Tester(IsBand)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBand)"]},{"name" : "IsBrandtSemigroup","type" : "GAP_Property","filters" : ["IsBrandtSemigroup","Tester(IsBrandtSemigroup)"]},{"name" : "Tester(IsBrandtSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBrandtSemigroup)"]},{"name" : "IsCliffordSemigroup","type" : "GAP_Property","filters" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCliffordSemigroup","Tester(IsCliffordSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},{"name" : "Tester(IsCliffordSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCliffordSemigroup)"]},{"name" : "IsCommutativeSemigroup","type" : "GAP_Property","filters" : ["IsCommutativeSemigroup","Tester(IsCommutativeSemigroup)"]},{"name" : "Tester(IsCommutativeSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCommutativeSemigroup)"]},{"name" : "IsCompletelyRegularSemigroup","type" : "GAP_Property","filters" : ["IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)"]},{"name" : "Tester(IsCompletelyRegularSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCompletelyRegularSemigroup)"]},{"name" : "IsCompletelySimpleSemigroup","type" : "GAP_Property","filters" : ["IsCompletelySimpleSemigroup","Tester(IsCompletelySimpleSemigroup)"]},{"name" : "Tester(IsCompletelySimpleSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCompletelySimpleSemigroup)"]},{"name" : "IsGroupAsSemigroup","type" : "GAP_Property","filters" : ["IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},{"name" : "Tester(IsGroupAsSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupAsSemigroup)"]},{"name" : "IsIdempotentGenerated","type" : "GAP_Property","filters" : ["IsIdempotentGenerated","Tester(IsIdempotentGenerated)","IsSemiband","Tester(IsSemiband)"]},{"name" : "Tester(IsIdempotentGenerated)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIdempotentGenerated)"]},{"name" : "IsLeftZeroSemigroup","type" : "GAP_Property","filters" : ["IsLeftZeroSemigroup","Tester(IsLeftZeroSemigroup)"]},{"name" : "Tester(IsLeftZeroSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLeftZeroSemigroup)"]},{"name" : "IsMonogenicSemigroup","type" : "GAP_Property","filters" : ["IsMonogenicSemigroup","Tester(IsMonogenicSemigroup)"]},{"name" : "Tester(IsMonogenicSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMonogenicSemigroup)"]},{"name" : "IsMonoidAsSemigroup","type" : "GAP_Property","filters" : ["IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)"]},{"name" : "Tester(IsMonoidAsSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMonoidAsSemigroup)"]},{"name" : "IsNilpotentSemigroup","type" : "GAP_Property","filters" : ["IsNilpotentSemigroup","Tester(IsNilpotentSemigroup)"]},{"name" : "Tester(IsNilpotentSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNilpotentSemigroup)"]},{"name" : "IsOrthodoxSemigroup","type" : "GAP_Property","filters" : ["IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},{"name" : "Tester(IsOrthodoxSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsOrthodoxSemigroup)"]},{"name" : "IsRectangularBand","type" : "GAP_Property","filters" : ["IsRectangularBand","Tester(IsRectangularBand)"]},{"name" : "Tester(IsRectangularBand)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRectangularBand)"]},{"name" : "IsRightZeroSemigroup","type" : "GAP_Property","filters" : ["IsRightZeroSemigroup","Tester(IsRightZeroSemigroup)"]},{"name" : "Tester(IsRightZeroSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRightZeroSemigroup)"]},{"name" : "IsSemiband","type" : "GAP_Property","filters" : ["IsSemiband","Tester(IsSemiband)"]},{"name" : "Tester(IsSemiband)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSemiband)"]},{"name" : "IsSemilattice","type" : "GAP_Property","filters" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsBand","Tester(IsBand)","IsCliffordSemigroup","Tester(IsCliffordSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsIdempotentGenerated","Tester(IsIdempotentGenerated)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSemiband","Tester(IsSemiband)","IsSemilattice","Tester(IsSemilattice)"]},{"name" : "Tester(IsSemilattice)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSemilattice)"]},{"name" : "IsZeroSemigroup","type" : "GAP_Property","filters" : ["IsZeroSemigroup","Tester(IsZeroSemigroup)"]},{"name" : "Tester(IsZeroSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZeroSemigroup)"]},{"name" : "IsLeftSemigroupIdeal","type" : "GAP_Property","filters" : ["IsLeftSemigroupIdeal","Tester(IsLeftSemigroupIdeal)"]},{"name" : "Tester(IsLeftSemigroupIdeal)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLeftSemigroupIdeal)"]},{"name" : "IsRightSemigroupIdeal","type" : "GAP_Property","filters" : ["IsRightSemigroupIdeal","Tester(IsRightSemigroupIdeal)"]},{"name" : "Tester(IsRightSemigroupIdeal)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRightSemigroupIdeal)"]},{"name" : "IsSemigroupIdeal","type" : "GAP_Property","filters" : ["IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]},{"name" : "Tester(IsSemigroupIdeal)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSemigroupIdeal)"]},{"name" : "Tester(ReesCongruenceOfSemigroupIdeal)","type" : "GAP_Attribute","filters" : ["Tester(ReesCongruenceOfSemigroupIdeal)"]},{"name" : "Tester(AsMonoid)","type" : "GAP_Attribute","filters" : ["Tester(AsMonoid)"]},{"name" : "Tester(NameIsomorphismClass)","type" : "GAP_Attribute","filters" : ["Tester(NameIsomorphismClass)"]},{"name" : "IsCyclic","type" : "GAP_Property","filters" : ["IsCyclic","Tester(IsCyclic)"]},{"name" : "Tester(IsCyclic)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCyclic)"]},{"name" : "IsElementaryAbelian","type" : "GAP_Property","filters" : ["IsElementaryAbelian","Tester(IsElementaryAbelian)"]},{"name" : "Tester(IsElementaryAbelian)","type" : "GAP_TrueProperty","implied" : ["Tester(IsElementaryAbelian)"]},{"name" : "IsFinitelyGeneratedGroup","type" : "GAP_Property","filters" : ["IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)"]},{"name" : "Tester(IsFinitelyGeneratedGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFinitelyGeneratedGroup)"]},{"name" : "IsSubsetLocallyFiniteGroup","type" : "GAP_Property","filters" : ["IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)"]},{"name" : "Tester(IsSubsetLocallyFiniteGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSubsetLocallyFiniteGroup)"]},{"name" : "CanEasilyTestMembership","type" : "GAP_Filter","implied" : ["CanEasilyTestMembership"]},{"name" : "CanEasilyComputeWithIndependentGensAbelianGroup","type" : "GAP_Filter","implied" : ["CanEasilyComputeWithIndependentGensAbelianGroup"]},{"name" : "CanComputeSizeAnySubgroup","type" : "GAP_Filter","implied" : ["CanComputeSize","CanComputeSizeAnySubgroup"]},{"name" : "KnowsHowToDecompose","type" : "GAP_Property","filters" : ["KnowsHowToDecompose","Tester(KnowsHowToDecompose)"]},{"name" : "Tester(KnowsHowToDecompose)","type" : "GAP_TrueProperty","implied" : ["Tester(KnowsHowToDecompose)"]},{"name" : "IsPGroup","type" : "GAP_Property","filters" : ["IsPGroup","Tester(IsPGroup)"]},{"name" : "Tester(IsPGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPGroup)"]},{"name" : "Tester(PrimePGroup)","type" : "GAP_Attribute","filters" : ["Tester(PrimePGroup)"]},{"name" : "Tester(PClassPGroup)","type" : "GAP_Attribute","filters" : ["Tester(PClassPGroup)"]},{"name" : "Tester(RankPGroup)","type" : "GAP_Attribute","filters" : ["Tester(RankPGroup)"]},{"name" : "IsNilpotentGroup","type" : "GAP_Property","filters" : ["IsNilpotentGroup","Tester(IsNilpotentGroup)","IsSupersolvableGroup","Tester(IsSupersolvableGroup)","IsSolvableGroup","Tester(IsSolvableGroup)","IsNilpotentByFinite","Tester(IsNilpotentByFinite)"]},{"name" : "Tester(IsNilpotentGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNilpotentGroup)"]},{"name" : "IsPerfectGroup","type" : "GAP_Property","filters" : ["IsPerfectGroup","Tester(IsPerfectGroup)"]},{"name" : "Tester(IsPerfectGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPerfectGroup)"]},{"name" : "IsSporadicSimpleGroup","type" : "GAP_Property","filters" : ["IsSporadicSimpleGroup","Tester(IsSporadicSimpleGroup)"]},{"name" : "Tester(IsSporadicSimpleGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSporadicSimpleGroup)"]},{"name" : "IsSimpleGroup","type" : "GAP_Property","filters" : ["IsSimpleGroup","Tester(IsSimpleGroup)"]},{"name" : "Tester(IsSimpleGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSimpleGroup)"]},{"name" : "IsAlmostSimpleGroup","type" : "GAP_Property","filters" : ["IsAlmostSimpleGroup","Tester(IsAlmostSimpleGroup)"]},{"name" : "Tester(IsAlmostSimpleGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAlmostSimpleGroup)"]},{"name" : "IsSupersolvableGroup","type" : "GAP_Property","filters" : ["IsSupersolvableGroup","Tester(IsSupersolvableGroup)","IsSolvableGroup","Tester(IsSolvableGroup)"]},{"name" : "Tester(IsSupersolvableGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSupersolvableGroup)"]},{"name" : "IsMonomialGroup","type" : "GAP_Property","filters" : ["IsMonomialGroup","Tester(IsMonomialGroup)","IsSolvableGroup","Tester(IsSolvableGroup)"]},{"name" : "Tester(IsMonomialGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMonomialGroup)"]},{"name" : "IsSolvableGroup","type" : "GAP_Property","filters" : ["IsSolvableGroup","Tester(IsSolvableGroup)"]},{"name" : "Tester(IsSolvableGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSolvableGroup)"]},{"name" : "IsPolycyclicGroup","type" : "GAP_Property","filters" : ["IsSolvableGroup","Tester(IsSolvableGroup)","IsPolycyclicGroup","Tester(IsPolycyclicGroup)"]},{"name" : "Tester(IsPolycyclicGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPolycyclicGroup)"]},{"name" : "Tester(AbelianInvariants)","type" : "GAP_Attribute","filters" : ["Tester(AbelianInvariants)"]},{"name" : "Tester(IsInfiniteAbelianizationGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsInfiniteAbelianizationGroup)"]},{"name" : "Tester(AsGroup)","type" : "GAP_Attribute","filters" : ["Tester(AsGroup)"]},{"name" : "Tester(ChiefSeries)","type" : "GAP_Attribute","filters" : ["Tester(ChiefSeries)"]},{"name" : "Tester(CommutatorFactorGroup)","type" : "GAP_Attribute","filters" : ["Tester(CommutatorFactorGroup)"]},{"name" : "Tester(CompositionSeries)","type" : "GAP_Attribute","filters" : ["Tester(CompositionSeries)"]},{"name" : "Tester(ConjugacyClasses)","type" : "GAP_Attribute","filters" : ["Tester(ConjugacyClasses)"]},{"name" : "Tester(ConjugacyClassesMaximalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ConjugacyClassesMaximalSubgroups)"]},{"name" : "Tester(MaximalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(MaximalSubgroups)"]},{"name" : "Tester(MaximalSubgroupClassReps)","type" : "GAP_Attribute","filters" : ["Tester(MaximalSubgroupClassReps)"]},{"name" : "Tester(PerfectResiduum)","type" : "GAP_Attribute","filters" : ["Tester(PerfectResiduum)"]},{"name" : "Tester(RepresentativesPerfectSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(RepresentativesPerfectSubgroups)"]},{"name" : "Tester(RepresentativesSimpleSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(RepresentativesSimpleSubgroups)"]},{"name" : "Tester(ConjugacyClassesPerfectSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ConjugacyClassesPerfectSubgroups)"]},{"name" : "Tester(ConjugacyClassesSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ConjugacyClassesSubgroups)"]},{"name" : "Tester(LatticeSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(LatticeSubgroups)"]},{"name" : "Tester(DerivedLength)","type" : "GAP_Attribute","filters" : ["Tester(DerivedLength)"]},{"name" : "Tester(HirschLength)","type" : "GAP_Attribute","filters" : ["Tester(HirschLength)"]},{"name" : "Tester(DerivedSeriesOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(DerivedSeriesOfGroup)"]},{"name" : "Tester(DerivedSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(DerivedSubgroup)"]},{"name" : "Tester(MaximalAbelianQuotient)","type" : "GAP_Attribute","filters" : ["Tester(MaximalAbelianQuotient)"]},{"name" : "Tester(CommutatorLength)","type" : "GAP_Attribute","filters" : ["Tester(CommutatorLength)"]},{"name" : "Tester(DimensionsLoewyFactors)","type" : "GAP_Attribute","filters" : ["Tester(DimensionsLoewyFactors)"]},{"name" : "Tester(ElementaryAbelianSeries)","type" : "GAP_Attribute","filters" : ["Tester(ElementaryAbelianSeries)"]},{"name" : "Tester(ElementaryAbelianSeriesLargeSteps)","type" : "GAP_Attribute","filters" : ["Tester(ElementaryAbelianSeriesLargeSteps)"]},{"name" : "Tester(Exponent)","type" : "GAP_Attribute","filters" : ["Tester(Exponent)"]},{"name" : "Tester(FittingSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(FittingSubgroup)"]},{"name" : "Tester(PrefrattiniSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(PrefrattiniSubgroup)"]},{"name" : "Tester(FrattiniSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(FrattiniSubgroup)"]},{"name" : "Tester(InvariantForm)","type" : "GAP_Attribute","filters" : ["Tester(InvariantForm)"]},{"name" : "Tester(JenningsSeries)","type" : "GAP_Attribute","filters" : ["Tester(JenningsSeries)"]},{"name" : "Tester(LowerCentralSeriesOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(LowerCentralSeriesOfGroup)"]},{"name" : "Tester(NilpotencyClassOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(NilpotencyClassOfGroup)"]},{"name" : "Tester(MaximalNormalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(MaximalNormalSubgroups)"]},{"name" : "Tester(NormalMaximalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(NormalMaximalSubgroups)"]},{"name" : "Tester(MinimalNormalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(MinimalNormalSubgroups)"]},{"name" : "Tester(NormalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(NormalSubgroups)"]},{"name" : "Tester(NrConjugacyClasses)","type" : "GAP_Attribute","filters" : ["Tester(NrConjugacyClasses)"]},{"name" : "Tester(ComputedOmegas)","type" : "GAP_Attribute","filters" : ["Tester(ComputedOmegas)"]},{"name" : "Tester(ComputedAgemos)","type" : "GAP_Attribute","filters" : ["Tester(ComputedAgemos)"]},{"name" : "Tester(RadicalGroup)","type" : "GAP_Attribute","filters" : ["Tester(RadicalGroup)"]},{"name" : "Tester(RationalClasses)","type" : "GAP_Attribute","filters" : ["Tester(RationalClasses)"]},{"name" : "Tester(GeneratorsSmallest)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsSmallest)"]},{"name" : "Tester(LargestElementGroup)","type" : "GAP_Attribute","filters" : ["Tester(LargestElementGroup)"]},{"name" : "Tester(MinimalGeneratingSet)","type" : "GAP_Attribute","filters" : ["Tester(MinimalGeneratingSet)"]},{"name" : "Tester(SmallGeneratingSet)","type" : "GAP_Attribute","filters" : ["Tester(SmallGeneratingSet)"]},{"name" : "Tester(SupersolvableResiduum)","type" : "GAP_Attribute","filters" : ["Tester(SupersolvableResiduum)"]},{"name" : "Tester(ComplementSystem)","type" : "GAP_Attribute","filters" : ["Tester(ComplementSystem)"]},{"name" : "Tester(SylowSystem)","type" : "GAP_Attribute","filters" : ["Tester(SylowSystem)"]},{"name" : "Tester(HallSystem)","type" : "GAP_Attribute","filters" : ["Tester(HallSystem)"]},{"name" : "Tester(Socle)","type" : "GAP_Attribute","filters" : ["Tester(Socle)"]},{"name" : "Tester(UpperCentralSeriesOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(UpperCentralSeriesOfGroup)"]},{"name" : "Tester(CoreInParent)","type" : "GAP_Attribute","filters" : ["Tester(CoreInParent)"]},{"name" : "Tester(IndexInParent)","type" : "GAP_Attribute","filters" : ["Tester(IndexInParent)"]},{"name" : "Tester(IndexInWholeGroup)","type" : "GAP_Attribute","filters" : ["Tester(IndexInWholeGroup)"]},{"name" : "Tester(IndependentGeneratorsOfAbelianGroup)","type" : "GAP_Attribute","filters" : ["Tester(IndependentGeneratorsOfAbelianGroup)"]},{"name" : "IsNormalInParent","type" : "GAP_Property","filters" : ["IsNormalInParent","Tester(IsNormalInParent)"]},{"name" : "Tester(IsNormalInParent)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNormalInParent)"]},{"name" : "Tester(ComputedIsPNilpotents)","type" : "GAP_Attribute","filters" : ["Tester(ComputedIsPNilpotents)"]},{"name" : "Tester(ComputedIsPSolvables)","type" : "GAP_Attribute","filters" : ["Tester(ComputedIsPSolvables)"]},{"name" : "Tester(NormalClosureInParent)","type" : "GAP_Attribute","filters" : ["Tester(NormalClosureInParent)"]},{"name" : "Tester(NormalizerInParent)","type" : "GAP_Attribute","filters" : ["Tester(NormalizerInParent)"]},{"name" : "Tester(ComputedPCentralSeriess)","type" : "GAP_Attribute","filters" : ["Tester(ComputedPCentralSeriess)"]},{"name" : "Tester(ComputedPRumps)","type" : "GAP_Attribute","filters" : ["Tester(ComputedPRumps)"]},{"name" : "Tester(ComputedPCores)","type" : "GAP_Attribute","filters" : ["Tester(ComputedPCores)"]},{"name" : "Tester(SubnormalSeriesInParent)","type" : "GAP_Attribute","filters" : ["Tester(SubnormalSeriesInParent)"]},{"name" : "Tester(ComputedSylowSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ComputedSylowSubgroups)"]},{"name" : "Tester(ComputedSylowComplements)","type" : "GAP_Attribute","filters" : ["Tester(ComputedSylowComplements)"]},{"name" : "Tester(ComputedHallSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ComputedHallSubgroups)"]},{"name" : "Tester(GrowthFunctionOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(GrowthFunctionOfGroup)"]},{"name" : "Tester(ElementTestFunction)","type" : "GAP_Attribute","filters" : ["Tester(ElementTestFunction)"]},{"name" : "IsRightTransversal","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsRightTransversal"]},{"name" : "CategoryCollections(IsRightTransversal)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsRightTransversal)"]},{"name" : "Tester(RightTransversalInParent)","type" : "GAP_Attribute","filters" : ["Tester(RightTransversalInParent)"]},{"name" : "Tester(IsomorphismTypeInfoFiniteSimpleGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismTypeInfoFiniteSimpleGroup)"]},{"name" : "Tester(IsomorphismPcGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismPcGroup)"]},{"name" : "Tester(IsomorphismSpecialPcGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismSpecialPcGroup)"]},{"name" : "Tester(IsomorphismPermGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismPermGroup)"]},{"name" : "Tester(IsomorphismFpGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismFpGroup)"]},{"name" : "Tester(PrimePowerComponents)","type" : "GAP_Attribute","filters" : ["Tester(PrimePowerComponents)"]},{"name" : "IsGroupOfFamily","type" : "GAP_Filter","implied" : ["IsGroupOfFamily"]},{"name" : "IsGeneratorsOfInverseSemigroup","type" : "GAP_Property","filters" : ["IsGeneratorsOfInverseSemigroup","Tester(IsGeneratorsOfInverseSemigroup)"]},{"name" : "Tester(IsGeneratorsOfInverseSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGeneratorsOfInverseSemigroup)"]},{"name" : "Tester(GeneratorsOfInverseMonoid)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfInverseMonoid)"]},{"name" : "Tester(GeneratorsOfInverseSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfInverseSemigroup)"]},{"name" : "Tester(AsInverseSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(AsInverseSemigroup)"]},{"name" : "Tester(AsInverseMonoid)","type" : "GAP_Attribute","filters" : ["Tester(AsInverseMonoid)"]},{"name" : "Tester(ReverseNaturalPartialOrder)","type" : "GAP_Attribute","filters" : ["Tester(ReverseNaturalPartialOrder)"]},{"name" : "Tester(NaturalPartialOrder)","type" : "GAP_Attribute","filters" : ["Tester(NaturalPartialOrder)"]},{"name" : "IsNearAdditiveMagma","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","IsGeneralizedDomain","IsNearAdditiveMagma"]},{"name" : "IsNearAdditiveMagmaWithZero","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","IsGeneralizedDomain","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero"]},{"name" : "IsNearAdditiveGroup","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","IsGeneralizedDomain","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup"]},{"name" : "IsAdditivelyCommutative","type" : "GAP_Property","filters" : ["IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]},{"name" : "Tester(IsAdditivelyCommutative)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAdditivelyCommutative)"]},{"name" : "Tester(GeneratorsOfNearAdditiveMagma)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfNearAdditiveMagma)"]},{"name" : "Tester(GeneratorsOfNearAdditiveMagmaWithZero)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]},{"name" : "Tester(GeneratorsOfNearAdditiveGroup)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfNearAdditiveGroup)"]},{"name" : "Tester(TrivialSubnearAdditiveMagmaWithZero)","type" : "GAP_Attribute","filters" : ["Tester(TrivialSubnearAdditiveMagmaWithZero)"]},{"name" : "Tester(AdditiveNeutralElement)","type" : "GAP_Attribute","filters" : ["Tester(AdditiveNeutralElement)"]},{"name" : "IsAdditiveCoset","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpESum","IsTrivialAOpEZero","IsAdditiveCoset"]},{"name" : "IsLDistributive","type" : "GAP_Property","filters" : ["IsLDistributive","Tester(IsLDistributive)"]},{"name" : "Tester(IsLDistributive)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLDistributive)"]},{"name" : "IsRDistributive","type" : "GAP_Property","filters" : ["IsRDistributive","Tester(IsRDistributive)"]},{"name" : "Tester(IsRDistributive)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRDistributive)"]},{"name" : "Tester(GeneratorsOfSemiring)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfSemiring)"]},{"name" : "Tester(GeneratorsOfSemiringWithOne)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfSemiringWithOne)"]},{"name" : "Tester(GeneratorsOfSemiringWithZero)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfSemiringWithZero)"]},{"name" : "Tester(GeneratorsOfSemiringWithOneAndZero)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfSemiringWithOneAndZero)"]},{"name" : "Tester(AsSemiring)","type" : "GAP_Attribute","filters" : ["Tester(AsSemiring)"]},{"name" : "Tester(AsSemiringWithOne)","type" : "GAP_Attribute","filters" : ["Tester(AsSemiringWithOne)"]},{"name" : "Tester(AsSemiringWithZero)","type" : "GAP_Attribute","filters" : ["Tester(AsSemiringWithZero)"]},{"name" : "Tester(AsSemiringWithOneAndZero)","type" : "GAP_Attribute","filters" : ["Tester(AsSemiringWithOneAndZero)"]},{"name" : "Tester(CentralIdempotentsOfSemiring)","type" : "GAP_Attribute","filters" : ["Tester(CentralIdempotentsOfSemiring)"]},{"name" : "Tester(AsNearRing)","type" : "GAP_Attribute","filters" : ["Tester(AsNearRing)"]},{"name" : "Tester(AsRing)","type" : "GAP_Attribute","filters" : ["Tester(AsRing)"]},{"name" : "Tester(GeneratorsOfRing)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfRing)"]},{"name" : "Tester(GeneratorsOfRingWithOne)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfRingWithOne)"]},{"name" : "IsUniqueFactorizationRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing"]},{"name" : "IsEuclideanRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing"]},{"name" : "IsAnticommutative","type" : "GAP_Property","filters" : ["IsAnticommutative","Tester(IsAnticommutative)"]},{"name" : "Tester(IsAnticommutative)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAnticommutative)"]},{"name" : "IsIntegralRing","type" : "GAP_Property","filters" : ["IsIntegralRing","Tester(IsIntegralRing)"]},{"name" : "Tester(IsIntegralRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIntegralRing)"]},{"name" : "IsJacobianRing","type" : "GAP_Property","filters" : ["IsJacobianRing","Tester(IsJacobianRing)"]},{"name" : "Tester(IsJacobianRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsJacobianRing)"]},{"name" : "IsZeroSquaredRing","type" : "GAP_Property","filters" : ["IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]},{"name" : "Tester(IsZeroSquaredRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZeroSquaredRing)"]},{"name" : "IsZeroMultiplicationRing","type" : "GAP_Property","filters" : ["IsZeroMultiplicationRing","Tester(IsZeroMultiplicationRing)"]},{"name" : "Tester(IsZeroMultiplicationRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZeroMultiplicationRing)"]},{"name" : "Tester(Units)","type" : "GAP_Attribute","filters" : ["Tester(Units)"]},{"name" : "IsGeneralizedCartanMatrix","type" : "GAP_Property","filters" : ["IsGeneralizedCartanMatrix","Tester(IsGeneralizedCartanMatrix)"]},{"name" : "Tester(IsGeneralizedCartanMatrix)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGeneralizedCartanMatrix)"]},{"name" : "Tester(BaseMat)","type" : "GAP_Attribute","filters" : ["Tester(BaseMat)"]},{"name" : "Tester(BaseOrthogonalSpaceMat)","type" : "GAP_Attribute","filters" : ["Tester(BaseOrthogonalSpaceMat)"]},{"name" : "Tester(DefaultFieldOfMatrix)","type" : "GAP_Attribute","filters" : ["Tester(DefaultFieldOfMatrix)"]},{"name" : "Tester(DepthOfUpperTriangularMatrix)","type" : "GAP_Attribute","filters" : ["Tester(DepthOfUpperTriangularMatrix)"]},{"name" : "Tester(DeterminantMat)","type" : "GAP_Attribute","filters" : ["Tester(DeterminantMat)"]},{"name" : "Tester(DimensionsMat)","type" : "GAP_Attribute","filters" : ["Tester(DimensionsMat)"]},{"name" : "Tester(NullspaceMat)","type" : "GAP_Attribute","filters" : ["Tester(NullspaceMat)"]},{"name" : "Tester(TriangulizedNullspaceMat)","type" : "GAP_Attribute","filters" : ["Tester(TriangulizedNullspaceMat)"]},{"name" : "Tester(ProjectiveOrder)","type" : "GAP_Attribute","filters" : ["Tester(ProjectiveOrder)"]},{"name" : "Tester(RankMat)","type" : "GAP_Attribute","filters" : ["Tester(RankMat)"]},{"name" : "Tester(SemiEchelonMat)","type" : "GAP_Attribute","filters" : ["Tester(SemiEchelonMat)"]},{"name" : "Tester(SemiEchelonMatTransformation)","type" : "GAP_Attribute","filters" : ["Tester(SemiEchelonMatTransformation)"]},{"name" : "Tester(TransposedMatImmutable)","type" : "GAP_Attribute","filters" : ["Tester(TransposedMatImmutable)"]},{"name" : "IsMonomialMatrix","type" : "GAP_Property","filters" : ["IsMonomialMatrix","Tester(IsMonomialMatrix)"]},{"name" : "Tester(IsMonomialMatrix)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMonomialMatrix)"]},{"name" : "Tester(JordanDecomposition)","type" : "GAP_Attribute","filters" : ["Tester(JordanDecomposition)"]},{"name" : "Tester(CharacteristicPolynomial)","type" : "GAP_Attribute","filters" : ["Tester(CharacteristicPolynomial)"]},{"name" : "Tester(BaseIntMat)","type" : "GAP_Attribute","filters" : ["Tester(BaseIntMat)"]},{"name" : "Tester(NullspaceIntMat)","type" : "GAP_Attribute","filters" : ["Tester(NullspaceIntMat)"]},{"name" : "Tester(AbelianInvariantsOfList)","type" : "GAP_Attribute","filters" : ["Tester(AbelianInvariantsOfList)"]},{"name" : "Tester(MatrixByBlockMatrix)","type" : "GAP_Attribute","filters" : ["Tester(MatrixByBlockMatrix)"]},{"name" : "IsTwoSidedIdealInParent","type" : "GAP_Property","filters" : ["IsTwoSidedIdealInParent","Tester(IsTwoSidedIdealInParent)","IsLeftIdealInParent","Tester(IsLeftIdealInParent)","IsRightIdealInParent","Tester(IsRightIdealInParent)"]},{"name" : "Tester(IsTwoSidedIdealInParent)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTwoSidedIdealInParent)"]},{"name" : "IsLeftIdealInParent","type" : "GAP_Property","filters" : ["IsLeftIdealInParent","Tester(IsLeftIdealInParent)"]},{"name" : "Tester(IsLeftIdealInParent)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLeftIdealInParent)"]},{"name" : "IsRightIdealInParent","type" : "GAP_Property","filters" : ["IsRightIdealInParent","Tester(IsRightIdealInParent)"]},{"name" : "Tester(IsRightIdealInParent)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRightIdealInParent)"]},{"name" : "Tester(GeneratorsOfTwoSidedIdeal)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfTwoSidedIdeal)"]},{"name" : "Tester(GeneratorsOfLeftIdeal)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfLeftIdeal)"]},{"name" : "Tester(GeneratorsOfRightIdeal)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfRightIdeal)"]},{"name" : "Tester(LeftActingRingOfIdeal)","type" : "GAP_Attribute","filters" : ["Tester(LeftActingRingOfIdeal)"]},{"name" : "Tester(RightActingRingOfIdeal)","type" : "GAP_Attribute","filters" : ["Tester(RightActingRingOfIdeal)"]},{"name" : "IsFreeLeftModule","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule"]},{"name" : "IsFiniteDimensional","type" : "GAP_Property","filters" : ["IsFiniteDimensional","Tester(IsFiniteDimensional)"]},{"name" : "Tester(IsFiniteDimensional)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFiniteDimensional)"]},{"name" : "IsFullRowModule","type" : "GAP_Property","filters" : ["IsFullRowModule","Tester(IsFullRowModule)","IsRowModule","Tester(IsRowModule)"]},{"name" : "Tester(IsFullRowModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullRowModule)"]},{"name" : "IsFullMatrixModule","type" : "GAP_Property","filters" : ["IsFullMatrixModule","Tester(IsFullMatrixModule)","IsMatrixModule","Tester(IsMatrixModule)"]},{"name" : "Tester(IsFullMatrixModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullMatrixModule)"]},{"name" : "IsHandledByNiceBasis","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis"]},{"name" : "Tester(Dimension)","type" : "GAP_Attribute","filters" : ["Tester(Dimension)"]},{"name" : "Tester(GeneratorsOfLeftOperatorAdditiveGroup)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]},{"name" : "Tester(GeneratorsOfRightOperatorAdditiveGroup)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfRightOperatorAdditiveGroup)"]},{"name" : "IsRowModule","type" : "GAP_Property","filters" : ["IsRowModule","Tester(IsRowModule)"]},{"name" : "Tester(IsRowModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRowModule)"]},{"name" : "IsMatrixModule","type" : "GAP_Property","filters" : ["IsMatrixModule","Tester(IsMatrixModule)"]},{"name" : "Tester(IsMatrixModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMatrixModule)"]},{"name" : "Tester(DimensionOfVectors)","type" : "GAP_Attribute","filters" : ["Tester(DimensionOfVectors)"]},{"name" : "IsBasis","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis"]},{"name" : "IsCanonicalBasis","type" : "GAP_Property","filters" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)"]},{"name" : "Tester(IsCanonicalBasis)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCanonicalBasis)"]},{"name" : "IsCanonicalBasisFullRowModule","type" : "GAP_Property","filters" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullRowModule","Tester(IsCanonicalBasisFullRowModule)"]},{"name" : "Tester(IsCanonicalBasisFullRowModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCanonicalBasisFullRowModule)"]},{"name" : "IsCanonicalBasisFullMatrixModule","type" : "GAP_Property","filters" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullMatrixModule","Tester(IsCanonicalBasisFullMatrixModule)"]},{"name" : "Tester(IsCanonicalBasisFullMatrixModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCanonicalBasisFullMatrixModule)"]},{"name" : "IsIntegralBasis","type" : "GAP_Property","filters" : ["IsIntegralBasis","Tester(IsIntegralBasis)"]},{"name" : "Tester(IsIntegralBasis)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIntegralBasis)"]},{"name" : "IsNormalBasis","type" : "GAP_Property","filters" : ["IsNormalBasis","Tester(IsNormalBasis)"]},{"name" : "Tester(IsNormalBasis)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNormalBasis)"]},{"name" : "IsSemiEchelonized","type" : "GAP_Property","filters" : ["IsSemiEchelonized","Tester(IsSemiEchelonized)"]},{"name" : "Tester(IsSemiEchelonized)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSemiEchelonized)"]},{"name" : "Tester(BasisVectors)","type" : "GAP_Attribute","filters" : ["Tester(BasisVectors)"]},{"name" : "Tester(EnumeratorByBasis)","type" : "GAP_Attribute","filters" : ["Tester(EnumeratorByBasis)"]},{"name" : "Tester(StructureConstantsTable)","type" : "GAP_Attribute","filters" : ["Tester(StructureConstantsTable)"]},{"name" : "Tester(UnderlyingLeftModule)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingLeftModule)"]},{"name" : "Tester(Basis)","type" : "GAP_Attribute","filters" : ["Tester(Basis)"]},{"name" : "Tester(SemiEchelonBasis)","type" : "GAP_Attribute","filters" : ["Tester(SemiEchelonBasis)"]},{"name" : "IsGenericFiniteSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsGenericFiniteSpace"]},{"name" : "IsSpaceOfRationalFunctions","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsSpaceOfRationalFunctions"]},{"name" : "IsBasisByNiceBasis","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsFinite","Tester(IsFinite)","IsSmallList","Tester(IsSmallList)","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisByNiceBasis"]},{"name" : "Tester(NiceBasis)","type" : "GAP_Attribute","filters" : ["Tester(NiceBasis)"]},{"name" : "Tester(NiceFreeLeftModule)","type" : "GAP_Attribute","filters" : ["Tester(NiceFreeLeftModule)"]},{"name" : "Tester(NiceFreeLeftModuleInfo)","type" : "GAP_Attribute","filters" : ["Tester(NiceFreeLeftModuleInfo)"]},{"name" : "IsMutableBasis","type" : "GAP_Category","implied" : ["IsMutableBasis"]},{"name" : "IsGaussianSpace","type" : "GAP_Filter","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsGaussianSpace"]},{"name" : "Tester(CanonicalBasis)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalBasis)"]},{"name" : "IsNonGaussianRowSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsNonGaussianRowSpace"]},{"name" : "IsNonGaussianMatrixSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsNonGaussianMatrixSpace"]},{"name" : "Tester(NormedRowVectors)","type" : "GAP_Attribute","filters" : ["Tester(NormedRowVectors)"]},{"name" : "IsSubspacesVectorSpace","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsSubspacesVectorSpace"]},{"name" : "Tester(Subspaces)","type" : "GAP_Attribute","filters" : ["Tester(Subspaces)"]},{"name" : "Tester(OrthogonalSpaceInFullRowSpace)","type" : "GAP_Attribute","filters" : ["Tester(OrthogonalSpaceInFullRowSpace)"]},{"name" : "IsVectorSpaceHomomorphism","type" : "GAP_Property","filters" : ["IsVectorSpaceHomomorphism","Tester(IsVectorSpaceHomomorphism)"]},{"name" : "Tester(IsVectorSpaceHomomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsVectorSpaceHomomorphism)"]},{"name" : "Tester(AsLeftModuleGeneralMappingByImages)","type" : "GAP_Attribute","filters" : ["Tester(AsLeftModuleGeneralMappingByImages)"]},{"name" : "IsFullHomModule","type" : "GAP_Property","filters" : ["IsFullHomModule","Tester(IsFullHomModule)"]},{"name" : "Tester(IsFullHomModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullHomModule)"]},{"name" : "IsPseudoCanonicalBasisFullHomModule","type" : "GAP_Property","filters" : ["IsPseudoCanonicalBasisFullHomModule","Tester(IsPseudoCanonicalBasisFullHomModule)"]},{"name" : "Tester(IsPseudoCanonicalBasisFullHomModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPseudoCanonicalBasisFullHomModule)"]},{"name" : "IsLinearMappingsModule","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsFiniteDimensional","Tester(IsFiniteDimensional)","IsHandledByNiceBasis","IsLinearMappingsModule"]},{"name" : "IsSimpleAlgebra","type" : "GAP_Property","filters" : ["IsSimpleAlgebra","Tester(IsSimpleAlgebra)"]},{"name" : "Tester(IsSimpleAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSimpleAlgebra)"]},{"name" : "Tester(GeneratorsOfLeftOperatorRing)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfLeftOperatorRing)"]},{"name" : "Tester(GeneratorsOfLeftOperatorRingWithOne)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfLeftOperatorRingWithOne)"]},{"name" : "Tester(PowerSubalgebraSeries)","type" : "GAP_Attribute","filters" : ["Tester(PowerSubalgebraSeries)"]},{"name" : "Tester(AdjointBasis)","type" : "GAP_Attribute","filters" : ["Tester(AdjointBasis)"]},{"name" : "Tester(IndicesOfAdjointBasis)","type" : "GAP_Attribute","filters" : ["Tester(IndicesOfAdjointBasis)"]},{"name" : "Tester(RadicalOfAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(RadicalOfAlgebra)"]},{"name" : "Tester(DirectSumDecomposition)","type" : "GAP_Attribute","filters" : ["Tester(DirectSumDecomposition)"]},{"name" : "Tester(NullAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(NullAlgebra)"]},{"name" : "Tester(LieAlgebraByDomain)","type" : "GAP_Attribute","filters" : ["Tester(LieAlgebraByDomain)"]},{"name" : "IsQuaternion","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociative","Tester(IsAssociative)","IsQuaternion"]},{"name" : "CategoryCollections(IsQuaternion)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsQuaternion)"]},{"name" : "CategoryCollections(CategoryCollections(IsQuaternion))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsQuaternion))"]},{"name" : "Tester(LeviMalcevDecomposition)","type" : "GAP_Attribute","filters" : ["Tester(LeviMalcevDecomposition)"]},{"name" : "Tester(Grading)","type" : "GAP_Attribute","filters" : ["Tester(Grading)"]},{"name" : "IsElementOfMagmaRingModuloRelations","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsElementOfMagmaRingModuloRelations"]},{"name" : "CategoryCollections(IsElementOfMagmaRingModuloRelations)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsElementOfMagmaRingModuloRelations)"]},{"name" : "CategoryFamily(IsElementOfMagmaRingModuloRelations)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)"]},{"name" : "IsElementOfFreeMagmaRing","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsElementOfMagmaRingModuloRelations","IsElementOfFreeMagmaRing"]},{"name" : "CategoryCollections(IsElementOfFreeMagmaRing)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsElementOfMagmaRingModuloRelations)","CategoryCollections(IsElementOfFreeMagmaRing)"]},{"name" : "CategoryFamily(IsElementOfFreeMagmaRing)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)","CategoryFamily(IsElementOfFreeMagmaRing)"]},{"name" : "Tester(CoefficientsAndMagmaElements)","type" : "GAP_Attribute","filters" : ["Tester(CoefficientsAndMagmaElements)"]},{"name" : "Tester(ZeroCoefficient)","type" : "GAP_Attribute","filters" : ["Tester(ZeroCoefficient)"]},{"name" : "IsMagmaRingModuloRelations","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMagmaRingModuloRelations"]},{"name" : "IsFreeMagmaRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMagmaRingModuloRelations","IsFreeMagmaRing"]},{"name" : "IsGroupRing","type" : "GAP_Property","filters" : ["IsGroupRing","Tester(IsGroupRing)"]},{"name" : "Tester(IsGroupRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupRing)"]},{"name" : "Tester(UnderlyingMagma)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingMagma)"]},{"name" : "Tester(AugmentationIdeal)","type" : "GAP_Attribute","filters" : ["Tester(AugmentationIdeal)"]},{"name" : "IsMagmaRingModuloSpanOfZero","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMagmaRingModuloRelations","IsMagmaRingModuloSpanOfZero"]},{"name" : "IsElementOfMagmaRingModuloSpanOfZeroFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)","IsElementOfMagmaRingModuloSpanOfZeroFamily"]},{"name" : "IsSpaceOfElementsOfMagmaRing","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsSpaceOfElementsOfMagmaRing"]},{"name" : "IsElementOfFpAlgebra","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsElementOfFpAlgebra"]},{"name" : "CategoryCollections(IsElementOfFpAlgebra)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsElementOfFpAlgebra)"]},{"name" : "CategoryFamily(IsElementOfFpAlgebra)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfFpAlgebra)"]},{"name" : "IsSubalgebraFpAlgebra","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsSubalgebraFpAlgebra"]},{"name" : "IsFullFpAlgebra","type" : "GAP_Property","filters" : ["IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]},{"name" : "Tester(IsFullFpAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullFpAlgebra)"]},{"name" : "Tester(FreeGeneratorsOfFpAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(FreeGeneratorsOfFpAlgebra)"]},{"name" : "Tester(RelatorsOfFpAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(RelatorsOfFpAlgebra)"]},{"name" : "Tester(FreeAlgebraOfFpAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(FreeAlgebraOfFpAlgebra)"]},{"name" : "IsNormalForm","type" : "GAP_Property","filters" : ["IsNormalForm","Tester(IsNormalForm)"]},{"name" : "Tester(IsNormalForm)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNormalForm)"]},{"name" : "Tester(NiceNormalFormByExtRepFunction)","type" : "GAP_Attribute","filters" : ["Tester(NiceNormalFormByExtRepFunction)"]},{"name" : "Tester(NiceAlgebraMonomorphism)","type" : "GAP_Attribute","filters" : ["Tester(NiceAlgebraMonomorphism)"]},{"name" : "IsFpAlgebraElementsSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsFpAlgebraElementsSpace"]},{"name" : "IsLieAbelian","type" : "GAP_Property","filters" : ["IsLieAbelian","Tester(IsLieAbelian)","IsLieNilpotent","Tester(IsLieNilpotent)","IsLieSolvable","Tester(IsLieSolvable)"]},{"name" : "Tester(IsLieAbelian)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieAbelian)"]},{"name" : "IsLieNilpotent","type" : "GAP_Property","filters" : ["IsLieNilpotent","Tester(IsLieNilpotent)","IsLieSolvable","Tester(IsLieSolvable)"]},{"name" : "Tester(IsLieNilpotent)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieNilpotent)"]},{"name" : "IsRestrictedLieAlgebra","type" : "GAP_Property","filters" : ["IsRestrictedLieAlgebra","Tester(IsRestrictedLieAlgebra)"]},{"name" : "Tester(IsRestrictedLieAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRestrictedLieAlgebra)"]},{"name" : "Tester(LieDerivedSubalgebra)","type" : "GAP_Attribute","filters" : ["Tester(LieDerivedSubalgebra)"]},{"name" : "Tester(LieDerivedSeries)","type" : "GAP_Attribute","filters" : ["Tester(LieDerivedSeries)"]},{"name" : "IsLieSolvable","type" : "GAP_Property","filters" : ["IsLieSolvable","Tester(IsLieSolvable)"]},{"name" : "Tester(IsLieSolvable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieSolvable)"]},{"name" : "Tester(LieLowerCentralSeries)","type" : "GAP_Attribute","filters" : ["Tester(LieLowerCentralSeries)"]},{"name" : "Tester(LieUpperCentralSeries)","type" : "GAP_Attribute","filters" : ["Tester(LieUpperCentralSeries)"]},{"name" : "Tester(LieCentre)","type" : "GAP_Attribute","filters" : ["Tester(LieCentre)"]},{"name" : "Tester(RightDerivations)","type" : "GAP_Attribute","filters" : ["Tester(RightDerivations)"]},{"name" : "Tester(LeftDerivations)","type" : "GAP_Attribute","filters" : ["Tester(LeftDerivations)"]},{"name" : "Tester(KillingMatrix)","type" : "GAP_Attribute","filters" : ["Tester(KillingMatrix)"]},{"name" : "Tester(CartanSubalgebra)","type" : "GAP_Attribute","filters" : ["Tester(CartanSubalgebra)"]},{"name" : "Tester(PthPowerImages)","type" : "GAP_Attribute","filters" : ["Tester(PthPowerImages)"]},{"name" : "Tester(NonNilpotentElement)","type" : "GAP_Attribute","filters" : ["Tester(NonNilpotentElement)"]},{"name" : "Tester(LieNilRadical)","type" : "GAP_Attribute","filters" : ["Tester(LieNilRadical)"]},{"name" : "Tester(LieSolvableRadical)","type" : "GAP_Attribute","filters" : ["Tester(LieSolvableRadical)"]},{"name" : "Tester(SemiSimpleType)","type" : "GAP_Attribute","filters" : ["Tester(SemiSimpleType)"]},{"name" : "Tester(LieCentralizerInParent)","type" : "GAP_Attribute","filters" : ["Tester(LieCentralizerInParent)"]},{"name" : "Tester(LieNormalizerInParent)","type" : "GAP_Attribute","filters" : ["Tester(LieNormalizerInParent)"]},{"name" : "Tester(PowerS)","type" : "GAP_Attribute","filters" : ["Tester(PowerS)"]},{"name" : "IsRootSystem","type" : "GAP_Category","implied" : ["IsRootSystem"]},{"name" : "IsRootSystemFromLieAlgebra","type" : "GAP_Category","implied" : ["IsRootSystem","IsRootSystemFromLieAlgebra"]},{"name" : "Tester(UnderlyingLieAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingLieAlgebra)"]},{"name" : "Tester(RootSystem)","type" : "GAP_Attribute","filters" : ["Tester(RootSystem)"]},{"name" : "Tester(PositiveRoots)","type" : "GAP_Attribute","filters" : ["Tester(PositiveRoots)"]},{"name" : "Tester(NegativeRoots)","type" : "GAP_Attribute","filters" : ["Tester(NegativeRoots)"]},{"name" : "Tester(PositiveRootVectors)","type" : "GAP_Attribute","filters" : ["Tester(PositiveRootVectors)"]},{"name" : "Tester(NegativeRootVectors)","type" : "GAP_Attribute","filters" : ["Tester(NegativeRootVectors)"]},{"name" : "Tester(SimpleSystem)","type" : "GAP_Attribute","filters" : ["Tester(SimpleSystem)"]},{"name" : "Tester(CartanMatrix)","type" : "GAP_Attribute","filters" : ["Tester(CartanMatrix)"]},{"name" : "Tester(BilinearFormMat)","type" : "GAP_Attribute","filters" : ["Tester(BilinearFormMat)"]},{"name" : "Tester(CanonicalGenerators)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalGenerators)"]},{"name" : "Tester(ChevalleyBasis)","type" : "GAP_Attribute","filters" : ["Tester(ChevalleyBasis)"]},{"name" : "Tester(UniversalEnvelopingAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(UniversalEnvelopingAlgebra)"]},{"name" : "IsFamilyElementOfFreeLieAlgebra","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)","IsFamilyElementOfFreeLieAlgebra"]},{"name" : "IsFptoSCAMorphism","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsFptoSCAMorphism"]},{"name" : "Tester(JenningsLieAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(JenningsLieAlgebra)"]},{"name" : "Tester(PCentralLieAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(PCentralLieAlgebra)"]},{"name" : "Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)","type" : "GAP_Attribute","filters" : ["Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)"]},{"name" : "IsFamilyOverFullCoefficientsFamily","type" : "GAP_Category","implied" : ["IsFamily","IsFamilyOverFullCoefficientsFamily"]},{"name" : "IsSCAlgebraObj","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsSCAlgebraObj"]},{"name" : "CategoryCollections(IsSCAlgebraObj)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsSCAlgebraObj)"]},{"name" : "CategoryCollections(CategoryCollections(IsSCAlgebraObj))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsSCAlgebraObj))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))"]},{"name" : "CategoryFamily(IsSCAlgebraObj)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsSCAlgebraObj)"]},{"name" : "IsFullSCAlgebra","type" : "GAP_Property","filters" : ["IsFullSCAlgebra","Tester(IsFullSCAlgebra)"]},{"name" : "Tester(IsFullSCAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullSCAlgebra)"]},{"name" : "IsCanonicalBasisFullSCAlgebra","type" : "GAP_Property","filters" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullSCAlgebra","Tester(IsCanonicalBasisFullSCAlgebra)"]},{"name" : "Tester(IsCanonicalBasisFullSCAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCanonicalBasisFullSCAlgebra)"]},{"name" : "IsSCAlgebraObjSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsSCAlgebraObjSpace"]},{"name" : "Tester(IsomorphismFpFLMLOR)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismFpFLMLOR)"]},{"name" : "Tester(IsomorphismMatrixFLMLOR)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismMatrixFLMLOR)"]},{"name" : "Tester(IsomorphismSCFLMLOR)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismSCFLMLOR)"]},{"name" : "IsLieObject","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement","IsZeroSquaredElement","IsLieObject"]},{"name" : "CategoryCollections(IsLieObject)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)","CategoryCollections(IsZeroSquaredElement)","CategoryCollections(IsLieObject)"]},{"name" : "CategoryCollections((IsLieObject and IsRestrictedJacobianElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)","CategoryCollections(IsRestrictedJacobianElement)","CategoryCollections(IsZeroSquaredElement)","CategoryCollections(IsLieObject)","CategoryCollections((IsLieObject and IsRestrictedJacobianElement))"]},{"name" : "Tester(LieFamily)","type" : "GAP_Attribute","filters" : ["Tester(LieFamily)"]},{"name" : "Tester(UnderlyingFamily)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingFamily)"]},{"name" : "Tester(LieObject)","type" : "GAP_Attribute","filters" : ["Tester(LieObject)"]},{"name" : "Tester(UnderlyingRingElement)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingRingElement)"]},{"name" : "IsLieObjectsModule","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsLieObjectsModule"]},{"name" : "IsAlgebraModuleElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsAlgebraModuleElement"]},{"name" : "CategoryCollections(IsAlgebraModuleElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsAlgebraModuleElement)"]},{"name" : "CategoryFamily(IsAlgebraModuleElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsAlgebraModuleElement)"]},{"name" : "IsLeftAlgebraModuleElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsAlgebraModuleElement","IsLeftAlgebraModuleElement"]},{"name" : "CategoryCollections(IsLeftAlgebraModuleElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsAlgebraModuleElement)","CategoryCollections(IsLeftAlgebraModuleElement)"]},{"name" : "IsRightAlgebraModuleElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsAlgebraModuleElement","IsRightAlgebraModuleElement"]},{"name" : "CategoryCollections(IsRightAlgebraModuleElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsAlgebraModuleElement)","CategoryCollections(IsRightAlgebraModuleElement)"]},{"name" : "IsAlgebraModule","type" : "GAP_Property","filters" : ["IsAlgebraModule","Tester(IsAlgebraModule)"]},{"name" : "Tester(IsAlgebraModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAlgebraModule)"]},{"name" : "IsLeftAlgebraModule","type" : "GAP_Property","filters" : ["IsLeftAlgebraModule","Tester(IsLeftAlgebraModule)"]},{"name" : "Tester(IsLeftAlgebraModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLeftAlgebraModule)"]},{"name" : "IsRightAlgebraModule","type" : "GAP_Property","filters" : ["IsRightAlgebraModule","Tester(IsRightAlgebraModule)"]},{"name" : "Tester(IsRightAlgebraModule)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRightAlgebraModule)"]},{"name" : "Tester(LeftActingAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(LeftActingAlgebra)"]},{"name" : "Tester(RightActingAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(RightActingAlgebra)"]},{"name" : "Tester(GeneratorsOfAlgebraModule)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfAlgebraModule)"]},{"name" : "IsBasisOfAlgebraModuleElementSpace","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisOfAlgebraModuleElementSpace"]},{"name" : "Tester(AdjointModule)","type" : "GAP_Attribute","filters" : ["Tester(AdjointModule)"]},{"name" : "Tester(FaithfulModule)","type" : "GAP_Attribute","filters" : ["Tester(FaithfulModule)"]},{"name" : "IsMonomialElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement"]},{"name" : "CategoryCollections(IsMonomialElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)"]},{"name" : "CategoryFamily(IsMonomialElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsMonomialElement)"]},{"name" : "IsTensorElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement","IsTensorElement"]},{"name" : "CategoryCollections(IsTensorElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)","CategoryCollections(IsTensorElement)"]},{"name" : "IsWedgeElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement","IsWedgeElement"]},{"name" : "CategoryCollections(IsWedgeElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)","CategoryCollections(IsWedgeElement)"]},{"name" : "IsSymmetricPowerElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement","IsSymmetricPowerElement"]},{"name" : "CategoryCollections(IsSymmetricPowerElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)","CategoryCollections(IsSymmetricPowerElement)"]},{"name" : "IsDirectSumElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsDirectSumElement"]},{"name" : "CategoryCollections(IsDirectSumElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsDirectSumElement)"]},{"name" : "CategoryFamily(IsDirectSumElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsDirectSumElement)"]},{"name" : "IsSparseRowSpaceElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsSparseRowSpaceElement"]},{"name" : "CategoryCollections(IsSparseRowSpaceElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsSparseRowSpaceElement)"]},{"name" : "CategoryFamily(IsSparseRowSpaceElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsSparseRowSpaceElement)"]},{"name" : "IsDirectSumElementsSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsDirectSumElementsSpace"]},{"name" : "IsCochain","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsCochain"]},{"name" : "CategoryCollections(IsCochain)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsCochain)"]},{"name" : "IsWeylGroup","type" : "GAP_Property","filters" : ["IsWeylGroup","Tester(IsWeylGroup)"]},{"name" : "Tester(IsWeylGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsWeylGroup)"]},{"name" : "Tester(WeylGroup)","type" : "GAP_Attribute","filters" : ["Tester(WeylGroup)"]},{"name" : "Tester(SparseCartanMatrix)","type" : "GAP_Attribute","filters" : ["Tester(SparseCartanMatrix)"]},{"name" : "Tester(LongestWeylWordPerm)","type" : "GAP_Attribute","filters" : ["Tester(LongestWeylWordPerm)"]},{"name" : "Tester(PositiveRootsAsWeights)","type" : "GAP_Attribute","filters" : ["Tester(PositiveRootsAsWeights)"]},{"name" : "IsUEALatticeElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsUEALatticeElement"]},{"name" : "CategoryCollections(IsUEALatticeElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsUEALatticeElement)"]},{"name" : "CategoryFamily(IsUEALatticeElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsUEALatticeElement)"]},{"name" : "Tester(LatticeGeneratorsInUEA)","type" : "GAP_Attribute","filters" : ["Tester(LatticeGeneratorsInUEA)"]},{"name" : "IsWeightRepElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsWeightRepElement"]},{"name" : "CategoryCollections(IsWeightRepElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsWeightRepElement)"]},{"name" : "CategoryFamily(IsWeightRepElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsWeightRepElement)"]},{"name" : "IsBasisOfWeightRepElementSpace","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisOfWeightRepElementSpace"]},{"name" : "IsCochainsSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsCochainsSpace"]},{"name" : "IsSearchTable","type" : "GAP_Category","implied" : ["IsSearchTable"]},{"name" : "IsVectorSearchTable","type" : "GAP_Category","implied" : ["IsSearchTable","IsVectorSearchTable"]},{"name" : "IsIntegers","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsFreeLeftModule","IsIntegers"]},{"name" : "IsPositiveIntegers","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPositiveIntegers"]},{"name" : "IsNonnegativeIntegers","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsNonnegativeIntegers"]},{"name" : "IsGaussianIntegers","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsFreeLeftModule","IsFiniteDimensional","Tester(IsFiniteDimensional)","IsGaussianIntegers"]},{"name" : "Tester(PrimeDivisors)","type" : "GAP_Attribute","filters" : ["Tester(PrimeDivisors)"]},{"name" : "IsSCRingObj","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsSCRingObj"]},{"name" : "CategoryCollections(IsSCRingObj)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsSCRingObj)"]},{"name" : "CategoryCollections(CategoryCollections(IsSCRingObj))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsSCRingObj))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsSCRingObj)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsSCRingObj)))"]},{"name" : "CategoryFamily(IsSCRingObj)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsSCRingObj)"]},{"name" : "Tester(StandardGeneratorsSubringSCRing)","type" : "GAP_Attribute","filters" : ["Tester(StandardGeneratorsSubringSCRing)"]},{"name" : "Tester(Subrings)","type" : "GAP_Attribute","filters" : ["Tester(Subrings)"]},{"name" : "Tester(Ideals)","type" : "GAP_Attribute","filters" : ["Tester(Ideals)"]},{"name" : "Tester(DirectSumInfo)","type" : "GAP_Attribute","filters" : ["Tester(DirectSumInfo)"]},{"name" : "IsPolynomialFunction","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction"]},{"name" : "IsRationalFunction","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction"]},{"name" : "CategoryCollections(IsPolynomialFunction)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsPolynomialFunction)"]},{"name" : "CategoryCollections(IsRationalFunction)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsPolynomialFunction)","CategoryCollections(IsRationalFunction)"]},{"name" : "IsPolynomialFunctionsFamilyElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsPolynomialFunctionsFamilyElement"]},{"name" : "IsRationalFunctionsFamilyElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsPolynomialFunctionsFamilyElement","IsRationalFunctionsFamilyElement"]},{"name" : "IsPolynomialFunctionsFamily","type" : "GAP_Category","implied" : ["IsFamily","IsPolynomialFunctionsFamily"]},{"name" : "IsRationalFunctionsFamily","type" : "GAP_Category","implied" : ["IsFamily","IsUFDFamily","Tester(IsUFDFamily)","IsPolynomialFunctionsFamily","IsRationalFunctionsFamily"]},{"name" : "IsRationalFunctionOverField","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsRationalFunctionOverField"]},{"name" : "Tester(RationalFunctionsFamily)","type" : "GAP_Attribute","filters" : ["Tester(RationalFunctionsFamily)"]},{"name" : "Tester(CoefficientsFamily)","type" : "GAP_Attribute","filters" : ["Tester(CoefficientsFamily)"]},{"name" : "Tester(NumeratorOfRationalFunction)","type" : "GAP_Attribute","filters" : ["Tester(NumeratorOfRationalFunction)"]},{"name" : "Tester(DenominatorOfRationalFunction)","type" : "GAP_Attribute","filters" : ["Tester(DenominatorOfRationalFunction)"]},{"name" : "IsPolynomial","type" : "GAP_Property","filters" : ["IsPolynomial","Tester(IsPolynomial)"]},{"name" : "Tester(IsPolynomial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPolynomial)"]},{"name" : "Tester(AsPolynomial)","type" : "GAP_Attribute","filters" : ["Tester(AsPolynomial)"]},{"name" : "IsUnivariateRationalFunction","type" : "GAP_Property","filters" : ["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]},{"name" : "Tester(IsUnivariateRationalFunction)","type" : "GAP_TrueProperty","implied" : ["Tester(IsUnivariateRationalFunction)"]},{"name" : "IsLaurentPolynomial","type" : "GAP_Property","filters" : ["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]},{"name" : "Tester(IsLaurentPolynomial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLaurentPolynomial)"]},{"name" : "IsConstantRationalFunction","type" : "GAP_Property","filters" : ["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsConstantRationalFunction","Tester(IsConstantRationalFunction)"]},{"name" : "Tester(IsConstantRationalFunction)","type" : "GAP_TrueProperty","implied" : ["Tester(IsConstantRationalFunction)"]},{"name" : "IsRationalFunctionDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsRationalFunctionDefaultRep"]},{"name" : "IsPolynomialDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)","IsPolynomialDefaultRep"]},{"name" : "IsLaurentPolynomialDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)","IsLaurentPolynomialDefaultRep"]},{"name" : "IsUnivariateRationalFunctionDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsUnivariateRationalFunctionDefaultRep"]},{"name" : "Tester(ExtRepNumeratorRatFun)","type" : "GAP_Attribute","filters" : ["Tester(ExtRepNumeratorRatFun)"]},{"name" : "Tester(ExtRepDenominatorRatFun)","type" : "GAP_Attribute","filters" : ["Tester(ExtRepDenominatorRatFun)"]},{"name" : "Tester(ExtRepPolynomialRatFun)","type" : "GAP_Attribute","filters" : ["Tester(ExtRepPolynomialRatFun)"]},{"name" : "Tester(CoefficientsOfLaurentPolynomial)","type" : "GAP_Attribute","filters" : ["Tester(CoefficientsOfLaurentPolynomial)"]},{"name" : "Tester(IndeterminateNumberOfUnivariateRationalFunction)","type" : "GAP_Attribute","filters" : ["Tester(IndeterminateNumberOfUnivariateRationalFunction)"]},{"name" : "Tester(IndeterminateOfUnivariateRationalFunction)","type" : "GAP_Attribute","filters" : ["Tester(IndeterminateOfUnivariateRationalFunction)"]},{"name" : "Tester(CoefficientsOfUnivariatePolynomial)","type" : "GAP_Attribute","filters" : ["Tester(CoefficientsOfUnivariatePolynomial)"]},{"name" : "Tester(DegreeOfLaurentPolynomial)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOfLaurentPolynomial)"]},{"name" : "Tester(CoefficientsOfUnivariateRationalFunction)","type" : "GAP_Attribute","filters" : ["Tester(CoefficientsOfUnivariateRationalFunction)"]},{"name" : "Tester(Derivative)","type" : "GAP_Attribute","filters" : ["Tester(Derivative)"]},{"name" : "Tester(Discriminant)","type" : "GAP_Attribute","filters" : ["Tester(Discriminant)"]},{"name" : "IsLaurentPolynomialsFamilyElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsLaurentPolynomialsFamilyElement"]},{"name" : "IsUnivariatePolynomialsFamilyElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsUnivariatePolynomialsFamilyElement"]},{"name" : "IsLaurentPolynomialsFamily","type" : "GAP_Category","implied" : ["IsFamily","Tester(OneImmutable)","IsCommutativeFamily","Tester(IsCommutativeFamily)","IsLaurentPolynomialsFamily"]},{"name" : "IsUnivariatePolynomialsFamily","type" : "GAP_Category","implied" : ["IsFamily","IsUnivariatePolynomialsFamily"]},{"name" : "Tester(PrimeField)","type" : "GAP_Attribute","filters" : ["Tester(PrimeField)"]},{"name" : "IsPrimeField","type" : "GAP_Property","filters" : ["IsPrimeField","Tester(IsPrimeField)"]},{"name" : "Tester(IsPrimeField)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPrimeField)"]},{"name" : "Tester(DefiningPolynomial)","type" : "GAP_Attribute","filters" : ["Tester(DefiningPolynomial)"]},{"name" : "Tester(DegreeOverPrimeField)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOverPrimeField)"]},{"name" : "Tester(GeneratorsOfDivisionRing)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfDivisionRing)"]},{"name" : "Tester(NormalBase)","type" : "GAP_Attribute","filters" : ["Tester(NormalBase)"]},{"name" : "Tester(PrimitiveElement)","type" : "GAP_Attribute","filters" : ["Tester(PrimitiveElement)"]},{"name" : "Tester(PrimitiveRoot)","type" : "GAP_Attribute","filters" : ["Tester(PrimitiveRoot)"]},{"name" : "Tester(RootOfDefiningPolynomial)","type" : "GAP_Attribute","filters" : ["Tester(RootOfDefiningPolynomial)"]},{"name" : "Tester(Subfields)","type" : "GAP_Attribute","filters" : ["Tester(Subfields)"]},{"name" : "IsFieldControlledByGaloisGroup","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsNonTrivial","Tester(IsNonTrivial)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(MultiplicativeNeutralElement)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsIntegralRing","Tester(IsIntegralRing)","IsFreeLeftModule","IsFieldControlledByGaloisGroup"]},{"name" : "Tester(Conjugates)","type" : "GAP_Attribute","filters" : ["Tester(Conjugates)"]},{"name" : "Tester(Norm)","type" : "GAP_Attribute","filters" : ["Tester(Norm)"]},{"name" : "Tester(Trace)","type" : "GAP_Attribute","filters" : ["Tester(Trace)"]},{"name" : "Tester(GaloisGroup)","type" : "GAP_Attribute","filters" : ["Tester(GaloisGroup)"]},{"name" : "Tester(ComplexConjugate)","type" : "GAP_Attribute","filters" : ["Tester(ComplexConjugate)"]},{"name" : "Tester(RealPart)","type" : "GAP_Attribute","filters" : ["Tester(RealPart)"]},{"name" : "Tester(ImaginaryPart)","type" : "GAP_Attribute","filters" : ["Tester(ImaginaryPart)"]},{"name" : "Tester(FrobeniusAutomorphism)","type" : "GAP_Attribute","filters" : ["Tester(FrobeniusAutomorphism)"]},{"name" : "IsFieldElementsSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsFieldElementsSpace"]},{"name" : "IsZmodnZObj","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsZmodnZObj"]},{"name" : "IsZmodnZObjNonprime","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsZmodnZObj","IsZmodnZObjNonprime"]},{"name" : "CategoryFamily(IsZmodnZObjNonprime)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsAdditivelyCommutativeElement)","CategoryFamily(IsZmodnZObjNonprime)"]},{"name" : "CategoryCollections(IsZmodnZObjNonprime)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsZmodnZObjNonprime)"]},{"name" : "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))"]},{"name" : "Tester(ModulusOfZmodnZObj)","type" : "GAP_Attribute","filters" : ["Tester(ModulusOfZmodnZObj)"]},{"name" : "IsZmodnZepsObj","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZmodnZepsObj"]},{"name" : "CategoryCollections(IsZmodnZepsObj)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZmodnZepsObj)"]},{"name" : "IsZmodnZepsRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsZmodnZepsRep"]},{"name" : "Tester(Cyclotomic)","type" : "GAP_Attribute","filters" : ["Tester(Cyclotomic)"]},{"name" : "Tester(IsRingOfIntegralCyclotomics)","type" : "GAP_Attribute","filters" : ["Tester(IsRingOfIntegralCyclotomics)"]},{"name" : "Tester(GaloisMat)","type" : "GAP_Attribute","filters" : ["Tester(GaloisMat)"]},{"name" : "Tester(RationalizedMat)","type" : "GAP_Attribute","filters" : ["Tester(RationalizedMat)"]},{"name" : "IsNumberField","type" : "GAP_Property","filters" : ["IsNumberField","Tester(IsNumberField)"]},{"name" : "Tester(IsNumberField)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNumberField)"]},{"name" : "IsAbelianNumberField","type" : "GAP_Property","filters" : ["IsNumberField","Tester(IsNumberField)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]},{"name" : "Tester(IsAbelianNumberField)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAbelianNumberField)"]},{"name" : "IsCyclotomicField","type" : "GAP_Property","filters" : ["IsNumberField","Tester(IsNumberField)","IsAbelianNumberField","Tester(IsAbelianNumberField)","IsCyclotomicField","Tester(IsCyclotomicField)"]},{"name" : "Tester(IsCyclotomicField)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCyclotomicField)"]},{"name" : "Tester(GaloisStabilizer)","type" : "GAP_Attribute","filters" : ["Tester(GaloisStabilizer)"]},{"name" : "IsGaussianRationals","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsNonTrivial","Tester(IsNonTrivial)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneralizedDomain","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(MultiplicativeNeutralElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsIntegralRing","Tester(IsIntegralRing)","IsFreeLeftModule","IsGaussianRationals"]},{"name" : "Tester(ExponentOfPowering)","type" : "GAP_Attribute","filters" : ["Tester(ExponentOfPowering)"]},{"name" : "IsPadicNumber","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsCommutativeElement","IsPadicNumber"]},{"name" : "CategoryCollections(IsPadicNumber)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsPadicNumber)"]},{"name" : "CategoryCollections(CategoryCollections(IsPadicNumber))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(CategoryCollections(IsPadicNumber))"]},{"name" : "CategoryFamily(IsPadicNumber)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsPadicNumber)"]},{"name" : "IsPurePadicNumber","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsCommutativeElement","IsPadicNumber","IsPurePadicNumber"]},{"name" : "CategoryFamily(IsPurePadicNumber)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsPadicNumber)","CategoryFamily(IsPurePadicNumber)"]},{"name" : "IsPadicExtensionNumber","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsCommutativeElement","IsPadicNumber","IsPadicExtensionNumber"]},{"name" : "CategoryFamily(IsPadicExtensionNumber)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsPadicNumber)","CategoryFamily(IsPadicExtensionNumber)"]},{"name" : "IsPolynomialRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing"]},{"name" : "IsFunctionField","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFunctionField"]},{"name" : "IsUnivariatePolynomialRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsUnivariatePolynomialRing"]},{"name" : "IsFiniteFieldPolynomialRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsFiniteFieldPolynomialRing"]},{"name" : "IsAbelianNumberFieldPolynomialRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsAbelianNumberFieldPolynomialRing"]},{"name" : "IsAlgebraicExtensionPolynomialRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsAlgebraicExtensionPolynomialRing"]},{"name" : "IsRationalsPolynomialRing","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsAbelianNumberFieldPolynomialRing","IsRationalsPolynomialRing"]},{"name" : "Tester(CoefficientsRing)","type" : "GAP_Attribute","filters" : ["Tester(CoefficientsRing)"]},{"name" : "Tester(IndeterminatesOfPolynomialRing)","type" : "GAP_Attribute","filters" : ["Tester(IndeterminatesOfPolynomialRing)"]},{"name" : "Tester(SplittingField)","type" : "GAP_Attribute","filters" : ["Tester(SplittingField)"]},{"name" : "Tester(IrrFacsPol)","type" : "GAP_Attribute","filters" : ["Tester(IrrFacsPol)"]},{"name" : "Tester(MinimizedBombieriNorm)","type" : "GAP_Attribute","filters" : ["Tester(MinimizedBombieriNorm)"]},{"name" : "IsAlgebraicElement","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsAlgebraicElement"]},{"name" : "CategoryCollections(IsAlgebraicElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsAlgebraicElement)"]},{"name" : "CategoryCollections(CategoryCollections(IsAlgebraicElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(CategoryCollections(IsAlgebraicElement))"]},{"name" : "CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))"]},{"name" : "CategoryFamily(IsAlgebraicElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsAdditivelyCommutativeElement)","CategoryFamily(IsAlgebraicElement)"]},{"name" : "IsAlgebraicExtension","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsNonTrivial","Tester(IsNonTrivial)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(MultiplicativeNeutralElement)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsIntegralRing","Tester(IsIntegralRing)","IsFreeLeftModule","IsAlgebraicExtension"]},{"name" : "Tester(AlgebraicElementsFamilies)","type" : "GAP_Attribute","filters" : ["Tester(AlgebraicElementsFamilies)"]},{"name" : "Tester(DefectApproximation)","type" : "GAP_Attribute","filters" : ["Tester(DefectApproximation)"]},{"name" : "IsUnknown","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsUnknown"]},{"name" : "IsWord","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsWord"]},{"name" : "CategoryCollections(IsWord)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsWord)"]},{"name" : "IsNonassocWord","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsWord","IsNonassocWord"]},{"name" : "CategoryCollections(IsNonassocWord)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsWord)","CategoryCollections(IsNonassocWord)"]},{"name" : "CategoryCollections((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsWord)","CategoryCollections(IsNonassocWord)","CategoryCollections((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))"]},{"name" : "CategoryFamily(IsNonassocWord)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsNonassocWord)"]},{"name" : "CategoryFamily((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsNonassocWord)","CategoryFamily((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))"]},{"name" : "CategoryCollections((IsWord and IsAssociativeElement))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))"]},{"name" : "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]},{"name" : "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]},{"name" : "CategoryFamily((IsWord and IsAssociativeElement))","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"]},{"name" : "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]},{"name" : "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]},{"name" : "IsSyllableWordsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily"]},{"name" : "Is8BitsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","Is8BitsFamily"]},{"name" : "Is16BitsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","Is16BitsFamily"]},{"name" : "Is32BitsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","Is32BitsFamily"]},{"name" : "IsInfBitsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","IsInfBitsFamily"]},{"name" : "IsSyllableAssocWordRep","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]},{"name" : "IsLetterAssocWordRep","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsLetterAssocWordRep"]},{"name" : "IsBLetterAssocWordRep","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsLetterAssocWordRep","IsBLetterAssocWordRep"]},{"name" : "IsWLetterAssocWordRep","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsLetterAssocWordRep","IsWLetterAssocWordRep"]},{"name" : "IsLetterWordsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily"]},{"name" : "IsBLetterWordsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily","IsBLetterWordsFamily"]},{"name" : "IsWLetterWordsFamily","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily","IsWLetterWordsFamily"]},{"name" : "IsFreeSemigroup","type" : "GAP_Property","filters" : ["IsFreeSemigroup","Tester(IsFreeSemigroup)"]},{"name" : "Tester(IsFreeSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFreeSemigroup)"]},{"name" : "IsFreeMonoid","type" : "GAP_Property","filters" : ["IsFreeMonoid","Tester(IsFreeMonoid)"]},{"name" : "Tester(IsFreeMonoid)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFreeMonoid)"]},{"name" : "Tester(NumberSyllables)","type" : "GAP_Attribute","filters" : ["Tester(NumberSyllables)"]},{"name" : "Tester(BaseDomain)","type" : "GAP_Attribute","filters" : ["Tester(BaseDomain)"]},{"name" : "Tester(RowLength)","type" : "GAP_Attribute","filters" : ["Tester(RowLength)"]},{"name" : "IsPlistVectorRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","IsPlistVectorRep"]},{"name" : "IsPlistMatrixRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","IsPlistMatrixRep"]},{"name" : "IsIntVector","type" : "GAP_Filter","implied" : ["IsIntVector"]},{"name" : "IsFFEVector","type" : "GAP_Filter","implied" : ["IsFFEVector"]},{"name" : "IsCheckingVector","type" : "GAP_Filter","implied" : ["IsCheckingVector"]},{"name" : "IsCheckingMatrix","type" : "GAP_Filter","implied" : ["IsCheckingMatrix"]},{"name" : "IsRewritingSystem","type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem"]},{"name" : "IsReducedConfluentRewritingSystem","type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsReducedConfluentRewritingSystem"]},{"name" : "IsBuiltFromAdditiveMagmaWithInverses","type" : "GAP_Property","filters" : ["IsBuiltFromAdditiveMagmaWithInverses","Tester(IsBuiltFromAdditiveMagmaWithInverses)"]},{"name" : "Tester(IsBuiltFromAdditiveMagmaWithInverses)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBuiltFromAdditiveMagmaWithInverses)"]},{"name" : "IsBuiltFromMagma","type" : "GAP_Property","filters" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)"]},{"name" : "Tester(IsBuiltFromMagma)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBuiltFromMagma)"]},{"name" : "IsBuiltFromMagmaWithOne","type" : "GAP_Property","filters" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)"]},{"name" : "Tester(IsBuiltFromMagmaWithOne)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBuiltFromMagmaWithOne)"]},{"name" : "IsBuiltFromMagmaWithInverses","type" : "GAP_Property","filters" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)"]},{"name" : "Tester(IsBuiltFromMagmaWithInverses)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBuiltFromMagmaWithInverses)"]},{"name" : "IsBuiltFromGroup","type" : "GAP_Property","filters" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]},{"name" : "Tester(IsBuiltFromGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBuiltFromGroup)"]},{"name" : "IsBuiltFromSemigroup","type" : "GAP_Property","filters" : ["IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)"]},{"name" : "Tester(IsBuiltFromSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBuiltFromSemigroup)"]},{"name" : "IsBuiltFromMonoid","type" : "GAP_Property","filters" : ["IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)"]},{"name" : "Tester(IsBuiltFromMonoid)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBuiltFromMonoid)"]},{"name" : "Tester(SemigroupOfRewritingSystem)","type" : "GAP_Attribute","filters" : ["Tester(SemigroupOfRewritingSystem)"]},{"name" : "Tester(MonoidOfRewritingSystem)","type" : "GAP_Attribute","filters" : ["Tester(MonoidOfRewritingSystem)"]},{"name" : "Tester(ConfluentRws)","type" : "GAP_Attribute","filters" : ["Tester(ConfluentRws)"]},{"name" : "Tester(GeneratorsOfRws)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsOfRws)"]},{"name" : "Tester(NumberGeneratorsOfRws)","type" : "GAP_Attribute","filters" : ["Tester(NumberGeneratorsOfRws)"]},{"name" : "Tester(Rules)","type" : "GAP_Attribute","filters" : ["Tester(Rules)"]},{"name" : "Tester(OrderingOfRewritingSystem)","type" : "GAP_Attribute","filters" : ["Tester(OrderingOfRewritingSystem)"]},{"name" : "IsConfluent","type" : "GAP_Property","filters" : ["IsConfluent","Tester(IsConfluent)"]},{"name" : "Tester(IsConfluent)","type" : "GAP_TrueProperty","implied" : ["Tester(IsConfluent)"]},{"name" : "IsReduced","type" : "GAP_Property","filters" : ["IsReduced","Tester(IsReduced)"]},{"name" : "Tester(IsReduced)","type" : "GAP_TrueProperty","implied" : ["Tester(IsReduced)"]},{"name" : "IsPolycyclicCollector","type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector"]},{"name" : "IsPowerConjugateCollector","type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector","IsPowerConjugateCollector"]},{"name" : "IsPowerCommutatorCollector","type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector","IsPowerCommutatorCollector"]},{"name" : "Tester(RelativeOrders)","type" : "GAP_Attribute","filters" : ["Tester(RelativeOrders)"]},{"name" : "IsUpToDatePolycyclicCollector","type" : "GAP_Filter","implied" : ["IsUpToDatePolycyclicCollector"]},{"name" : "IsElementsFamilyByRws","type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws"]},{"name" : "IsMultiplicativeElementWithInverseByRws","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMultiplicativeElementWithInverseByRws"]},{"name" : "IsElementFinitePolycyclicGroup","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsElementFinitePolycyclicGroup"]},{"name" : "CategoryCollections(IsElementFinitePolycyclicGroup)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)","CategoryCollections(IsElementFinitePolycyclicGroup)"]},{"name" : "IsMultiplicativeElementWithInverseByPolycyclicCollector","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsMultiplicativeElementWithInverseByRws","IsMultiplicativeElementWithInverseByPolycyclicCollector"]},{"name" : "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]},{"name" : "Tester(DefiningPcgs)","type" : "GAP_Attribute","filters" : ["Tester(DefiningPcgs)"]},{"name" : "IsKernelPcWord","type" : "GAP_Filter","implied" : ["IsKernelPcWord"]},{"name" : "IsElementsFamilyBy8BitsSingleCollector","type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws","IsElementsFamilyBy8BitsSingleCollector"]},{"name" : "IsElementsFamilyBy16BitsSingleCollector","type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws","IsElementsFamilyBy16BitsSingleCollector"]},{"name" : "IsElementsFamilyBy32BitsSingleCollector","type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws","IsElementsFamilyBy32BitsSingleCollector"]},{"name" : "IsMonomialOrdering","type" : "GAP_Category","implied" : ["IsMonomialOrdering"]},{"name" : "IsMonomialOrderingDefaultRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsComponentObjectRep","IsAttributeStoringRep","IsMonomialOrdering","IsMonomialOrderingDefaultRep"]},{"name" : "Tester(MonomialComparisonFunction)","type" : "GAP_Attribute","filters" : ["Tester(MonomialComparisonFunction)"]},{"name" : "Tester(MonomialExtrepComparisonFun)","type" : "GAP_Attribute","filters" : ["Tester(MonomialExtrepComparisonFun)"]},{"name" : "Tester(OccuringVariableIndices)","type" : "GAP_Attribute","filters" : ["Tester(OccuringVariableIndices)"]},{"name" : "Tester(StoredGroebnerBasis)","type" : "GAP_Attribute","filters" : ["Tester(StoredGroebnerBasis)"]},{"name" : "IsGeneralPcgs","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs"]},{"name" : "IsModuloPcgs","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs"]},{"name" : "IsPcgs","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs","IsPcgs"]},{"name" : "IsPcgsFamily","type" : "GAP_Category","implied" : ["IsFamily","IsPcgsFamily"]},{"name" : "IsPcgsDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep"]},{"name" : "Tester(PcGroupWithPcgs)","type" : "GAP_Attribute","filters" : ["Tester(PcGroupWithPcgs)"]},{"name" : "Tester(GroupOfPcgs)","type" : "GAP_Attribute","filters" : ["Tester(GroupOfPcgs)"]},{"name" : "Tester(OneOfPcgs)","type" : "GAP_Attribute","filters" : ["Tester(OneOfPcgs)"]},{"name" : "Tester(PcSeries)","type" : "GAP_Attribute","filters" : ["Tester(PcSeries)"]},{"name" : "IsPcgsElementaryAbelianSeries","type" : "GAP_Property","filters" : ["IsPcgsElementaryAbelianSeries","Tester(IsPcgsElementaryAbelianSeries)"]},{"name" : "Tester(IsPcgsElementaryAbelianSeries)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPcgsElementaryAbelianSeries)"]},{"name" : "Tester(PcgsElementaryAbelianSeries)","type" : "GAP_Attribute","filters" : ["Tester(PcgsElementaryAbelianSeries)"]},{"name" : "Tester(IndicesEANormalSteps)","type" : "GAP_Attribute","filters" : ["Tester(IndicesEANormalSteps)"]},{"name" : "Tester(EANormalSeriesByPcgs)","type" : "GAP_Attribute","filters" : ["Tester(EANormalSeriesByPcgs)"]},{"name" : "IsPcgsCentralSeries","type" : "GAP_Property","filters" : ["IsPcgsCentralSeries","Tester(IsPcgsCentralSeries)"]},{"name" : "Tester(IsPcgsCentralSeries)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPcgsCentralSeries)"]},{"name" : "Tester(PcgsCentralSeries)","type" : "GAP_Attribute","filters" : ["Tester(PcgsCentralSeries)"]},{"name" : "Tester(IndicesCentralNormalSteps)","type" : "GAP_Attribute","filters" : ["Tester(IndicesCentralNormalSteps)"]},{"name" : "Tester(CentralNormalSeriesByPcgs)","type" : "GAP_Attribute","filters" : ["Tester(CentralNormalSeriesByPcgs)"]},{"name" : "IsPcgsPCentralSeriesPGroup","type" : "GAP_Property","filters" : ["IsPcgsPCentralSeriesPGroup","Tester(IsPcgsPCentralSeriesPGroup)"]},{"name" : "Tester(IsPcgsPCentralSeriesPGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPcgsPCentralSeriesPGroup)"]},{"name" : "Tester(PcgsPCentralSeriesPGroup)","type" : "GAP_Attribute","filters" : ["Tester(PcgsPCentralSeriesPGroup)"]},{"name" : "Tester(IndicesPCentralNormalStepsPGroup)","type" : "GAP_Attribute","filters" : ["Tester(IndicesPCentralNormalStepsPGroup)"]},{"name" : "Tester(PCentralNormalSeriesByPcgsPGroup)","type" : "GAP_Attribute","filters" : ["Tester(PCentralNormalSeriesByPcgsPGroup)"]},{"name" : "IsPcgsChiefSeries","type" : "GAP_Property","filters" : ["IsPcgsChiefSeries","Tester(IsPcgsChiefSeries)"]},{"name" : "Tester(IsPcgsChiefSeries)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPcgsChiefSeries)"]},{"name" : "Tester(PcgsChiefSeries)","type" : "GAP_Attribute","filters" : ["Tester(PcgsChiefSeries)"]},{"name" : "Tester(IndicesChiefNormalSteps)","type" : "GAP_Attribute","filters" : ["Tester(IndicesChiefNormalSteps)"]},{"name" : "Tester(ChiefNormalSeriesByPcgs)","type" : "GAP_Attribute","filters" : ["Tester(ChiefNormalSeriesByPcgs)"]},{"name" : "Tester(IndicesNormalSteps)","type" : "GAP_Attribute","filters" : ["Tester(IndicesNormalSteps)"]},{"name" : "Tester(NormalSeriesByPcgs)","type" : "GAP_Attribute","filters" : ["Tester(NormalSeriesByPcgs)"]},{"name" : "IsPrimeOrdersPcgs","type" : "GAP_Property","filters" : ["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)"]},{"name" : "Tester(IsPrimeOrdersPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPrimeOrdersPcgs)"]},{"name" : "IsFiniteOrdersPcgs","type" : "GAP_Property","filters" : ["IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)"]},{"name" : "Tester(IsFiniteOrdersPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFiniteOrdersPcgs)"]},{"name" : "Tester(RefinedPcGroup)","type" : "GAP_Attribute","filters" : ["Tester(RefinedPcGroup)"]},{"name" : "Tester(IsomorphismRefinedPcGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismRefinedPcGroup)"]},{"name" : "IsInducedPcgs","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs","IsPcgs","IsInducedPcgs"]},{"name" : "Tester(LeadCoeffsIGS)","type" : "GAP_Attribute","filters" : ["Tester(LeadCoeffsIGS)"]},{"name" : "Tester(ParentPcgs)","type" : "GAP_Attribute","filters" : ["Tester(ParentPcgs)"]},{"name" : "Tester(CanonicalPcgs)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalPcgs)"]},{"name" : "IsCanonicalPcgs","type" : "GAP_Property","filters" : ["IsCanonicalPcgs","Tester(IsCanonicalPcgs)"]},{"name" : "Tester(IsCanonicalPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCanonicalPcgs)"]},{"name" : "IsParentPcgsFamilyPcgs","type" : "GAP_Property","filters" : ["IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)"]},{"name" : "Tester(IsParentPcgsFamilyPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsParentPcgsFamilyPcgs)"]},{"name" : "Tester(ElementaryAbelianSubseries)","type" : "GAP_Attribute","filters" : ["Tester(ElementaryAbelianSubseries)"]},{"name" : "IsFamilyPcgs","type" : "GAP_Property","filters" : ["IsCanonicalPcgs","Tester(IsCanonicalPcgs)","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsFamilyPcgs","Tester(IsFamilyPcgs)"]},{"name" : "Tester(IsFamilyPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFamilyPcgs)"]},{"name" : "Tester(DenominatorOfModuloPcgs)","type" : "GAP_Attribute","filters" : ["Tester(DenominatorOfModuloPcgs)"]},{"name" : "Tester(NumeratorOfModuloPcgs)","type" : "GAP_Attribute","filters" : ["Tester(NumeratorOfModuloPcgs)"]},{"name" : "IsNumeratorParentPcgsFamilyPcgs","type" : "GAP_Property","filters" : ["IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)"]},{"name" : "Tester(IsNumeratorParentPcgsFamilyPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNumeratorParentPcgsFamilyPcgs)"]},{"name" : "IsPcgsPermGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)","IsPcgsPermGroupRep"]},{"name" : "IsModuloPcgsPermGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)","IsPcgsPermGroupRep","IsModuloPcgsPermGroupRep"]},{"name" : "IsSpecialPcgs","type" : "GAP_Property","filters" : ["IsPcgsElementaryAbelianSeries","Tester(IsPcgsElementaryAbelianSeries)","IsSpecialPcgs","Tester(IsSpecialPcgs)"]},{"name" : "Tester(IsSpecialPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSpecialPcgs)"]},{"name" : "Tester(SpecialPcgs)","type" : "GAP_Attribute","filters" : ["Tester(SpecialPcgs)"]},{"name" : "Tester(LGHeads)","type" : "GAP_Attribute","filters" : ["Tester(LGHeads)"]},{"name" : "Tester(LGTails)","type" : "GAP_Attribute","filters" : ["Tester(LGTails)"]},{"name" : "Tester(LGWeights)","type" : "GAP_Attribute","filters" : ["Tester(LGWeights)"]},{"name" : "Tester(LGLayers)","type" : "GAP_Attribute","filters" : ["Tester(LGLayers)"]},{"name" : "Tester(LGFirst)","type" : "GAP_Attribute","filters" : ["Tester(LGFirst)"]},{"name" : "Tester(LGLength)","type" : "GAP_Attribute","filters" : ["Tester(LGLength)"]},{"name" : "Tester(InducedPcgsWrtSpecialPcgs)","type" : "GAP_Attribute","filters" : ["Tester(InducedPcgsWrtSpecialPcgs)"]},{"name" : "Tester(CanonicalPcgsWrtSpecialPcgs)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalPcgsWrtSpecialPcgs)"]},{"name" : "IsInducedPcgsWrtSpecialPcgs","type" : "GAP_Property","filters" : ["IsInducedPcgsWrtSpecialPcgs","Tester(IsInducedPcgsWrtSpecialPcgs)"]},{"name" : "Tester(IsInducedPcgsWrtSpecialPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsInducedPcgsWrtSpecialPcgs)"]},{"name" : "IsCanonicalPcgsWrtSpecialPcgs","type" : "GAP_Property","filters" : ["IsCanonicalPcgsWrtSpecialPcgs","Tester(IsCanonicalPcgsWrtSpecialPcgs)"]},{"name" : "Tester(IsCanonicalPcgsWrtSpecialPcgs)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCanonicalPcgsWrtSpecialPcgs)"]},{"name" : "Tester(CanonicalPcgsWrtFamilyPcgs)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalPcgsWrtFamilyPcgs)"]},{"name" : "Tester(CanonicalPcgsWrtHomePcgs)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalPcgsWrtHomePcgs)"]},{"name" : "Tester(FamilyPcgs)","type" : "GAP_Attribute","filters" : ["Tester(FamilyPcgs)"]},{"name" : "Tester(HomePcgs)","type" : "GAP_Attribute","filters" : ["Tester(HomePcgs)"]},{"name" : "Tester(InducedPcgsWrtFamilyPcgs)","type" : "GAP_Attribute","filters" : ["Tester(InducedPcgsWrtFamilyPcgs)"]},{"name" : "Tester(ComputedInducedPcgses)","type" : "GAP_Attribute","filters" : ["Tester(ComputedInducedPcgses)"]},{"name" : "Tester(InducedPcgsWrtHomePcgs)","type" : "GAP_Attribute","filters" : ["Tester(InducedPcgsWrtHomePcgs)"]},{"name" : "Tester(Pcgs)","type" : "GAP_Attribute","filters" : ["Tester(Pcgs)"]},{"name" : "Tester(GeneralizedPcgs)","type" : "GAP_Attribute","filters" : ["Tester(GeneralizedPcgs)"]},{"name" : "CanEasilyComputePcgs","type" : "GAP_Filter","implied" : ["IsListOrCollection","IsCollection","CanComputeSize","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","CanComputeSizeAnySubgroup","IsSolvableGroup","Tester(IsSolvableGroup)","CanEasilyComputePcgs"]},{"name" : "Tester(OmegaSeries)","type" : "GAP_Attribute","filters" : ["Tester(OmegaSeries)"]},{"name" : "Tester(NormalizerInHomePcgs)","type" : "GAP_Attribute","filters" : ["Tester(NormalizerInHomePcgs)"]},{"name" : "Tester(MultiplicationTable)","type" : "GAP_Attribute","filters" : ["Tester(MultiplicationTable)"]},{"name" : "Tester(AllBlocks)","type" : "GAP_Attribute","filters" : ["Tester(AllBlocks)"]},{"name" : "Tester(TransitiveIdentification)","type" : "GAP_Attribute","filters" : ["Tester(TransitiveIdentification)"]},{"name" : "Tester(PrimitiveIdentification)","type" : "GAP_Attribute","filters" : ["Tester(PrimitiveIdentification)"]},{"name" : "Tester(ONanScottType)","type" : "GAP_Attribute","filters" : ["Tester(ONanScottType)"]},{"name" : "Tester(SocleTypePrimitiveGroup)","type" : "GAP_Attribute","filters" : ["Tester(SocleTypePrimitiveGroup)"]},{"name" : "Tester(TwoClosure)","type" : "GAP_Attribute","filters" : ["Tester(TwoClosure)"]},{"name" : "IsGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages"]},{"name" : "IsPreimagesByAsGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages"]},{"name" : "IsGroupGeneralMappingByAsGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]},{"name" : "Tester(AsGroupGeneralMappingByImages)","type" : "GAP_Attribute","filters" : ["Tester(AsGroupGeneralMappingByImages)"]},{"name" : "Tester(MappingOfWhichItIsAsGGMBI)","type" : "GAP_Attribute","filters" : ["Tester(MappingOfWhichItIsAsGGMBI)"]},{"name" : "Tester(NaturalHomomorphismByNormalSubgroupNCInParent)","type" : "GAP_Attribute","filters" : ["Tester(NaturalHomomorphismByNormalSubgroupNCInParent)"]},{"name" : "IsConjugatorIsomorphism","type" : "GAP_Property","filters" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]},{"name" : "Tester(IsConjugatorIsomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsConjugatorIsomorphism)"]},{"name" : "IsInnerAutomorphism","type" : "GAP_Property","filters" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)","IsInnerAutomorphism","Tester(IsInnerAutomorphism)"]},{"name" : "Tester(IsInnerAutomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsInnerAutomorphism)"]},{"name" : "Tester(ConjugatorOfConjugatorIsomorphism)","type" : "GAP_Attribute","filters" : ["Tester(ConjugatorOfConjugatorIsomorphism)"]},{"name" : "Tester(ImagesSmallestGenerators)","type" : "GAP_Attribute","filters" : ["Tester(ImagesSmallestGenerators)"]},{"name" : "Tester(RegularActionHomomorphism)","type" : "GAP_Attribute","filters" : ["Tester(RegularActionHomomorphism)"]},{"name" : "IsGroupGeneralMappingByPcgs","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsGroupGeneralMappingByPcgs"]},{"name" : "IsPcGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsGroupGeneralMappingByPcgs","IsPcGroupGeneralMappingByImages"]},{"name" : "IsToPcGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsToPcGroupGeneralMappingByImages"]},{"name" : "IsNaturalHomomorphismPcGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsNaturalHomomorphismPcGroupRep"]},{"name" : "IsPcgsToPcgsGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsGroupGeneralMappingByPcgs","IsPcGroupGeneralMappingByImages","IsToPcGroupGeneralMappingByImages","IsPcgsToPcgsGeneralMappingByImages"]},{"name" : "Tester(DirectProductInfo)","type" : "GAP_Attribute","filters" : ["Tester(DirectProductInfo)"]},{"name" : "Tester(SubdirectProductInfo)","type" : "GAP_Attribute","filters" : ["Tester(SubdirectProductInfo)"]},{"name" : "Tester(SemidirectProductInfo)","type" : "GAP_Attribute","filters" : ["Tester(SemidirectProductInfo)"]},{"name" : "Tester(WreathProductInfo)","type" : "GAP_Attribute","filters" : ["Tester(WreathProductInfo)"]},{"name" : "Tester(FreeProductInfo)","type" : "GAP_Attribute","filters" : ["Tester(FreeProductInfo)"]},{"name" : "IsWreathProductElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWreathProductElement"]},{"name" : "CategoryCollections(IsWreathProductElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWreathProductElement)"]},{"name" : "IsWreathProductElementDefaultRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWreathProductElement","IsWreathProductElementDefaultRep"]},{"name" : "IsPermGroupGeneralMapping","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPermGroupGeneralMapping"]},{"name" : "IsPermGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsPermGroupGeneralMapping","IsPermGroupGeneralMappingByImages"]},{"name" : "IsToPermGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsToPermGroupGeneralMappingByImages"]},{"name" : "IsNaturalSymmetricGroup","type" : "GAP_Property","filters" : ["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)","IsSymmetricGroup","Tester(IsSymmetricGroup)"]},{"name" : "Tester(IsNaturalSymmetricGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNaturalSymmetricGroup)"]},{"name" : "IsNaturalAlternatingGroup","type" : "GAP_Property","filters" : ["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)","IsAlternatingGroup","Tester(IsAlternatingGroup)"]},{"name" : "Tester(IsNaturalAlternatingGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNaturalAlternatingGroup)"]},{"name" : "IsAlternatingGroup","type" : "GAP_Property","filters" : ["IsAlternatingGroup","Tester(IsAlternatingGroup)"]},{"name" : "Tester(IsAlternatingGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAlternatingGroup)"]},{"name" : "IsSymmetricGroup","type" : "GAP_Property","filters" : ["IsSymmetricGroup","Tester(IsSymmetricGroup)"]},{"name" : "Tester(IsSymmetricGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSymmetricGroup)"]},{"name" : "Tester(SymmetricParentGroup)","type" : "GAP_Attribute","filters" : ["Tester(SymmetricParentGroup)"]},{"name" : "Tester(AlternatingSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(AlternatingSubgroup)"]},{"name" : "Tester(OrbitStabilizingParentGroup)","type" : "GAP_Attribute","filters" : ["Tester(OrbitStabilizingParentGroup)"]},{"name" : "Tester(DirectFactorsOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(DirectFactorsOfGroup)"]},{"name" : "Tester(SemidirectFactorsOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(SemidirectFactorsOfGroup)"]},{"name" : "Tester(DecompositionTypesOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(DecompositionTypesOfGroup)"]},{"name" : "IsDihedralGroup","type" : "GAP_Property","filters" : ["IsDihedralGroup","Tester(IsDihedralGroup)"]},{"name" : "Tester(IsDihedralGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsDihedralGroup)"]},{"name" : "Tester(DihedralGenerators)","type" : "GAP_Attribute","filters" : ["Tester(DihedralGenerators)"]},{"name" : "IsQuaternionGroup","type" : "GAP_Property","filters" : ["IsQuaternionGroup","Tester(IsQuaternionGroup)"]},{"name" : "Tester(IsQuaternionGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsQuaternionGroup)"]},{"name" : "Tester(QuaternionGenerators)","type" : "GAP_Attribute","filters" : ["Tester(QuaternionGenerators)"]},{"name" : "IsQuasiDihedralGroup","type" : "GAP_Property","filters" : ["IsQuasiDihedralGroup","Tester(IsQuasiDihedralGroup)"]},{"name" : "Tester(IsQuasiDihedralGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsQuasiDihedralGroup)"]},{"name" : "Tester(QuasiDihedralGenerators)","type" : "GAP_Attribute","filters" : ["Tester(QuasiDihedralGenerators)"]},{"name" : "IsPSL","type" : "GAP_Property","filters" : ["IsPSL","Tester(IsPSL)"]},{"name" : "Tester(IsPSL)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPSL)"]},{"name" : "Tester(ParametersOfGroupViewedAsPSL)","type" : "GAP_Attribute","filters" : ["Tester(ParametersOfGroupViewedAsPSL)"]},{"name" : "Tester(ParametersOfGroupViewedAsSL)","type" : "GAP_Attribute","filters" : ["Tester(ParametersOfGroupViewedAsSL)"]},{"name" : "Tester(ParametersOfGroupViewedAsGL)","type" : "GAP_Attribute","filters" : ["Tester(ParametersOfGroupViewedAsGL)"]},{"name" : "Tester(AlternatingDegree)","type" : "GAP_Attribute","filters" : ["Tester(AlternatingDegree)"]},{"name" : "Tester(SymmetricDegree)","type" : "GAP_Attribute","filters" : ["Tester(SymmetricDegree)"]},{"name" : "Tester(PSLDegree)","type" : "GAP_Attribute","filters" : ["Tester(PSLDegree)"]},{"name" : "Tester(PSLUnderlyingField)","type" : "GAP_Attribute","filters" : ["Tester(PSLUnderlyingField)"]},{"name" : "Tester(SLDegree)","type" : "GAP_Attribute","filters" : ["Tester(SLDegree)"]},{"name" : "Tester(SLUnderlyingField)","type" : "GAP_Attribute","filters" : ["Tester(SLUnderlyingField)"]},{"name" : "Tester(GLDegree)","type" : "GAP_Attribute","filters" : ["Tester(GLDegree)"]},{"name" : "Tester(GLUnderlyingField)","type" : "GAP_Attribute","filters" : ["Tester(GLUnderlyingField)"]},{"name" : "Tester(StructureDescription)","type" : "GAP_Attribute","filters" : ["Tester(StructureDescription)"]},{"name" : "IsQuotientSystem","type" : "GAP_Category","implied" : ["IsQuotientSystem"]},{"name" : "IsPQuotientSystem","type" : "GAP_Property","filters" : ["IsPQuotientSystem","Tester(IsPQuotientSystem)"]},{"name" : "Tester(IsPQuotientSystem)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPQuotientSystem)"]},{"name" : "IsNilpQuotientSystem","type" : "GAP_Property","filters" : ["IsNilpQuotientSystem","Tester(IsNilpQuotientSystem)"]},{"name" : "Tester(IsNilpQuotientSystem)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNilpQuotientSystem)"]},{"name" : "IsExternalSet","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet"]},{"name" : "IsExternalSubset","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset"]},{"name" : "IsExternalOrbit","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit"]},{"name" : "IsExternalSetByPcgs","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSetByPcgs"]},{"name" : "IsExternalSetDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSetDefaultRep"]},{"name" : "IsExternalSetByActorsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSetByActorsRep"]},{"name" : "Tester(ActingDomain)","type" : "GAP_Attribute","filters" : ["Tester(ActingDomain)"]},{"name" : "Tester(HomeEnumerator)","type" : "GAP_Attribute","filters" : ["Tester(HomeEnumerator)"]},{"name" : "IsActionHomomorphism","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism"]},{"name" : "IsActionHomomorphismByActors","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismByActors"]},{"name" : "IsActionHomomorphismSubset","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismSubset"]},{"name" : "Tester(ActionKernelExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(ActionKernelExternalSet)"]},{"name" : "IsActionHomomorphismByBase","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismByBase"]},{"name" : "IsConstituentHomomorphism","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsConstituentHomomorphism"]},{"name" : "IsBlocksHomomorphism","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsBlocksHomomorphism"]},{"name" : "IsLinearActionHomomorphism","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsLinearActionHomomorphism"]},{"name" : "IsProjectiveActionHomomorphism","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsProjectiveActionHomomorphism"]},{"name" : "Tester(LinearActionBasis)","type" : "GAP_Attribute","filters" : ["Tester(LinearActionBasis)"]},{"name" : "Tester(FunctionAction)","type" : "GAP_Attribute","filters" : ["Tester(FunctionAction)"]},{"name" : "Tester(StabilizerOfExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(StabilizerOfExternalSet)"]},{"name" : "Tester(CanonicalRepresentativeOfExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalRepresentativeOfExternalSet)","Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]},{"name" : "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalRepresentativeDeterminatorOfExternalSet)","Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]},{"name" : "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]},{"name" : "Tester(ActorOfExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(ActorOfExternalSet)"]},{"name" : "Tester(ActionHomomorphismAttr)","type" : "GAP_Attribute","filters" : ["Tester(ActionHomomorphismAttr)"]},{"name" : "Tester(SurjectiveActionHomomorphismAttr)","type" : "GAP_Attribute","filters" : ["Tester(SurjectiveActionHomomorphismAttr)"]},{"name" : "Tester(UnderlyingExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingExternalSet)"]},{"name" : "Tester(ExternalSet)","type" : "GAP_Attribute","filters" : ["Tester(ExternalSet)"]},{"name" : "Tester(Orbits)","type" : "GAP_Attribute","filters" : ["Tester(Orbits)"]},{"name" : "Tester(OrbitsDomain)","type" : "GAP_Attribute","filters" : ["Tester(OrbitsDomain)"]},{"name" : "Tester(OrbitLengths)","type" : "GAP_Attribute","filters" : ["Tester(OrbitLengths)"]},{"name" : "Tester(OrbitLengthsDomain)","type" : "GAP_Attribute","filters" : ["Tester(OrbitLengthsDomain)"]},{"name" : "Tester(ExternalOrbits)","type" : "GAP_Attribute","filters" : ["Tester(ExternalOrbits)"]},{"name" : "Tester(ExternalOrbitsStabilizers)","type" : "GAP_Attribute","filters" : ["Tester(ExternalOrbitsStabilizers)"]},{"name" : "Tester(Transitivity)","type" : "GAP_Attribute","filters" : ["Tester(Transitivity)"]},{"name" : "Tester(BlocksAttr)","type" : "GAP_Attribute","filters" : ["Tester(BlocksAttr)"]},{"name" : "Tester(MaximalBlocksAttr)","type" : "GAP_Attribute","filters" : ["Tester(MaximalBlocksAttr)"]},{"name" : "Tester(RepresentativesMinimalBlocksAttr)","type" : "GAP_Attribute","filters" : ["Tester(RepresentativesMinimalBlocksAttr)"]},{"name" : "Tester(Earns)","type" : "GAP_Attribute","filters" : ["Tester(Earns)"]},{"name" : "IsTransitive","type" : "GAP_Property","filters" : ["IsTransitive","Tester(IsTransitive)"]},{"name" : "Tester(IsTransitive)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTransitive)"]},{"name" : "IsPrimitive","type" : "GAP_Property","filters" : ["IsPrimitive","Tester(IsPrimitive)"]},{"name" : "Tester(IsPrimitive)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPrimitive)"]},{"name" : "IsPrimitiveAffine","type" : "GAP_Property","filters" : ["IsPrimitiveAffine","Tester(IsPrimitiveAffine)"]},{"name" : "Tester(IsPrimitiveAffine)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPrimitiveAffine)"]},{"name" : "IsSemiRegular","type" : "GAP_Property","filters" : ["IsSemiRegular","Tester(IsSemiRegular)"]},{"name" : "Tester(IsSemiRegular)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSemiRegular)"]},{"name" : "IsRegular","type" : "GAP_Property","filters" : ["IsRegular","Tester(IsRegular)"]},{"name" : "Tester(IsRegular)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRegular)"]},{"name" : "Tester(RankAction)","type" : "GAP_Attribute","filters" : ["Tester(RankAction)"]},{"name" : "Tester(StabChainMutable)","type" : "GAP_Attribute","filters" : ["Tester(StabChainMutable)"]},{"name" : "Tester(StabChainImmutable)","type" : "GAP_Attribute","filters" : ["Tester(StabChainImmutable)"]},{"name" : "Tester(StabChainOptions)","type" : "GAP_Attribute","filters" : ["Tester(StabChainOptions)"]},{"name" : "Tester(BaseOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(BaseOfGroup)"]},{"name" : "Tester(MinimalStabChain)","type" : "GAP_Attribute","filters" : ["Tester(MinimalStabChain)"]},{"name" : "IsPermOnEnumerator","type" : "GAP_Category","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement","IsPermOnEnumerator"]},{"name" : "IsExternalOrbitByStabilizerRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsExternalOrbitByStabilizerRep"]},{"name" : "IsConjugacyClassGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsConjugacyClassGroupRep"]},{"name" : "IsConjugacyClassPermGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsExternalOrbitByStabilizerRep","IsConjugacyClassGroupRep","IsConjugacyClassPermGroupRep"]},{"name" : "IsRationalClassGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsRationalClassGroupRep"]},{"name" : "IsRationalClassPermGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsRationalClassGroupRep","IsRationalClassPermGroupRep"]},{"name" : "Tester(DecomposedRationalClass)","type" : "GAP_Attribute","filters" : ["Tester(DecomposedRationalClass)"]},{"name" : "Tester(StoredPermliftSeries)","type" : "GAP_Attribute","filters" : ["Tester(StoredPermliftSeries)"]},{"name" : "Tester(ComputedAscendingChains)","type" : "GAP_Attribute","filters" : ["Tester(ComputedAscendingChains)"]},{"name" : "IsDoubleCoset","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsExtRSet","IsDoubleCoset"]},{"name" : "Tester(LeftActingGroup)","type" : "GAP_Attribute","filters" : ["Tester(LeftActingGroup)"]},{"name" : "Tester(RightActingGroup)","type" : "GAP_Attribute","filters" : ["Tester(RightActingGroup)"]},{"name" : "Tester(RepresentativesContainedRightCosets)","type" : "GAP_Attribute","filters" : ["Tester(RepresentativesContainedRightCosets)"]},{"name" : "IsRightCoset","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsRightCoset"]},{"name" : "Tester(NaturalHomomorphismsPool)","type" : "GAP_Attribute","filters" : ["Tester(NaturalHomomorphismsPool)"]},{"name" : "Tester(SocleComplement)","type" : "GAP_Attribute","filters" : ["Tester(SocleComplement)"]},{"name" : "Tester(SocleDimensions)","type" : "GAP_Attribute","filters" : ["Tester(SocleDimensions)"]},{"name" : "Tester(ModuleOfExtension)","type" : "GAP_Attribute","filters" : ["Tester(ModuleOfExtension)"]},{"name" : "Tester(OmegaAndLowerPCentralSeries)","type" : "GAP_Attribute","filters" : ["Tester(OmegaAndLowerPCentralSeries)"]},{"name" : "Tester(SchurCover)","type" : "GAP_Attribute","filters" : ["Tester(SchurCover)"]},{"name" : "Tester(EpimorphismSchurCover)","type" : "GAP_Attribute","filters" : ["Tester(EpimorphismSchurCover)"]},{"name" : "Tester(AbelianInvariantsMultiplier)","type" : "GAP_Attribute","filters" : ["Tester(AbelianInvariantsMultiplier)"]},{"name" : "Tester(Epicentre)","type" : "GAP_Attribute","filters" : ["Tester(Epicentre)"]},{"name" : "IsCentralFactor","type" : "GAP_Property","filters" : ["IsCentralFactor","Tester(IsCentralFactor)"]},{"name" : "Tester(IsCentralFactor)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCentralFactor)"]},{"name" : "IsConjugacyClassSubgroupsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsConjugacyClassSubgroupsRep"]},{"name" : "IsConjugacyClassSubgroupsByStabilizerRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsExternalOrbitByStabilizerRep","IsConjugacyClassSubgroupsRep","IsConjugacyClassSubgroupsByStabilizerRep"]},{"name" : "IsLatticeSubgroupsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLatticeSubgroupsRep"]},{"name" : "Tester(Zuppos)","type" : "GAP_Attribute","filters" : ["Tester(Zuppos)"]},{"name" : "Tester(MaximalSubgroupsLattice)","type" : "GAP_Attribute","filters" : ["Tester(MaximalSubgroupsLattice)"]},{"name" : "Tester(MinimalSupergroupsLattice)","type" : "GAP_Attribute","filters" : ["Tester(MinimalSupergroupsLattice)"]},{"name" : "Tester(TomDataAlmostSimpleRecognition)","type" : "GAP_Attribute","filters" : ["Tester(TomDataAlmostSimpleRecognition)"]},{"name" : "IsFrattiniFree","type" : "GAP_Property","filters" : ["IsFrattiniFree","Tester(IsFrattiniFree)"]},{"name" : "Tester(IsFrattiniFree)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFrattiniFree)"]},{"name" : "IsStraightLineProgram","type" : "GAP_Category","implied" : ["IsStraightLineProgram"]},{"name" : "Tester(LinesOfStraightLineProgram)","type" : "GAP_Attribute","filters" : ["Tester(LinesOfStraightLineProgram)"]},{"name" : "Tester(NrInputsOfStraightLineProgram)","type" : "GAP_Attribute","filters" : ["Tester(NrInputsOfStraightLineProgram)"]},{"name" : "StraightLineProgramElmRankFilter","type" : "GAP_Filter","implied" : ["StraightLineProgramElmRankFilter"]},{"name" : "IsStraightLineProgElm","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","StraightLineProgramElmRankFilter","IsStraightLineProgElm"]},{"name" : "Tester(StraightLineProgElmType)","type" : "GAP_Attribute","filters" : ["Tester(StraightLineProgElmType)"]},{"name" : "Tester(SlotUsagePattern)","type" : "GAP_Attribute","filters" : ["Tester(SlotUsagePattern)"]},{"name" : "Tester(LargestNrSlots)","type" : "GAP_Attribute","filters" : ["Tester(LargestNrSlots)"]},{"name" : "IsObjWithMemoryRankFilter","type" : "GAP_Filter","implied" : ["IsObjWithMemoryRankFilter"]},{"name" : "IsObjWithMemory","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsObjWithMemoryRankFilter","IsObjWithMemory"]},{"name" : "Tester(TypeOfObjWithMemory)","type" : "GAP_Attribute","filters" : ["Tester(TypeOfObjWithMemory)"]},{"name" : "IsSubgroupFgGroup","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSubgroupFgGroup"]},{"name" : "IsSubgroupFpGroup","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSubgroupFgGroup","IsSubgroupFpGroup"]},{"name" : "IsElementOfFpGroup","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsElementOfFpGroup"]},{"name" : "CategoryCollections(IsElementOfFpGroup)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsElementOfFpGroup)"]},{"name" : "CategoryFamily(IsElementOfFpGroup)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsElementOfFpGroup)"]},{"name" : "Tester(FpElmEqualityMethod)","type" : "GAP_Attribute","filters" : ["Tester(FpElmEqualityMethod)"]},{"name" : "Tester(FpElmComparisonMethod)","type" : "GAP_Attribute","filters" : ["Tester(FpElmComparisonMethod)"]},{"name" : "Tester(FpElementNFFunction)","type" : "GAP_Attribute","filters" : ["Tester(FpElementNFFunction)"]},{"name" : "Tester(CosetTableInWholeGroup)","type" : "GAP_Attribute","filters" : ["Tester(CosetTableInWholeGroup)"]},{"name" : "Tester(CosetTableNormalClosureInWholeGroup)","type" : "GAP_Attribute","filters" : ["Tester(CosetTableNormalClosureInWholeGroup)"]},{"name" : "IsSubgroupOfWholeGroupByQuotientRep","type" : "GAP_Representation","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSubgroupFgGroup","IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]},{"name" : "Tester(AsSubgroupOfWholeGroupByQuotient)","type" : "GAP_Attribute","filters" : ["Tester(AsSubgroupOfWholeGroupByQuotient)"]},{"name" : "Tester(FreeGeneratorsOfFpGroup)","type" : "GAP_Attribute","filters" : ["Tester(FreeGeneratorsOfFpGroup)"]},{"name" : "Tester(RelatorsOfFpGroup)","type" : "GAP_Attribute","filters" : ["Tester(RelatorsOfFpGroup)"]},{"name" : "Tester(FreeGroupOfFpGroup)","type" : "GAP_Attribute","filters" : ["Tester(FreeGroupOfFpGroup)"]},{"name" : "Tester(IndicesInvolutaryGenerators)","type" : "GAP_Attribute","filters" : ["Tester(IndicesInvolutaryGenerators)"]},{"name" : "Tester(StoredExcludedOrders)","type" : "GAP_Attribute","filters" : ["Tester(StoredExcludedOrders)"]},{"name" : "Tester(FPFaithHom)","type" : "GAP_Attribute","filters" : ["Tester(FPFaithHom)"]},{"name" : "Tester(AugmentedCosetTableMtcInWholeGroup)","type" : "GAP_Attribute","filters" : ["Tester(AugmentedCosetTableMtcInWholeGroup)"]},{"name" : "Tester(AugmentedCosetTableRrsInWholeGroup)","type" : "GAP_Attribute","filters" : ["Tester(AugmentedCosetTableRrsInWholeGroup)"]},{"name" : "Tester(AugmentedCosetTableNormalClosureInWholeGroup)","type" : "GAP_Attribute","filters" : ["Tester(AugmentedCosetTableNormalClosureInWholeGroup)"]},{"name" : "IsPresentation","type" : "GAP_Category","implied" : ["IsCopyable","IsPresentation"]},{"name" : "Tester(PrimaryGeneratorWords)","type" : "GAP_Attribute","filters" : ["Tester(PrimaryGeneratorWords)"]},{"name" : "Tester(TietzeOrigin)","type" : "GAP_Attribute","filters" : ["Tester(TietzeOrigin)"]},{"name" : "Tester(TzOptions)","type" : "GAP_Attribute","filters" : ["Tester(TzOptions)"]},{"name" : "Extrarankfilter","type" : "GAP_Filter","implied" : ["Extrarankfilter"]},{"name" : "IsFromFpGroupGeneralMapping","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","Extrarankfilter","IsFromFpGroupGeneralMapping"]},{"name" : "IsFromFpGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsFromFpGroupGeneralMapping","IsFromFpGroupGeneralMappingByImages"]},{"name" : "IsFromFpGroupStdGensGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsFromFpGroupGeneralMapping","IsFromFpGroupGeneralMappingByImages","IsFromFpGroupStdGensGeneralMappingByImages"]},{"name" : "IsToFpGroupGeneralMappingByImages","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsToFpGroupGeneralMappingByImages"]},{"name" : "IsWordDecompHomomorphism","type" : "GAP_Property","filters" : ["IsWordDecompHomomorphism","Tester(IsWordDecompHomomorphism)"]},{"name" : "Tester(IsWordDecompHomomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsWordDecompHomomorphism)"]},{"name" : "Tester(CosetTableFpHom)","type" : "GAP_Attribute","filters" : ["Tester(CosetTableFpHom)"]},{"name" : "Tester(IsomorphismSimplifiedFpGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismSimplifiedFpGroup)"]},{"name" : "Tester(EpimorphismFromFreeGroup)","type" : "GAP_Attribute","filters" : ["Tester(EpimorphismFromFreeGroup)"]},{"name" : "IsCanonicalBasisIntegersRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisIntegersRep"]},{"name" : "Tester(NiceMonomorphism)","type" : "GAP_Attribute","filters" : ["Tester(NiceMonomorphism)"]},{"name" : "IsNiceMonomorphism","type" : "GAP_Filter","implied" : ["IsNiceMonomorphism"]},{"name" : "IsCanonicalNiceMonomorphism","type" : "GAP_Property","filters" : ["IsCanonicalNiceMonomorphism","Tester(IsCanonicalNiceMonomorphism)"]},{"name" : "Tester(IsCanonicalNiceMonomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCanonicalNiceMonomorphism)"]},{"name" : "Tester(CanonicalNiceMonomorphism)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalNiceMonomorphism)"]},{"name" : "Tester(NiceObject)","type" : "GAP_Attribute","filters" : ["Tester(NiceObject)"]},{"name" : "IsHandledByNiceMonomorphism","type" : "GAP_Property","filters" : ["CanEasilyTestMembership","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]},{"name" : "Tester(IsHandledByNiceMonomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsHandledByNiceMonomorphism)"]},{"name" : "Tester(SeedFaithfulAction)","type" : "GAP_Attribute","filters" : ["Tester(SeedFaithfulAction)"]},{"name" : "Tester(AutomorphismGroup)","type" : "GAP_Attribute","filters" : ["Tester(AutomorphismGroup)"]},{"name" : "IsGroupOfAutomorphisms","type" : "GAP_Property","filters" : ["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"]},{"name" : "Tester(IsGroupOfAutomorphisms)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupOfAutomorphisms)"]},{"name" : "IsGroupOfAutomorphismsFiniteGroup","type" : "GAP_Property","filters" : ["IsFinite","Tester(IsFinite)","CanEasilyTestMembership","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)","IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)","IsGroupOfAutomorphismsFiniteGroup","Tester(IsGroupOfAutomorphismsFiniteGroup)"]},{"name" : "Tester(IsGroupOfAutomorphismsFiniteGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupOfAutomorphismsFiniteGroup)"]},{"name" : "Tester(AutomorphismDomain)","type" : "GAP_Attribute","filters" : ["Tester(AutomorphismDomain)"]},{"name" : "IsAutomorphismGroup","type" : "GAP_Property","filters" : ["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)","IsAutomorphismGroup","Tester(IsAutomorphismGroup)"]},{"name" : "Tester(IsAutomorphismGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAutomorphismGroup)"]},{"name" : "Tester(InnerAutomorphismsAutomorphismGroup)","type" : "GAP_Attribute","filters" : ["Tester(InnerAutomorphismsAutomorphismGroup)"]},{"name" : "Tester(DefaultFieldOfMatrixGroup)","type" : "GAP_Attribute","filters" : ["Tester(DefaultFieldOfMatrixGroup)"]},{"name" : "Tester(DimensionOfMatrixGroup)","type" : "GAP_Attribute","filters" : ["Tester(DimensionOfMatrixGroup)"]},{"name" : "Tester(FieldOfMatrixGroup)","type" : "GAP_Attribute","filters" : ["Tester(FieldOfMatrixGroup)"]},{"name" : "Tester(TransposedMatrixGroup)","type" : "GAP_Attribute","filters" : ["Tester(TransposedMatrixGroup)"]},{"name" : "IsGeneralLinearGroup","type" : "GAP_Property","filters" : ["IsGeneralLinearGroup","Tester(IsGeneralLinearGroup)"]},{"name" : "Tester(IsGeneralLinearGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGeneralLinearGroup)"]},{"name" : "IsNaturalGL","type" : "GAP_Property","filters" : ["IsGeneralLinearGroup","Tester(IsGeneralLinearGroup)","IsNaturalGL","Tester(IsNaturalGL)"]},{"name" : "Tester(IsNaturalGL)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNaturalGL)"]},{"name" : "IsSpecialLinearGroup","type" : "GAP_Property","filters" : ["IsSpecialLinearGroup","Tester(IsSpecialLinearGroup)"]},{"name" : "Tester(IsSpecialLinearGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSpecialLinearGroup)"]},{"name" : "IsNaturalSL","type" : "GAP_Property","filters" : ["IsSpecialLinearGroup","Tester(IsSpecialLinearGroup)","IsNaturalSL","Tester(IsNaturalSL)","IsSubgroupSL","Tester(IsSubgroupSL)"]},{"name" : "Tester(IsNaturalSL)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNaturalSL)"]},{"name" : "IsSubgroupSL","type" : "GAP_Property","filters" : ["IsSubgroupSL","Tester(IsSubgroupSL)"]},{"name" : "Tester(IsSubgroupSL)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSubgroupSL)"]},{"name" : "Tester(InvariantBilinearForm)","type" : "GAP_Attribute","filters" : ["Tester(InvariantBilinearForm)"]},{"name" : "IsFullSubgroupGLorSLRespectingBilinearForm","type" : "GAP_Property","filters" : ["IsFullSubgroupGLorSLRespectingBilinearForm","Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"]},{"name" : "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"]},{"name" : "Tester(InvariantSesquilinearForm)","type" : "GAP_Attribute","filters" : ["Tester(InvariantSesquilinearForm)"]},{"name" : "IsFullSubgroupGLorSLRespectingSesquilinearForm","type" : "GAP_Property","filters" : ["IsFullSubgroupGLorSLRespectingSesquilinearForm","Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]},{"name" : "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]},{"name" : "Tester(InvariantQuadraticForm)","type" : "GAP_Attribute","filters" : ["Tester(InvariantQuadraticForm)"]},{"name" : "IsFullSubgroupGLorSLRespectingQuadraticForm","type" : "GAP_Property","filters" : ["IsFullSubgroupGLorSLRespectingQuadraticForm","Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"]},{"name" : "Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"]},{"name" : "CanComputeFittingFree","type" : "GAP_Filter","implied" : ["IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsFiniteOrderElement)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsCompletelySimpleSemigroup","Tester(IsCompletelySimpleSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)","CanComputeFittingFree","IsNilpotentByFinite","Tester(IsNilpotentByFinite)"]},{"name" : "Tester(FittingFreeLiftSetup)","type" : "GAP_Attribute","filters" : ["Tester(FittingFreeLiftSetup)"]},{"name" : "Tester(RecogDecompinfoHomomorphism)","type" : "GAP_Attribute","filters" : ["Tester(RecogDecompinfoHomomorphism)"]},{"name" : "Tester(DirectFactorsFittingFreeSocle)","type" : "GAP_Attribute","filters" : ["Tester(DirectFactorsFittingFreeSocle)"]},{"name" : "Tester(ChiefSeriesTF)","type" : "GAP_Attribute","filters" : ["Tester(ChiefSeriesTF)"]},{"name" : "IsRationalMatrixGroup","type" : "GAP_Property","filters" : ["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)"]},{"name" : "Tester(IsRationalMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRationalMatrixGroup)"]},{"name" : "IsIntegerMatrixGroup","type" : "GAP_Property","filters" : ["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)","IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"]},{"name" : "Tester(IsIntegerMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIntegerMatrixGroup)"]},{"name" : "Tester(ZClassRepsQClass)","type" : "GAP_Attribute","filters" : ["Tester(ZClassRepsQClass)"]},{"name" : "Tester(NormalizerInGLnZ)","type" : "GAP_Attribute","filters" : ["Tester(NormalizerInGLnZ)"]},{"name" : "Tester(CentralizerInGLnZ)","type" : "GAP_Attribute","filters" : ["Tester(CentralizerInGLnZ)"]},{"name" : "IsBravaisGroup","type" : "GAP_Property","filters" : ["IsBravaisGroup","Tester(IsBravaisGroup)"]},{"name" : "Tester(IsBravaisGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBravaisGroup)"]},{"name" : "Tester(BravaisGroup)","type" : "GAP_Attribute","filters" : ["Tester(BravaisGroup)"]},{"name" : "Tester(BravaisSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(BravaisSubgroups)"]},{"name" : "Tester(BravaisSupergroups)","type" : "GAP_Attribute","filters" : ["Tester(BravaisSupergroups)"]},{"name" : "Tester(NormalizerInGLnZBravaisGroup)","type" : "GAP_Attribute","filters" : ["Tester(NormalizerInGLnZBravaisGroup)"]},{"name" : "Tester(InvariantLattice)","type" : "GAP_Attribute","filters" : ["Tester(InvariantLattice)"]},{"name" : "IsPerfectLibraryGroup","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsPerfectLibraryGroup"]},{"name" : "Tester(PerfectIdentification)","type" : "GAP_Attribute","filters" : ["Tester(PerfectIdentification)"]},{"name" : "Tester(DataAboutSimpleGroup)","type" : "GAP_Attribute","filters" : ["Tester(DataAboutSimpleGroup)"]},{"name" : "IsImfMatrixGroup","type" : "GAP_Filter","implied" : ["IsImfMatrixGroup"]},{"name" : "Tester(ImfRecord)","type" : "GAP_Attribute","filters" : ["Tester(ImfRecord)"]},{"name" : "IsOrdering","type" : "GAP_Category","implied" : ["IsOrdering"]},{"name" : "Tester(OrderingsFamily)","type" : "GAP_Attribute","filters" : ["Tester(OrderingsFamily)"]},{"name" : "IsWellFoundedOrdering","type" : "GAP_Property","filters" : ["IsWellFoundedOrdering","Tester(IsWellFoundedOrdering)"]},{"name" : "Tester(IsWellFoundedOrdering)","type" : "GAP_TrueProperty","implied" : ["Tester(IsWellFoundedOrdering)"]},{"name" : "IsTotalOrdering","type" : "GAP_Property","filters" : ["IsTotalOrdering","Tester(IsTotalOrdering)"]},{"name" : "Tester(IsTotalOrdering)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTotalOrdering)"]},{"name" : "Tester(FamilyForOrdering)","type" : "GAP_Attribute","filters" : ["Tester(FamilyForOrdering)"]},{"name" : "Tester(LessThanFunction)","type" : "GAP_Attribute","filters" : ["Tester(LessThanFunction)"]},{"name" : "Tester(LessThanOrEqualFunction)","type" : "GAP_Attribute","filters" : ["Tester(LessThanOrEqualFunction)"]},{"name" : "IsOrderingOnFamilyOfAssocWords","type" : "GAP_Property","filters" : ["IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]},{"name" : "Tester(IsOrderingOnFamilyOfAssocWords)","type" : "GAP_TrueProperty","implied" : ["Tester(IsOrderingOnFamilyOfAssocWords)"]},{"name" : "Tester(LetterRepWordsLessFunc)","type" : "GAP_Attribute","filters" : ["Tester(LetterRepWordsLessFunc)"]},{"name" : "IsTranslationInvariantOrdering","type" : "GAP_Property","filters" : ["IsTranslationInvariantOrdering","Tester(IsTranslationInvariantOrdering)"]},{"name" : "Tester(IsTranslationInvariantOrdering)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTranslationInvariantOrdering)"]},{"name" : "Tester(OrderingOnGenerators)","type" : "GAP_Attribute","filters" : ["Tester(OrderingOnGenerators)"]},{"name" : "IsShortLexOrdering","type" : "GAP_Property","filters" : ["IsShortLexOrdering","Tester(IsShortLexOrdering)"]},{"name" : "Tester(IsShortLexOrdering)","type" : "GAP_TrueProperty","implied" : ["Tester(IsShortLexOrdering)"]},{"name" : "Tester(WeightOfGenerators)","type" : "GAP_Attribute","filters" : ["Tester(WeightOfGenerators)"]},{"name" : "IsWeightLexOrdering","type" : "GAP_Property","filters" : ["IsWeightLexOrdering","Tester(IsWeightLexOrdering)"]},{"name" : "Tester(IsWeightLexOrdering)","type" : "GAP_TrueProperty","implied" : ["Tester(IsWeightLexOrdering)"]},{"name" : "IsBasicWreathProductOrdering","type" : "GAP_Property","filters" : ["IsBasicWreathProductOrdering","Tester(IsBasicWreathProductOrdering)"]},{"name" : "Tester(IsBasicWreathProductOrdering)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBasicWreathProductOrdering)"]},{"name" : "IsWreathProductOrdering","type" : "GAP_Property","filters" : ["IsWreathProductOrdering","Tester(IsWreathProductOrdering)"]},{"name" : "Tester(IsWreathProductOrdering)","type" : "GAP_TrueProperty","implied" : ["Tester(IsWreathProductOrdering)"]},{"name" : "Tester(LevelsOfGenerators)","type" : "GAP_Attribute","filters" : ["Tester(LevelsOfGenerators)"]},{"name" : "Tester(LargestImageOfMovedPoint)","type" : "GAP_Attribute","filters" : ["Tester(LargestImageOfMovedPoint)"]},{"name" : "Tester(SmallestImageOfMovedPoint)","type" : "GAP_Attribute","filters" : ["Tester(SmallestImageOfMovedPoint)"]},{"name" : "Tester(RankOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(RankOfTransformation)"]},{"name" : "Tester(AsPermutation)","type" : "GAP_Attribute","filters" : ["Tester(AsPermutation)"]},{"name" : "Tester(AsTransformation)","type" : "GAP_Attribute","filters" : ["Tester(AsTransformation)"]},{"name" : "Tester(PermutationOfImage)","type" : "GAP_Attribute","filters" : ["Tester(PermutationOfImage)"]},{"name" : "Tester(DegreeOfTransformationCollection)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOfTransformationCollection)"]},{"name" : "Tester(FlatKernelOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(FlatKernelOfTransformation)"]},{"name" : "Tester(ImageSetOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(ImageSetOfTransformation)"]},{"name" : "Tester(IndexPeriodOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(IndexPeriodOfTransformation)"]},{"name" : "Tester(KernelOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(KernelOfTransformation)"]},{"name" : "Tester(SmallestIdempotentPower)","type" : "GAP_Attribute","filters" : ["Tester(SmallestIdempotentPower)"]},{"name" : "Tester(ComponentRepsOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(ComponentRepsOfTransformation)"]},{"name" : "Tester(NrComponentsOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(NrComponentsOfTransformation)"]},{"name" : "Tester(ComponentsOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(ComponentsOfTransformation)"]},{"name" : "Tester(CyclesOfTransformation)","type" : "GAP_Attribute","filters" : ["Tester(CyclesOfTransformation)"]},{"name" : "Tester(LeftOne)","type" : "GAP_Attribute","filters" : ["Tester(LeftOne)"]},{"name" : "Tester(RightOne)","type" : "GAP_Attribute","filters" : ["Tester(RightOne)"]},{"name" : "Tester(DomainOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(DomainOfPartialPerm)"]},{"name" : "Tester(ImageListOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(ImageListOfPartialPerm)"]},{"name" : "Tester(ImageSetOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(ImageSetOfPartialPerm)"]},{"name" : "Tester(IndexPeriodOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(IndexPeriodOfPartialPerm)"]},{"name" : "Tester(ComponentRepsOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(ComponentRepsOfPartialPerm)"]},{"name" : "Tester(NrComponentsOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(NrComponentsOfPartialPerm)"]},{"name" : "Tester(ComponentsOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(ComponentsOfPartialPerm)"]},{"name" : "Tester(FixedPointsOfPartialPerm)","type" : "GAP_Attribute","filters" : ["Tester(FixedPointsOfPartialPerm)"]},{"name" : "Tester(NrFixedPoints)","type" : "GAP_Attribute","filters" : ["Tester(NrFixedPoints)"]},{"name" : "Tester(DegreeOfPartialPermCollection)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOfPartialPermCollection)"]},{"name" : "Tester(CodegreeOfPartialPermCollection)","type" : "GAP_Attribute","filters" : ["Tester(CodegreeOfPartialPermCollection)"]},{"name" : "Tester(RankOfPartialPermCollection)","type" : "GAP_Attribute","filters" : ["Tester(RankOfPartialPermCollection)"]},{"name" : "Tester(DomainOfPartialPermCollection)","type" : "GAP_Attribute","filters" : ["Tester(DomainOfPartialPermCollection)"]},{"name" : "Tester(ImageOfPartialPermCollection)","type" : "GAP_Attribute","filters" : ["Tester(ImageOfPartialPermCollection)"]},{"name" : "Tester(TransformationRepresentation)","type" : "GAP_Attribute","filters" : ["Tester(TransformationRepresentation)"]},{"name" : "IsElementOfFpSemigroup","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsElementOfFpSemigroup"]},{"name" : "CategoryCollections(IsElementOfFpSemigroup)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsElementOfFpSemigroup)"]},{"name" : "CategoryFamily(IsElementOfFpSemigroup)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsElementOfFpSemigroup)"]},{"name" : "Tester(FreeGeneratorsOfFpSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(FreeGeneratorsOfFpSemigroup)"]},{"name" : "Tester(FreeSemigroupOfFpSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(FreeSemigroupOfFpSemigroup)"]},{"name" : "Tester(RelationsOfFpSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(RelationsOfFpSemigroup)"]},{"name" : "Tester(IsomorphismFpSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismFpSemigroup)"]},{"name" : "IsElementOfFpMonoid","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsAssociativeElement","IsElementOfFpMonoid"]},{"name" : "CategoryCollections(IsElementOfFpMonoid)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsElementOfFpMonoid)"]},{"name" : "CategoryFamily(IsElementOfFpMonoid)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsElementOfFpMonoid)"]},{"name" : "Tester(FreeGeneratorsOfFpMonoid)","type" : "GAP_Attribute","filters" : ["Tester(FreeGeneratorsOfFpMonoid)"]},{"name" : "Tester(FreeMonoidOfFpMonoid)","type" : "GAP_Attribute","filters" : ["Tester(FreeMonoidOfFpMonoid)"]},{"name" : "Tester(RelationsOfFpMonoid)","type" : "GAP_Attribute","filters" : ["Tester(RelationsOfFpMonoid)"]},{"name" : "Tester(IsomorphismFpMonoid)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismFpMonoid)"]},{"name" : "Tester(ReducedConfluentRewritingSystem)","type" : "GAP_Attribute","filters" : ["Tester(ReducedConfluentRewritingSystem)"]},{"name" : "Tester(FreeMonoidOfRewritingSystem)","type" : "GAP_Attribute","filters" : ["Tester(FreeMonoidOfRewritingSystem)"]},{"name" : "Tester(FamilyForRewritingSystem)","type" : "GAP_Attribute","filters" : ["Tester(FamilyForRewritingSystem)"]},{"name" : "Tester(FreeSemigroupOfRewritingSystem)","type" : "GAP_Attribute","filters" : ["Tester(FreeSemigroupOfRewritingSystem)"]},{"name" : "IsKnuthBendixRewritingSystem","type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsKnuthBendixRewritingSystem"]},{"name" : "Tester(TzRules)","type" : "GAP_Attribute","filters" : ["Tester(TzRules)"]},{"name" : "Tester(CosetTableOfFpSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(CosetTableOfFpSemigroup)"]},{"name" : "IsMonoidByAdjoiningIdentityElt","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsAssociativeElement","IsMonoidByAdjoiningIdentityElt"]},{"name" : "IsMonoidByAdjoiningIdentity","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsMonoidByAdjoiningIdentity"]},{"name" : "Tester(AdjoinedIdentityFamily)","type" : "GAP_Attribute","filters" : ["Tester(AdjoinedIdentityFamily)"]},{"name" : "Tester(UnderlyingSemigroupFamily)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingSemigroupFamily)"]},{"name" : "Tester(AdjoinedIdentityDefaultType)","type" : "GAP_Attribute","filters" : ["Tester(AdjoinedIdentityDefaultType)"]},{"name" : "IsMonoidByAdjoiningIdentityEltRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsMonoidByAdjoiningIdentityEltRep"]},{"name" : "Tester(MonoidByAdjoiningIdentity)","type" : "GAP_Attribute","filters" : ["Tester(MonoidByAdjoiningIdentity)"]},{"name" : "Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)"]},{"name" : "Tester(MonoidByAdjoiningIdentityElt)","type" : "GAP_Attribute","filters" : ["Tester(MonoidByAdjoiningIdentityElt)"]},{"name" : "Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)"]},{"name" : "IsGreensRelation","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation"]},{"name" : "IsGreensRRelation","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensRRelation"]},{"name" : "IsGreensLRelation","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensLRelation"]},{"name" : "IsGreensJRelation","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensJRelation"]},{"name" : "IsGreensHRelation","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensHRelation"]},{"name" : "IsGreensDRelation","type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensDRelation"]},{"name" : "IsFiniteSemigroupGreensRelation","type" : "GAP_Property","filters" : ["IsFiniteSemigroupGreensRelation","Tester(IsFiniteSemigroupGreensRelation)"]},{"name" : "Tester(IsFiniteSemigroupGreensRelation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFiniteSemigroupGreensRelation)"]},{"name" : "Tester(GreensRRelation)","type" : "GAP_Attribute","filters" : ["Tester(GreensRRelation)"]},{"name" : "Tester(GreensLRelation)","type" : "GAP_Attribute","filters" : ["Tester(GreensLRelation)"]},{"name" : "Tester(GreensJRelation)","type" : "GAP_Attribute","filters" : ["Tester(GreensJRelation)"]},{"name" : "Tester(GreensDRelation)","type" : "GAP_Attribute","filters" : ["Tester(GreensDRelation)"]},{"name" : "Tester(GreensHRelation)","type" : "GAP_Attribute","filters" : ["Tester(GreensHRelation)"]},{"name" : "Tester(AssociatedConcreteSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(AssociatedConcreteSemigroup)"]},{"name" : "Tester(AssociatedFpSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(AssociatedFpSemigroup)"]},{"name" : "IsGreensClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass"]},{"name" : "IsGreensRClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensRClass"]},{"name" : "IsGreensLClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensLClass"]},{"name" : "IsGreensJClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensJClass"]},{"name" : "IsGreensHClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensHClass"]},{"name" : "IsGreensDClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensDClass"]},{"name" : "Tester(GreensRClasses)","type" : "GAP_Attribute","filters" : ["Tester(GreensRClasses)"]},{"name" : "Tester(GreensLClasses)","type" : "GAP_Attribute","filters" : ["Tester(GreensLClasses)"]},{"name" : "Tester(GreensJClasses)","type" : "GAP_Attribute","filters" : ["Tester(GreensJClasses)"]},{"name" : "Tester(GreensDClasses)","type" : "GAP_Attribute","filters" : ["Tester(GreensDClasses)"]},{"name" : "Tester(GreensHClasses)","type" : "GAP_Attribute","filters" : ["Tester(GreensHClasses)"]},{"name" : "Tester(RClassOfHClass)","type" : "GAP_Attribute","filters" : ["Tester(RClassOfHClass)"]},{"name" : "Tester(LClassOfHClass)","type" : "GAP_Attribute","filters" : ["Tester(LClassOfHClass)"]},{"name" : "Tester(DClassOfHClass)","type" : "GAP_Attribute","filters" : ["Tester(DClassOfHClass)"]},{"name" : "Tester(DClassOfLClass)","type" : "GAP_Attribute","filters" : ["Tester(DClassOfLClass)"]},{"name" : "Tester(DClassOfRClass)","type" : "GAP_Attribute","filters" : ["Tester(DClassOfRClass)"]},{"name" : "Tester(GroupHClassOfGreensDClass)","type" : "GAP_Attribute","filters" : ["Tester(GroupHClassOfGreensDClass)"]},{"name" : "IsRegularDClass","type" : "GAP_Property","filters" : ["IsRegularDClass","Tester(IsRegularDClass)"]},{"name" : "Tester(IsRegularDClass)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRegularDClass)"]},{"name" : "IsGroupHClass","type" : "GAP_Property","filters" : ["IsGroupHClass","Tester(IsGroupHClass)"]},{"name" : "Tester(IsGroupHClass)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupHClass)"]},{"name" : "Tester(EggBoxOfDClass)","type" : "GAP_Attribute","filters" : ["Tester(EggBoxOfDClass)"]},{"name" : "Tester(InternalRepGreensRelation)","type" : "GAP_Attribute","filters" : ["Tester(InternalRepGreensRelation)"]},{"name" : "Tester(CanonicalGreensClass)","type" : "GAP_Attribute","filters" : ["Tester(CanonicalGreensClass)"]},{"name" : "IsSemigroupGeneralMappingRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupGeneralMappingRep"]},{"name" : "IsSemigroupHomomorphismByImagesRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsSemigroupHomomorphismByImagesRep"]},{"name" : "IsFpSemigpReducedElt","type" : "GAP_Property","filters" : ["IsFpSemigpReducedElt","Tester(IsFpSemigpReducedElt)"]},{"name" : "Tester(IsFpSemigpReducedElt)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFpSemigpReducedElt)"]},{"name" : "IsFpMonoidReducedElt","type" : "GAP_Property","filters" : ["IsFpMonoidReducedElt","Tester(IsFpMonoidReducedElt)"]},{"name" : "Tester(IsFpMonoidReducedElt)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFpMonoidReducedElt)"]},{"name" : "IsFullTransformationSemigroup","type" : "GAP_Property","filters" : ["IsFullTransformationSemigroup","Tester(IsFullTransformationSemigroup)"]},{"name" : "Tester(IsFullTransformationSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFullTransformationSemigroup)"]},{"name" : "Tester(DegreeOfTransformationSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOfTransformationSemigroup)"]},{"name" : "Tester(IsomorphismTransformationSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismTransformationSemigroup)"]},{"name" : "Tester(IsomorphismTransformationMonoid)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismTransformationMonoid)"]},{"name" : "Tester(AntiIsomorphismTransformationSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(AntiIsomorphismTransformationSemigroup)"]},{"name" : "IsReesMatrixSemigroupElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsReesMatrixSemigroupElement"]},{"name" : "IsReesZeroMatrixSemigroupElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsReesZeroMatrixSemigroupElement"]},{"name" : "CategoryCollections(IsReesMatrixSemigroupElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsReesMatrixSemigroupElement)"]},{"name" : "CategoryCollections(IsReesZeroMatrixSemigroupElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]},{"name" : "IsReesMatrixSemigroup","type" : "GAP_Property","filters" : ["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]},{"name" : "Tester(IsReesMatrixSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsReesMatrixSemigroup)"]},{"name" : "IsReesZeroMatrixSemigroup","type" : "GAP_Property","filters" : ["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]},{"name" : "Tester(IsReesZeroMatrixSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsReesZeroMatrixSemigroup)"]},{"name" : "Tester(Matrix)","type" : "GAP_Attribute","filters" : ["Tester(Matrix)"]},{"name" : "Tester(Rows)","type" : "GAP_Attribute","filters" : ["Tester(Rows)"]},{"name" : "Tester(Columns)","type" : "GAP_Attribute","filters" : ["Tester(Columns)"]},{"name" : "Tester(UnderlyingSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingSemigroup)"]},{"name" : "Tester(AssociatedReesMatrixSemigroupOfDClass)","type" : "GAP_Attribute","filters" : ["Tester(AssociatedReesMatrixSemigroupOfDClass)"]},{"name" : "Tester(IsomorphismReesMatrixSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismReesMatrixSemigroup)"]},{"name" : "Tester(IsomorphismReesZeroMatrixSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismReesZeroMatrixSemigroup)"]},{"name" : "Tester(ReesMatrixSemigroupOfFamily)","type" : "GAP_Attribute","filters" : ["Tester(ReesMatrixSemigroupOfFamily)"]},{"name" : "Tester(TypeReesMatrixSemigroupElements)","type" : "GAP_Attribute","filters" : ["Tester(TypeReesMatrixSemigroupElements)"]},{"name" : "IsQuotientSemigroup","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsAssociative","Tester(IsAssociative)","IsQuotientSemigroup"]},{"name" : "Tester(QuotientSemigroupPreimage)","type" : "GAP_Attribute","filters" : ["Tester(QuotientSemigroupPreimage)"]},{"name" : "Tester(QuotientSemigroupCongruence)","type" : "GAP_Attribute","filters" : ["Tester(QuotientSemigroupCongruence)"]},{"name" : "Tester(QuotientSemigroupHomomorphism)","type" : "GAP_Attribute","filters" : ["Tester(QuotientSemigroupHomomorphism)"]},{"name" : "Tester(DegreeOfPartialPermSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOfPartialPermSemigroup)"]},{"name" : "Tester(CodegreeOfPartialPermSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(CodegreeOfPartialPermSemigroup)"]},{"name" : "Tester(RankOfPartialPermSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(RankOfPartialPermSemigroup)"]},{"name" : "IsSymmetricInverseSemigroup","type" : "GAP_Property","filters" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSymmetricInverseSemigroup","Tester(IsSymmetricInverseSemigroup)"]},{"name" : "Tester(IsSymmetricInverseSemigroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSymmetricInverseSemigroup)"]},{"name" : "Tester(IsomorphismPartialPermSemigroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismPartialPermSemigroup)"]},{"name" : "Tester(IsomorphismPartialPermMonoid)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismPartialPermMonoid)"]},{"name" : "IsNearlyCharacterTable","type" : "GAP_Category","implied" : ["IsNearlyCharacterTable"]},{"name" : "IsCharacterTable","type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable"]},{"name" : "IsOrdinaryTable","type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable","IsOrdinaryTable"]},{"name" : "IsBrauerTable","type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable","IsBrauerTable"]},{"name" : "IsCharacterTableInProgress","type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTableInProgress"]},{"name" : "Tester(UnderlyingGroup)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingGroup)"]},{"name" : "Tester(IdentificationOfConjugacyClasses)","type" : "GAP_Attribute","filters" : ["Tester(IdentificationOfConjugacyClasses)"]},{"name" : "Tester(CharacterDegrees)","type" : "GAP_Attribute","filters" : ["Tester(CharacterDegrees)"]},{"name" : "Tester(Irr)","type" : "GAP_Attribute","filters" : ["Tester(Irr)"]},{"name" : "Tester(LinearCharacters)","type" : "GAP_Attribute","filters" : ["Tester(LinearCharacters)"]},{"name" : "Tester(IBr)","type" : "GAP_Attribute","filters" : ["Tester(IBr)"]},{"name" : "Tester(OrdinaryCharacterTable)","type" : "GAP_Attribute","filters" : ["Tester(OrdinaryCharacterTable)"]},{"name" : "IsAlmostSimpleCharacterTable","type" : "GAP_Property","filters" : ["IsAlmostSimpleCharacterTable","Tester(IsAlmostSimpleCharacterTable)"]},{"name" : "Tester(IsAlmostSimpleCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAlmostSimpleCharacterTable)"]},{"name" : "IsMonomialCharacterTable","type" : "GAP_Property","filters" : ["IsMonomialCharacterTable","Tester(IsMonomialCharacterTable)"]},{"name" : "Tester(IsMonomialCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMonomialCharacterTable)"]},{"name" : "IsNilpotentCharacterTable","type" : "GAP_Property","filters" : ["IsNilpotentCharacterTable","Tester(IsNilpotentCharacterTable)"]},{"name" : "Tester(IsNilpotentCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNilpotentCharacterTable)"]},{"name" : "IsPerfectCharacterTable","type" : "GAP_Property","filters" : ["IsPerfectCharacterTable","Tester(IsPerfectCharacterTable)"]},{"name" : "Tester(IsPerfectCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPerfectCharacterTable)"]},{"name" : "IsSimpleCharacterTable","type" : "GAP_Property","filters" : ["IsSimpleCharacterTable","Tester(IsSimpleCharacterTable)"]},{"name" : "Tester(IsSimpleCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSimpleCharacterTable)"]},{"name" : "IsSolvableCharacterTable","type" : "GAP_Property","filters" : ["IsSolvableCharacterTable","Tester(IsSolvableCharacterTable)"]},{"name" : "Tester(IsSolvableCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSolvableCharacterTable)"]},{"name" : "IsSporadicSimpleCharacterTable","type" : "GAP_Property","filters" : ["IsSporadicSimpleCharacterTable","Tester(IsSporadicSimpleCharacterTable)"]},{"name" : "Tester(IsSporadicSimpleCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSporadicSimpleCharacterTable)"]},{"name" : "IsSupersolvableCharacterTable","type" : "GAP_Property","filters" : ["IsSupersolvableCharacterTable","Tester(IsSupersolvableCharacterTable)"]},{"name" : "Tester(IsSupersolvableCharacterTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSupersolvableCharacterTable)"]},{"name" : "Tester(OrdersClassRepresentatives)","type" : "GAP_Attribute","filters" : ["Tester(OrdersClassRepresentatives)"]},{"name" : "Tester(SizesCentralizers)","type" : "GAP_Attribute","filters" : ["Tester(SizesCentralizers)"]},{"name" : "Tester(SizesConjugacyClasses)","type" : "GAP_Attribute","filters" : ["Tester(SizesConjugacyClasses)"]},{"name" : "Tester(AutomorphismsOfTable)","type" : "GAP_Attribute","filters" : ["Tester(AutomorphismsOfTable)"]},{"name" : "Tester(UnderlyingCharacteristic)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingCharacteristic)"]},{"name" : "Tester(ClassNames)","type" : "GAP_Attribute","filters" : ["Tester(ClassNames)"]},{"name" : "Tester(CharacterNames)","type" : "GAP_Attribute","filters" : ["Tester(CharacterNames)"]},{"name" : "Tester(ClassParameters)","type" : "GAP_Attribute","filters" : ["Tester(ClassParameters)"]},{"name" : "Tester(CharacterParameters)","type" : "GAP_Attribute","filters" : ["Tester(CharacterParameters)"]},{"name" : "Tester(Identifier)","type" : "GAP_Attribute","filters" : ["Tester(Identifier)"]},{"name" : "Tester(InverseClasses)","type" : "GAP_Attribute","filters" : ["Tester(InverseClasses)"]},{"name" : "Tester(RealClasses)","type" : "GAP_Attribute","filters" : ["Tester(RealClasses)"]},{"name" : "Tester(ClassRoots)","type" : "GAP_Attribute","filters" : ["Tester(ClassRoots)"]},{"name" : "Tester(ClassPositionsOfNormalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfNormalSubgroups)"]},{"name" : "Tester(ClassPositionsOfMaximalNormalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfMaximalNormalSubgroups)"]},{"name" : "Tester(ClassPositionsOfMinimalNormalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfMinimalNormalSubgroups)"]},{"name" : "Tester(ClassPositionsOfCentre)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfCentre)"]},{"name" : "Tester(ClassPositionsOfDirectProductDecompositions)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfDirectProductDecompositions)"]},{"name" : "Tester(ClassPositionsOfDerivedSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfDerivedSubgroup)"]},{"name" : "Tester(ClassPositionsOfElementaryAbelianSeries)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfElementaryAbelianSeries)"]},{"name" : "Tester(ClassPositionsOfFittingSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfFittingSubgroup)"]},{"name" : "Tester(ClassPositionsOfSolvableRadical)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfSolvableRadical)"]},{"name" : "Tester(ClassPositionsOfLowerCentralSeries)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfLowerCentralSeries)"]},{"name" : "Tester(ClassPositionsOfUpperCentralSeries)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfUpperCentralSeries)"]},{"name" : "Tester(ClassPositionsOfSolvableResiduum)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfSolvableResiduum)"]},{"name" : "Tester(ClassPositionsOfSupersolvableResiduum)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfSupersolvableResiduum)"]},{"name" : "Tester(ComputedPrimeBlockss)","type" : "GAP_Attribute","filters" : ["Tester(ComputedPrimeBlockss)"]},{"name" : "Tester(BlocksInfo)","type" : "GAP_Attribute","filters" : ["Tester(BlocksInfo)"]},{"name" : "Tester(DecompositionMatrix)","type" : "GAP_Attribute","filters" : ["Tester(DecompositionMatrix)"]},{"name" : "Tester(ComputedIsPSolvableCharacterTables)","type" : "GAP_Attribute","filters" : ["Tester(ComputedIsPSolvableCharacterTables)"]},{"name" : "Tester(ComputedIndicators)","type" : "GAP_Attribute","filters" : ["Tester(ComputedIndicators)"]},{"name" : "Tester(ComputedBrauerTables)","type" : "GAP_Attribute","filters" : ["Tester(ComputedBrauerTables)"]},{"name" : "Tester(DisplayOptions)","type" : "GAP_Attribute","filters" : ["Tester(DisplayOptions)"]},{"name" : "Tester(FactorsOfDirectProduct)","type" : "GAP_Attribute","filters" : ["Tester(FactorsOfDirectProduct)"]},{"name" : "Tester(CharacterTableIsoclinic)","type" : "GAP_Attribute","filters" : ["Tester(CharacterTableIsoclinic)"]},{"name" : "Tester(SourceOfIsoclinicTable)","type" : "GAP_Attribute","filters" : ["Tester(SourceOfIsoclinicTable)"]},{"name" : "Tester(ClassPermutation)","type" : "GAP_Attribute","filters" : ["Tester(ClassPermutation)"]},{"name" : "Tester(NormalSubgroupClassesInfo)","type" : "GAP_Attribute","filters" : ["Tester(NormalSubgroupClassesInfo)"]},{"name" : "IsLibraryCharacterTableRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLibraryCharacterTableRep"]},{"name" : "IsGenericCharacterTableRep","type" : "GAP_Representation","implied" : ["IsNearlyCharacterTable","IsGenericCharacterTableRep"]},{"name" : "IsClassFunction","type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsExtAElement","CategoryCollections(IsExtAElement)","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","IsMultiplicativeElement","CategoryCollections(IsMultiplicativeElement)","IsMultiplicativeElementWithOne","CategoryCollections(IsMultiplicativeElementWithOne)","IsMultiplicativeElementWithInverse","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedRowVector","IsAssociativeElement","IsCommutativeElement","IsClassFunction"]},{"name" : "Tester(UnderlyingCharacterTable)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingCharacterTable)"]},{"name" : "Tester(ValuesOfClassFunction)","type" : "GAP_Attribute","filters" : ["Tester(ValuesOfClassFunction)"]},{"name" : "Tester(GlobalPartitionOfClasses)","type" : "GAP_Attribute","filters" : ["Tester(GlobalPartitionOfClasses)"]},{"name" : "Tester(TrivialCharacter)","type" : "GAP_Attribute","filters" : ["Tester(TrivialCharacter)"]},{"name" : "Tester(NaturalCharacter)","type" : "GAP_Attribute","filters" : ["Tester(NaturalCharacter)"]},{"name" : "IsCharacter","type" : "GAP_Property","filters" : ["IsCharacter","Tester(IsCharacter)"]},{"name" : "Tester(IsCharacter)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCharacter)"]},{"name" : "IsVirtualCharacter","type" : "GAP_Property","filters" : ["IsVirtualCharacter","Tester(IsVirtualCharacter)"]},{"name" : "Tester(IsVirtualCharacter)","type" : "GAP_TrueProperty","implied" : ["Tester(IsVirtualCharacter)"]},{"name" : "IsIrreducibleCharacter","type" : "GAP_Property","filters" : ["IsIrreducibleCharacter","Tester(IsIrreducibleCharacter)"]},{"name" : "Tester(IsIrreducibleCharacter)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIrreducibleCharacter)"]},{"name" : "Tester(CentreOfCharacter)","type" : "GAP_Attribute","filters" : ["Tester(CentreOfCharacter)"]},{"name" : "Tester(ConstituentsOfCharacter)","type" : "GAP_Attribute","filters" : ["Tester(ConstituentsOfCharacter)"]},{"name" : "Tester(DegreeOfCharacter)","type" : "GAP_Attribute","filters" : ["Tester(DegreeOfCharacter)"]},{"name" : "Tester(KernelOfCharacter)","type" : "GAP_Attribute","filters" : ["Tester(KernelOfCharacter)"]},{"name" : "Tester(ClassPositionsOfKernel)","type" : "GAP_Attribute","filters" : ["Tester(ClassPositionsOfKernel)"]},{"name" : "Tester(CentralCharacter)","type" : "GAP_Attribute","filters" : ["Tester(CentralCharacter)"]},{"name" : "Tester(DeterminantOfCharacter)","type" : "GAP_Attribute","filters" : ["Tester(DeterminantOfCharacter)"]},{"name" : "Tester(BrauerCharacterValue)","type" : "GAP_Attribute","filters" : ["Tester(BrauerCharacterValue)"]},{"name" : "IsClassFunctionsSpace","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsClassFunctionsSpace"]},{"name" : "Tester(ComputedPowerMaps)","type" : "GAP_Attribute","filters" : ["Tester(ComputedPowerMaps)"]},{"name" : "Tester(FusionConjugacyClassesOp)","type" : "GAP_Attribute","filters" : ["Tester(FusionConjugacyClassesOp)"]},{"name" : "Tester(ComputedClassFusions)","type" : "GAP_Attribute","filters" : ["Tester(ComputedClassFusions)"]},{"name" : "Tester(NamesOfFusionSources)","type" : "GAP_Attribute","filters" : ["Tester(NamesOfFusionSources)"]},{"name" : "Tester(BaumClausenInfo)","type" : "GAP_Attribute","filters" : ["Tester(BaumClausenInfo)"]},{"name" : "Tester(IrreducibleRepresentations)","type" : "GAP_Attribute","filters" : ["Tester(IrreducibleRepresentations)"]},{"name" : "Tester(IrrBaumClausen)","type" : "GAP_Attribute","filters" : ["Tester(IrrBaumClausen)"]},{"name" : "Tester(IrrConlon)","type" : "GAP_Attribute","filters" : ["Tester(IrrConlon)"]},{"name" : "Tester(MolienSeriesInfo)","type" : "GAP_Attribute","filters" : ["Tester(MolienSeriesInfo)"]},{"name" : "Tester(Alpha)","type" : "GAP_Attribute","filters" : ["Tester(Alpha)"]},{"name" : "Tester(Delta)","type" : "GAP_Attribute","filters" : ["Tester(Delta)"]},{"name" : "IsBergerCondition","type" : "GAP_Property","filters" : ["IsBergerCondition","Tester(IsBergerCondition)"]},{"name" : "Tester(IsBergerCondition)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBergerCondition)"]},{"name" : "IsPrimitiveCharacter","type" : "GAP_Property","filters" : ["IsPrimitiveCharacter","Tester(IsPrimitiveCharacter)"]},{"name" : "Tester(IsPrimitiveCharacter)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPrimitiveCharacter)"]},{"name" : "Tester(TestQuasiPrimitive)","type" : "GAP_Attribute","filters" : ["Tester(TestQuasiPrimitive)"]},{"name" : "IsQuasiPrimitive","type" : "GAP_Property","filters" : ["IsQuasiPrimitive","Tester(IsQuasiPrimitive)"]},{"name" : "Tester(IsQuasiPrimitive)","type" : "GAP_TrueProperty","implied" : ["Tester(IsQuasiPrimitive)"]},{"name" : "IsInducedFromNormalSubgroup","type" : "GAP_Property","filters" : ["IsInducedFromNormalSubgroup","Tester(IsInducedFromNormalSubgroup)"]},{"name" : "Tester(IsInducedFromNormalSubgroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsInducedFromNormalSubgroup)"]},{"name" : "IsMonomialCharacter","type" : "GAP_Property","filters" : ["IsMonomialCharacter","Tester(IsMonomialCharacter)"]},{"name" : "Tester(IsMonomialCharacter)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMonomialCharacter)"]},{"name" : "IsMonomialNumber","type" : "GAP_Property","filters" : ["IsMonomialNumber","Tester(IsMonomialNumber)"]},{"name" : "Tester(IsMonomialNumber)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMonomialNumber)"]},{"name" : "Tester(TestMonomialQuick)","type" : "GAP_Attribute","filters" : ["Tester(TestMonomialQuick)"]},{"name" : "Tester(TestMonomial)","type" : "GAP_Attribute","filters" : ["Tester(TestMonomial)"]},{"name" : "Tester(TestSubnormallyMonomial)","type" : "GAP_Attribute","filters" : ["Tester(TestSubnormallyMonomial)"]},{"name" : "IsSubnormallyMonomial","type" : "GAP_Property","filters" : ["IsSubnormallyMonomial","Tester(IsSubnormallyMonomial)"]},{"name" : "Tester(IsSubnormallyMonomial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSubnormallyMonomial)"]},{"name" : "Tester(TestRelativelySM)","type" : "GAP_Attribute","filters" : ["Tester(TestRelativelySM)"]},{"name" : "IsRelativelySM","type" : "GAP_Property","filters" : ["IsRelativelySM","Tester(IsRelativelySM)"]},{"name" : "Tester(IsRelativelySM)","type" : "GAP_TrueProperty","implied" : ["Tester(IsRelativelySM)"]},{"name" : "IsMinimalNonmonomial","type" : "GAP_Property","filters" : ["IsMinimalNonmonomial","Tester(IsMinimalNonmonomial)"]},{"name" : "Tester(IsMinimalNonmonomial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMinimalNonmonomial)"]},{"name" : "Tester(DixonRecord)","type" : "GAP_Attribute","filters" : ["Tester(DixonRecord)"]},{"name" : "Tester(IrrDixonSchneider)","type" : "GAP_Attribute","filters" : ["Tester(IrrDixonSchneider)"]},{"name" : "Tester(TableOfMarks)","type" : "GAP_Attribute","filters" : ["Tester(TableOfMarks)"]},{"name" : "IsTableOfMarks","type" : "GAP_Category","implied" : ["IsTableOfMarks"]},{"name" : "Tester(PermutationTom)","type" : "GAP_Attribute","filters" : ["Tester(PermutationTom)"]},{"name" : "Tester(MarksTom)","type" : "GAP_Attribute","filters" : ["Tester(MarksTom)"]},{"name" : "Tester(SubsTom)","type" : "GAP_Attribute","filters" : ["Tester(SubsTom)"]},{"name" : "Tester(NrSubsTom)","type" : "GAP_Attribute","filters" : ["Tester(NrSubsTom)"]},{"name" : "Tester(OrdersTom)","type" : "GAP_Attribute","filters" : ["Tester(OrdersTom)"]},{"name" : "Tester(LengthsTom)","type" : "GAP_Attribute","filters" : ["Tester(LengthsTom)"]},{"name" : "Tester(ClassTypesTom)","type" : "GAP_Attribute","filters" : ["Tester(ClassTypesTom)"]},{"name" : "Tester(ClassNamesTom)","type" : "GAP_Attribute","filters" : ["Tester(ClassNamesTom)"]},{"name" : "Tester(FusionsTom)","type" : "GAP_Attribute","filters" : ["Tester(FusionsTom)"]},{"name" : "Tester(IdempotentsTom)","type" : "GAP_Attribute","filters" : ["Tester(IdempotentsTom)"]},{"name" : "Tester(IdempotentsTomInfo)","type" : "GAP_Attribute","filters" : ["Tester(IdempotentsTomInfo)"]},{"name" : "Tester(MatTom)","type" : "GAP_Attribute","filters" : ["Tester(MatTom)"]},{"name" : "Tester(MoebiusTom)","type" : "GAP_Attribute","filters" : ["Tester(MoebiusTom)"]},{"name" : "Tester(WeightsTom)","type" : "GAP_Attribute","filters" : ["Tester(WeightsTom)"]},{"name" : "IsAbelianTom","type" : "GAP_Property","filters" : ["IsAbelianTom","Tester(IsAbelianTom)"]},{"name" : "Tester(IsAbelianTom)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAbelianTom)"]},{"name" : "IsCyclicTom","type" : "GAP_Property","filters" : ["IsCyclicTom","Tester(IsCyclicTom)"]},{"name" : "Tester(IsCyclicTom)","type" : "GAP_TrueProperty","implied" : ["Tester(IsCyclicTom)"]},{"name" : "IsNilpotentTom","type" : "GAP_Property","filters" : ["IsNilpotentTom","Tester(IsNilpotentTom)"]},{"name" : "Tester(IsNilpotentTom)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNilpotentTom)"]},{"name" : "IsPerfectTom","type" : "GAP_Property","filters" : ["IsPerfectTom","Tester(IsPerfectTom)"]},{"name" : "Tester(IsPerfectTom)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPerfectTom)"]},{"name" : "IsSolvableTom","type" : "GAP_Property","filters" : ["IsSolvableTom","Tester(IsSolvableTom)"]},{"name" : "Tester(IsSolvableTom)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSolvableTom)"]},{"name" : "Tester(DerivedSubgroupsTomPossible)","type" : "GAP_Attribute","filters" : ["Tester(DerivedSubgroupsTomPossible)"]},{"name" : "Tester(DerivedSubgroupsTomUnique)","type" : "GAP_Attribute","filters" : ["Tester(DerivedSubgroupsTomUnique)"]},{"name" : "Tester(NormalizersTom)","type" : "GAP_Attribute","filters" : ["Tester(NormalizersTom)"]},{"name" : "Tester(CyclicExtensionsTom)","type" : "GAP_Attribute","filters" : ["Tester(CyclicExtensionsTom)"]},{"name" : "Tester(ComputedCyclicExtensionsTom)","type" : "GAP_Attribute","filters" : ["Tester(ComputedCyclicExtensionsTom)"]},{"name" : "Tester(MaximalSubgroupsTom)","type" : "GAP_Attribute","filters" : ["Tester(MaximalSubgroupsTom)"]},{"name" : "Tester(GeneratorsSubgroupsTom)","type" : "GAP_Attribute","filters" : ["Tester(GeneratorsSubgroupsTom)"]},{"name" : "Tester(StraightLineProgramsTom)","type" : "GAP_Attribute","filters" : ["Tester(StraightLineProgramsTom)"]},{"name" : "IsTableOfMarksWithGens","type" : "GAP_Filter","implied" : ["IsTableOfMarksWithGens"]},{"name" : "IsUnicodeString","type" : "GAP_Filter","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsString","IsListOrCollection","IsConstantTimeAccessList","IsUnicodeString"]},{"name" : "IsUnicodeCharacter","type" : "GAP_Filter","implied" : ["IsInt","IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsChar","IsCyclotomic","IsUnicodeCharacter"]},{"name" : "IsObjToBePrinted","type" : "GAP_Filter","implied" : ["IsObjToBePrinted"]},{"name" : "IsFile","type" : "GAP_Category","implied" : ["IsFile"]},{"name" : "Tester(ProcessID)","type" : "GAP_Attribute","filters" : ["Tester(ProcessID)"]},{"name" : "IO_Result","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IO_Result"]},{"name" : "IsRealRandomSource","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsRandomSource","IsRealRandomSource"]},{"name" : "IsBackgroundJob","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBackgroundJob"]},{"name" : "IsBackgroundJobByFork","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBackgroundJob","IsBackgroundJobByFork"]},{"name" : "IsWorkerFarm","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsWorkerFarm"]},{"name" : "IsWorkerFarmByFork","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsWorkerFarm","IsWorkerFarmByFork"]},{"name" : "IsIOHubCat","type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsIOHubCat"]},{"name" : "IsIOHub","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsIOHubCat","IsIOHub"]},{"name" : "IsEmptyRowVectorRep","type" : "GAP_Representation","implied" : ["IsList","IsPositionalObjectRep","IsListOrCollection","IsConstantTimeAccessList","IsEmptyRowVectorRep"]},{"name" : "IsNullMapMatrix","type" : "GAP_Representation","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","IsMultiplicativeElement","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVector","IsNullMapMatrix"]},{"name" : "IsBlockMatrixRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsBlockMatrixRep"]},{"name" : "IsDefaultGeneralMappingRep","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","Tester(Range)","Tester(Source)","IsDefaultGeneralMappingRep"]},{"name" : "IsMappingByFunctionRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsMappingByFunctionRep"]},{"name" : "IsMappingByFunctionWithInverseRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsMappingByFunctionRep","IsMappingByFunctionWithInverseRep"]},{"name" : "IsNonSPMappingByFunctionRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsMappingByFunctionRep","IsNonSPMappingByFunctionRep"]},{"name" : "IsNonSPMappingByFunctionWithInverseRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsMappingByFunctionRep","IsMappingByFunctionWithInverseRep","IsNonSPMappingByFunctionRep","IsNonSPMappingByFunctionWithInverseRep"]},{"name" : "IsSPMappingByFunctionRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsMappingByFunctionRep","IsSPMappingByFunctionRep"]},{"name" : "IsSPMappingByFunctionWithInverseRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsMappingByFunctionRep","IsMappingByFunctionWithInverseRep","IsSPMappingByFunctionRep","IsSPMappingByFunctionWithInverseRep"]},{"name" : "IsInverseGeneralMappingRep","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping","IsInverseGeneralMappingRep"]},{"name" : "IsBinaryRelationDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBinaryRelationDefaultRep"]},{"name" : "IsBinaryRelationOnPointsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBinaryRelationOnPointsRep"]},{"name" : "IsEquivalenceRelationDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEquivalenceRelationDefaultRep"]},{"name" : "IsEquivalenceClassDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEquivalenceClassDefaultRep"]},{"name" : "IsRightTransversalRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep"]},{"name" : "IsAdditiveCosetDefaultRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsAdditiveCosetDefaultRep"]},{"name" : "IsRelativeBasisDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsRelativeBasisDefaultRep"]},{"name" : "IsBasisWithReplacedLeftModuleRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBasisWithReplacedLeftModuleRep"]},{"name" : "IsMutableBasisByImmutableBasisRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisByImmutableBasisRep"]},{"name" : "IsMutableBasisViaNiceMutableBasisRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisViaNiceMutableBasisRep"]},{"name" : "IsSubspacesVectorSpaceDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsSubspacesVectorSpaceDefaultRep"]},{"name" : "IsSemiEchelonBasisOfGaussianRowSpaceRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsSemiEchelonBasisOfGaussianRowSpaceRep"]},{"name" : "IsSubspacesFullRowSpaceDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsSubspacesVectorSpaceDefaultRep","IsSubspacesFullRowSpaceDefaultRep"]},{"name" : "IsMutableBasisOfGaussianRowSpaceRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisOfGaussianRowSpaceRep"]},{"name" : "IsSemiEchelonBasisOfGaussianMatrixSpaceRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsSemiEchelonBasisOfGaussianMatrixSpaceRep"]},{"name" : "IsMutableBasisOfGaussianMatrixSpaceRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisOfGaussianMatrixSpaceRep"]},{"name" : "IsLinearGeneralMappingByImagesDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLinearGeneralMappingByImagesDefaultRep"]},{"name" : "IsLinearMappingByMatrixDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLinearMappingByMatrixDefaultRep"]},{"name" : "IsMagmaRingObjDefaultRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsMagmaRingObjDefaultRep"]},{"name" : "IsCanonicalBasisFreeMagmaRingRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFreeMagmaRingRep"]},{"name" : "IsEmbeddingRingMagmaRing","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","IsEmbeddingRingMagmaRing"]},{"name" : "IsEmbeddingMagmaMagmaRing","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","IsEmbeddingMagmaMagmaRing"]},{"name" : "IsAlgebraGeneralMappingByImagesDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsAlgebraGeneralMappingByImagesDefaultRep"]},{"name" : "IsPolynomialRingDefaultGeneratorMapping","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsAlgebraGeneralMappingByImagesDefaultRep","IsPolynomialRingDefaultGeneratorMapping"]},{"name" : "IsOperationAlgebraHomomorphismDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsOperationAlgebraHomomorphismDefaultRep"]},{"name" : "IsAlgebraHomomorphismFromFpRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsAlgebraHomomorphismFromFpRep"]},{"name" : "IsSpaceOfUEAElements","type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsSpaceOfUEAElements"]},{"name" : "IsDenseCoeffVectorRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsDenseCoeffVectorRep"]},{"name" : "IsLieEmbeddingRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLieEmbeddingRep"]},{"name" : "IsMutableBasisViaUnderlyingMutableBasisRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisViaUnderlyingMutableBasisRep"]},{"name" : "IsMonomialElementRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsMonomialElementRep"]},{"name" : "IsBasisOfMonomialSpaceRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsBasisOfMonomialSpaceRep"]},{"name" : "IsBasisOfSparseRowSpaceRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsBasisOfSparseRowSpaceRep"]},{"name" : "IsZeroCochainRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsPackedElementDefaultRep","IsZeroCochainRep"]},{"name" : "IsVectorSearchTableDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsSearchTable","IsVectorSearchTable","IsVectorSearchTableDefaultRep"]},{"name" : "IsRingGeneralMappingByImagesDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep"]},{"name" : "IsSCRingGeneralMappingByImagesDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep","IsSCRingGeneralMappingByImagesDefaultRep"]},{"name" : "IsAlgebraicExtensionDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsNonTrivial","Tester(IsNonTrivial)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(MultiplicativeNeutralElement)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsIntegralRing","Tester(IsIntegralRing)","IsFreeLeftModule","IsAlgebraicExtension","IsAlgebraicExtensionDefaultRep"]},{"name" : "IsAlgBFRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsAlgebraicElement","IsAlgBFRep"]},{"name" : "IsKroneckerConstRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsAlgebraicElement","IsKroneckerConstRep"]},{"name" : "IsCanonicalBasisAlgebraicExtension","type" : "GAP_Representation","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisAlgebraicExtension"]},{"name" : "IsUnknownDefaultRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsUnknownDefaultRep"]},{"name" : "IsBasisFiniteFieldRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBasisFiniteFieldRep"]},{"name" : "IsFrobeniusAutomorphism","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsFrobeniusAutomorphism"]},{"name" : "IsModulusRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsModulusRep"]},{"name" : "IsCoeffsModConwayPolRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsCoeffsModConwayPolRep"]},{"name" : "IsCanonicalBasisRationals","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisRationals"]},{"name" : "IsCanonicalBasisGaussianIntegersRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisGaussianIntegersRep"]},{"name" : "IsCanonicalBasisAbelianNumberFieldRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisAbelianNumberFieldRep"]},{"name" : "IsCanonicalBasisCyclotomicFieldRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisAbelianNumberFieldRep","IsCanonicalBasisCyclotomicFieldRep"]},{"name" : "IsANFAutomorphismRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsANFAutomorphismRep"]},{"name" : "IsLockedRepresentationVector","type" : "GAP_Filter","implied" : ["IsLockedRepresentationVector"]},{"name" : "IsBracketRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsBracketRep"]},{"name" : "Is8BitsAssocWord","type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","Is8BitsAssocWord"]},{"name" : "Is16BitsAssocWord","type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","Is16BitsAssocWord"]},{"name" : "Is32BitsAssocWord","type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","Is32BitsAssocWord"]},{"name" : "IsInfBitsAssocWord","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","IsInfBitsAssocWord"]},{"name" : "IsInfiniteListOfNamesRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInfiniteListOfNamesRep"]},{"name" : "IsInfiniteListOfGeneratorsRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInfiniteListOfGeneratorsRep"]},{"name" : "IsSingleCollectorRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep"]},{"name" : "Is8BitsSingleCollectorRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","Is8BitsSingleCollectorRep"]},{"name" : "Is16BitsSingleCollectorRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","Is16BitsSingleCollectorRep"]},{"name" : "Is32BitsSingleCollectorRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","Is32BitsSingleCollectorRep"]},{"name" : "IsDefaultRhsTypeSingleCollector","type" : "GAP_Filter","implied" : ["IsDefaultRhsTypeSingleCollector"]},{"name" : "IsCombinatorialCollectorRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","IsCombinatorialCollectorRep"]},{"name" : "IsNBitsPcWordRep","type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsNBitsPcWordRep"]},{"name" : "Is8BitsPcWordRep","type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsKernelPcWord","IsNBitsPcWordRep","Is8BitsPcWordRep"]},{"name" : "Is16BitsPcWordRep","type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsKernelPcWord","IsNBitsPcWordRep","Is16BitsPcWordRep"]},{"name" : "Is32BitsPcWordRep","type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsKernelPcWord","IsNBitsPcWordRep","Is32BitsPcWordRep"]},{"name" : "IsDeepThoughtCollectorRep","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsDeepThoughtCollectorRep"]},{"name" : "IsEnumeratorByPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEnumeratorByPcgsRep"]},{"name" : "IsPcgsByPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)","IsPcgsByPcgsRep"]},{"name" : "IsInducedPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsInducedPcgsRep"]},{"name" : "IsSubsetInducedPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsInducedPcgsRep","IsSubsetInducedPcgsRep"]},{"name" : "IsTailInducedPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsInducedPcgsRep","IsSubsetInducedPcgsRep","IsTailInducedPcgsRep"]},{"name" : "IsModuloPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep"]},{"name" : "IsModuloTailPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsModuloTailPcgsRep"]},{"name" : "IsSubsetInducedNumeratorModuloTailPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsModuloTailPcgsRep","IsSubsetInducedNumeratorModuloTailPcgsRep"]},{"name" : "IsModuloTailPcgsByListRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsModuloTailPcgsRep","IsModuloTailPcgsByListRep"]},{"name" : "IsNumeratorParentForExponentsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsNumeratorParentForExponentsRep"]},{"name" : "IsNumeratorParentLayersForExponentsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsNumeratorParentLayersForExponentsRep"]},{"name" : "IsUnsortedPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsUnsortedPcgsRep"]},{"name" : "IsSortedPcgsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsUnsortedPcgsRep","IsSortedPcgsRep"]},{"name" : "IsMemberPcSeriesPermGroup","type" : "GAP_Representation","implied" : ["IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","CanEasilyCompareElements","Tester(CanEasilyCompareElements)","CanEasilySortElements","Tester(CanEasilySortElements)","CanComputeSize","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsFiniteOrderElement)","IsGeneralizedDomain","CategoryCollections(IsPerm)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsCompletelySimpleSemigroup","Tester(IsCompletelySimpleSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)","CanEasilyTestMembership","CanComputeSizeAnySubgroup","KnowsHowToDecompose","Tester(KnowsHowToDecompose)","CanComputeFittingFree","IsMemberPcSeriesPermGroup","IsNilpotentByFinite","Tester(IsNilpotentByFinite)"]},{"name" : "IsMagmaByMultiplicationTableObj","type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMagmaByMultiplicationTableObj"]},{"name" : "IsPcgsDirectProductRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsPcgsDirectProductRep"]},{"name" : "IsBlocksOfActionHomomorphism","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismByBase","IsBlocksOfActionHomomorphism"]},{"name" : "IsEmbeddingDirectProductPermGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsEmbeddingDirectProductPermGroup"]},{"name" : "IsEmbeddingWreathProductPermGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsEmbeddingWreathProductPermGroup"]},{"name" : "IsEmbeddingImprimitiveWreathProductPermGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsEmbeddingWreathProductPermGroup","IsEmbeddingImprimitiveWreathProductPermGroup"]},{"name" : "IsEmbeddingProductActionWreathProductPermGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsGroupGeneralMappingByAsGroupGeneralMappingByImages","IsEmbeddingWreathProductPermGroup","IsEmbeddingProductActionWreathProductPermGroup"]},{"name" : "IsProjectionDirectProductPermGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsProjectionDirectProductPermGroup"]},{"name" : "IsProjectionSubdirectProductPermGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsProjectionSubdirectProductPermGroup"]},{"name" : "IsEmbeddingDirectProductMatrixGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsEmbeddingDirectProductMatrixGroup"]},{"name" : "IsProjectionDirectProductMatrixGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsProjectionDirectProductMatrixGroup"]},{"name" : "IsEmbeddingImprimitiveWreathProductMatrixGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsEmbeddingImprimitiveWreathProductMatrixGroup"]},{"name" : "IsSlicedPerm","type" : "GAP_Representation","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement","IsSlicedPerm"]},{"name" : "IsSlicedPermInv","type" : "GAP_Representation","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement","IsSlicedPermInv"]},{"name" : "IsRightCosetDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsRightCoset","IsRightCosetDefaultRep"]},{"name" : "IsDoubleCosetDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsExtRSet","IsDoubleCoset","IsDoubleCosetDefaultRep"]},{"name" : "IsRightTransversalViaCosetsRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalViaCosetsRep"]},{"name" : "IsFactoredTransversalRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsFactoredTransversalRep"]},{"name" : "IsRightTransversalPermGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalPermGroupRep"]},{"name" : "IsRightTransversalPcGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalPcGroupRep"]},{"name" : "IsEnumeratorByNiceomorphismRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEnumeratorByNiceomorphismRep"]},{"name" : "IsActionHomomorphismAutomGroup","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismByBase","IsActionHomomorphismAutomGroup"]},{"name" : "IsBlowUpIsomorphism","type" : "GAP_Filter","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsBlowUpIsomorphism"]},{"name" : "IsRightTransversalFpGroupRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalFpGroupRep"]},{"name" : "IsPresentationDefaultRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPresentationDefaultRep"]},{"name" : "IsModuloPcgsFpGroupRep","type" : "GAP_Representation","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs","IsPcgsDefaultRep","IsModuloPcgsFpGroupRep"]},{"name" : "IsTransformationRepOfEndo","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsTransformationRepOfEndo"]},{"name" : "IsKnuthBendixRewritingSystemRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsKnuthBendixRewritingSystemRep"]},{"name" : "IsFloatPseudoField","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFloatPseudoField"]},{"name" : "IsFloatRationalFunction","type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsFloatRationalFunction"]},{"name" : "IsIEEE754PseudoField","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFloatPseudoField","IsIEEE754PseudoField"]},{"name" : "Tester(IdGroup)","type" : "GAP_Attribute","filters" : ["Tester(IdGroup)"]},{"name" : "Tester(Gap3CatalogueIdGroup)","type" : "GAP_Attribute","filters" : ["Tester(Gap3CatalogueIdGroup)"]},{"name" : "Tester(FrattinifactorSize)","type" : "GAP_Attribute","filters" : ["Tester(FrattinifactorSize)"]},{"name" : "Tester(FrattinifactorId)","type" : "GAP_Attribute","filters" : ["Tester(FrattinifactorId)"]},{"name" : "Tester(GaloisType)","type" : "GAP_Attribute","filters" : ["Tester(GaloisType)"]},{"name" : "Tester(SimsNo)","type" : "GAP_Attribute","filters" : ["Tester(SimsNo)"]},{"name" : "Tester(MinimalBlockDimension)","type" : "GAP_Attribute","filters" : ["Tester(MinimalBlockDimension)"]},{"name" : "IsPrimitiveMatrixGroup","type" : "GAP_Property","filters" : ["IsPrimitiveMatrixGroup","Tester(IsPrimitiveMatrixGroup)"]},{"name" : "Tester(IsPrimitiveMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPrimitiveMatrixGroup)"]},{"name" : "IsPrimGrpIterRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsPrimGrpIterRep"]},{"name" : "IsPGAutomorphismRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsPGAutomorphismRep"]},{"name" : "Tester(IrrFacsAlgExtPol)","type" : "GAP_Attribute","filters" : ["Tester(IrrFacsAlgExtPol)"]},{"name" : "IsBasisOfMatrixField","type" : "GAP_Representation","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisOfMatrixField"]},{"name" : "IsUnitGroup","type" : "GAP_Property","filters" : ["IsUnitGroup","Tester(IsUnitGroup)"]},{"name" : "Tester(IsUnitGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsUnitGroup)"]},{"name" : "IsUnitGroupIsomorphism","type" : "GAP_Property","filters" : ["IsUnitGroupIsomorphism","Tester(IsUnitGroupIsomorphism)"]},{"name" : "Tester(IsUnitGroupIsomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsUnitGroupIsomorphism)"]},{"name" : "IsNumberFieldByMatrices","type" : "GAP_Property","filters" : ["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]},{"name" : "Tester(IsNumberFieldByMatrices)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNumberFieldByMatrices)"]},{"name" : "IsMultGroupByFieldElemsIsomorphism","type" : "GAP_Property","filters" : ["IsMultGroupByFieldElemsIsomorphism","Tester(IsMultGroupByFieldElemsIsomorphism)"]},{"name" : "Tester(IsMultGroupByFieldElemsIsomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMultGroupByFieldElemsIsomorphism)"]},{"name" : "Tester(IntegerDefiningPolynomial)","type" : "GAP_Attribute","filters" : ["Tester(IntegerDefiningPolynomial)"]},{"name" : "Tester(IntegerPrimitiveElement)","type" : "GAP_Attribute","filters" : ["Tester(IntegerPrimitiveElement)"]},{"name" : "Tester(EquationOrderBasis)","type" : "GAP_Attribute","filters" : ["Tester(EquationOrderBasis)"]},{"name" : "Tester(MaximalOrderBasis)","type" : "GAP_Attribute","filters" : ["Tester(MaximalOrderBasis)"]},{"name" : "Tester(UnitGroup)","type" : "GAP_Attribute","filters" : ["Tester(UnitGroup)"]},{"name" : "Tester(FieldOfUnitGroup)","type" : "GAP_Attribute","filters" : ["Tester(FieldOfUnitGroup)"]},{"name" : "IsFromTheLeftCollectorRep","type" : "GAP_Representation","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector","IsPowerConjugateCollector","IsFromTheLeftCollectorRep"]},{"name" : "IsWeightedCollector","type" : "GAP_Property","filters" : ["IsWeightedCollector","Tester(IsWeightedCollector)"]},{"name" : "Tester(IsWeightedCollector)","type" : "GAP_TrueProperty","implied" : ["Tester(IsWeightedCollector)"]},{"name" : "IsPolynomialCollector","type" : "GAP_Property","filters" : ["IsPolynomialCollector","Tester(IsPolynomialCollector)"]},{"name" : "Tester(IsPolynomialCollector)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPolynomialCollector)"]},{"name" : "UseLibraryCollector","type" : "GAP_Property","filters" : ["UseLibraryCollector","Tester(UseLibraryCollector)"]},{"name" : "Tester(UseLibraryCollector)","type" : "GAP_TrueProperty","implied" : ["Tester(UseLibraryCollector)"]},{"name" : "IsPolycyclicPresentation","type" : "GAP_Property","filters" : ["IsPolycyclicPresentation","Tester(IsPolycyclicPresentation)"]},{"name" : "Tester(IsPolycyclicPresentation)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPolycyclicPresentation)"]},{"name" : "IsPcpElement","type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsPcpElement"]},{"name" : "CategoryFamily(IsPcpElement)","type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsPcpElement)"]},{"name" : "CategoryCollections(IsPcpElement)","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","CategoryCollections(IsPcpElement)"]},{"name" : "IsPcpElementRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsPcpElementRep"]},{"name" : "Tester(TailOfElm)","type" : "GAP_Attribute","filters" : ["Tester(TailOfElm)"]},{"name" : "Tester(RelativeOrderPcp)","type" : "GAP_Attribute","filters" : ["Tester(RelativeOrderPcp)"]},{"name" : "Tester(RelativeIndex)","type" : "GAP_Attribute","filters" : ["Tester(RelativeIndex)"]},{"name" : "Tester(FactorOrder)","type" : "GAP_Attribute","filters" : ["Tester(FactorOrder)"]},{"name" : "Tester(Igs)","type" : "GAP_Attribute","filters" : ["Tester(Igs)"]},{"name" : "Tester(Ngs)","type" : "GAP_Attribute","filters" : ["Tester(Ngs)"]},{"name" : "Tester(Cgs)","type" : "GAP_Attribute","filters" : ["Tester(Cgs)"]},{"name" : "IsPcp","type" : "GAP_Category","implied" : ["IsPcp"]},{"name" : "IsPcpRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsPcpRep"]},{"name" : "Extrarankfilter","type" : "GAP_Filter","implied" : ["Extrarankfilter"]},{"name" : "IsFromPcpGHBI","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsFromPcpGHBI"]},{"name" : "Extrarankfilter","type" : "GAP_Filter","implied" : ["Extrarankfilter"]},{"name" : "IsToPcpGHBI","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsToPcpGHBI"]},{"name" : "Tester(EfaSeries)","type" : "GAP_Attribute","filters" : ["Tester(EfaSeries)"]},{"name" : "Tester(PcpsOfEfaSeries)","type" : "GAP_Attribute","filters" : ["Tester(PcpsOfEfaSeries)"]},{"name" : "Tester(IsomorphismPcpGroup)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismPcpGroup)"]},{"name" : "Tester(PcpGroupByEfaSeries)","type" : "GAP_Attribute","filters" : ["Tester(PcpGroupByEfaSeries)"]},{"name" : "IsHomomorphismIntoMatrixGroup","type" : "GAP_Property","filters" : ["IsHomomorphismIntoMatrixGroup","Tester(IsHomomorphismIntoMatrixGroup)"]},{"name" : "Tester(IsHomomorphismIntoMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsHomomorphismIntoMatrixGroup)"]},{"name" : "Tester(SemiSimpleEfaSeries)","type" : "GAP_Attribute","filters" : ["Tester(SemiSimpleEfaSeries)"]},{"name" : "Tester(FCCentre)","type" : "GAP_Attribute","filters" : ["Tester(FCCentre)"]},{"name" : "IsNilpotentByFinite","type" : "GAP_Property","filters" : ["IsNilpotentByFinite","Tester(IsNilpotentByFinite)"]},{"name" : "Tester(IsNilpotentByFinite)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNilpotentByFinite)"]},{"name" : "Tester(ComputedMaximalSubgroupClassesByIndexs)","type" : "GAP_Attribute","filters" : ["Tester(ComputedMaximalSubgroupClassesByIndexs)"]},{"name" : "Tester(ComputedLowIndexSubgroupClassess)","type" : "GAP_Attribute","filters" : ["Tester(ComputedLowIndexSubgroupClassess)"]},{"name" : "Tester(ComputedLowIndexNormalSubgroupss)","type" : "GAP_Attribute","filters" : ["Tester(ComputedLowIndexNormalSubgroupss)"]},{"name" : "Tester(SchurExtension)","type" : "GAP_Attribute","filters" : ["Tester(SchurExtension)"]},{"name" : "Tester(SchurExtensionEpimorphism)","type" : "GAP_Attribute","filters" : ["Tester(SchurExtensionEpimorphism)"]},{"name" : "Tester(NonAbelianTensorSquare)","type" : "GAP_Attribute","filters" : ["Tester(NonAbelianTensorSquare)"]},{"name" : "Tester(NonAbelianExteriorSquare)","type" : "GAP_Attribute","filters" : ["Tester(NonAbelianExteriorSquare)"]},{"name" : "Tester(TorsionSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(TorsionSubgroup)"]},{"name" : "Tester(NormalTorsionSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(NormalTorsionSubgroup)"]},{"name" : "Tester(FiniteSubgroupClasses)","type" : "GAP_Attribute","filters" : ["Tester(FiniteSubgroupClasses)"]},{"name" : "IsTorsionFree","type" : "GAP_Property","filters" : ["IsTorsionFree","Tester(IsTorsionFree)"]},{"name" : "Tester(IsTorsionFree)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTorsionFree)"]},{"name" : "IsFreeAbelian","type" : "GAP_Property","filters" : ["IsFreeAbelian","Tester(IsFreeAbelian)"]},{"name" : "Tester(IsFreeAbelian)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFreeAbelian)"]},{"name" : "IsClass","type" : "GAP_Category","implied" : ["IsListOrCollection","IsClass"]},{"name" : "Tester(MemberFunction)","type" : "GAP_Attribute","filters" : ["Tester(MemberFunction)"]},{"name" : "Tester(ComputedIsMembers)","type" : "GAP_Attribute","filters" : ["Tester(ComputedIsMembers)"]},{"name" : "IsGroupClass","type" : "GAP_Property","filters" : ["IsGroupClass","Tester(IsGroupClass)"]},{"name" : "Tester(IsGroupClass)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupClass)"]},{"name" : "Tester(GroupClass)","type" : "GAP_Attribute","filters" : ["Tester(GroupClass)"]},{"name" : "ContainsTrivialGroup","type" : "GAP_Property","filters" : ["ContainsTrivialGroup","Tester(ContainsTrivialGroup)"]},{"name" : "Tester(ContainsTrivialGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(ContainsTrivialGroup)"]},{"name" : "IsSubgroupClosed","type" : "GAP_Property","filters" : ["IsSubgroupClosed","Tester(IsSubgroupClosed)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)"]},{"name" : "Tester(IsSubgroupClosed)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSubgroupClosed)"]},{"name" : "IsNormalSubgroupClosed","type" : "GAP_Property","filters" : ["IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)"]},{"name" : "Tester(IsNormalSubgroupClosed)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNormalSubgroupClosed)"]},{"name" : "IsQuotientClosed","type" : "GAP_Property","filters" : ["IsQuotientClosed","Tester(IsQuotientClosed)"]},{"name" : "Tester(IsQuotientClosed)","type" : "GAP_TrueProperty","implied" : ["Tester(IsQuotientClosed)"]},{"name" : "IsResiduallyClosed","type" : "GAP_Property","filters" : ["IsResiduallyClosed","Tester(IsResiduallyClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)"]},{"name" : "Tester(IsResiduallyClosed)","type" : "GAP_TrueProperty","implied" : ["Tester(IsResiduallyClosed)"]},{"name" : "IsNormalProductClosed","type" : "GAP_Property","filters" : ["IsNormalProductClosed","Tester(IsNormalProductClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)"]},{"name" : "Tester(IsNormalProductClosed)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNormalProductClosed)"]},{"name" : "IsDirectProductClosed","type" : "GAP_Property","filters" : ["IsDirectProductClosed","Tester(IsDirectProductClosed)"]},{"name" : "Tester(IsDirectProductClosed)","type" : "GAP_TrueProperty","implied" : ["Tester(IsDirectProductClosed)"]},{"name" : "IsSchunckClass","type" : "GAP_Property","filters" : ["ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsSchunckClass","Tester(IsSchunckClass)","IsSaturated","Tester(IsSaturated)"]},{"name" : "Tester(IsSchunckClass)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSchunckClass)"]},{"name" : "IsSaturated","type" : "GAP_Property","filters" : ["IsSaturated","Tester(IsSaturated)"]},{"name" : "Tester(IsSaturated)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSaturated)"]},{"name" : "Tester(FittingClass)","type" : "GAP_Attribute","filters" : ["Tester(FittingClass)"]},{"name" : "Tester(InjectorFunction)","type" : "GAP_Attribute","filters" : ["Tester(InjectorFunction)"]},{"name" : "Tester(RadicalFunction)","type" : "GAP_Attribute","filters" : ["Tester(RadicalFunction)"]},{"name" : "IsPrimitiveSolvableGroup","type" : "GAP_Property","filters" : ["IsPrimitiveSolvableGroup","Tester(IsPrimitiveSolvableGroup)"]},{"name" : "Tester(IsPrimitiveSolvableGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPrimitiveSolvableGroup)"]},{"name" : "Tester(SchunckClass)","type" : "GAP_Attribute","filters" : ["Tester(SchunckClass)"]},{"name" : "Tester(Boundary)","type" : "GAP_Attribute","filters" : ["Tester(Boundary)"]},{"name" : "Tester(ProjectorFunction)","type" : "GAP_Attribute","filters" : ["Tester(ProjectorFunction)"]},{"name" : "Tester(BoundaryFunction)","type" : "GAP_Attribute","filters" : ["Tester(BoundaryFunction)"]},{"name" : "Tester(OrdinaryFormation)","type" : "GAP_Attribute","filters" : ["Tester(OrdinaryFormation)"]},{"name" : "Tester(SaturatedFormation)","type" : "GAP_Attribute","filters" : ["Tester(SaturatedFormation)"]},{"name" : "Tester(FittingFormation)","type" : "GAP_Attribute","filters" : ["Tester(FittingFormation)"]},{"name" : "Tester(SaturatedFittingFormation)","type" : "GAP_Attribute","filters" : ["Tester(SaturatedFittingFormation)"]},{"name" : "Tester(ResidualFunction)","type" : "GAP_Attribute","filters" : ["Tester(ResidualFunction)"]},{"name" : "Tester(LocalDefinitionFunction)","type" : "GAP_Attribute","filters" : ["Tester(LocalDefinitionFunction)"]},{"name" : "Tester(ComputedProjectors)","type" : "GAP_Attribute","filters" : ["Tester(ComputedProjectors)"]},{"name" : "Tester(ComputedCoveringSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(ComputedCoveringSubgroups)"]},{"name" : "Tester(ComputedInjectors)","type" : "GAP_Attribute","filters" : ["Tester(ComputedInjectors)"]},{"name" : "Tester(ComputedRadicals)","type" : "GAP_Attribute","filters" : ["Tester(ComputedRadicals)"]},{"name" : "Tester(ComputedResiduals)","type" : "GAP_Attribute","filters" : ["Tester(ComputedResiduals)"]},{"name" : "Tester(CharacteristicSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(CharacteristicSubgroups)"]},{"name" : "Tester(NormalGeneratorsOfNilpotentResidual)","type" : "GAP_Attribute","filters" : ["Tester(NormalGeneratorsOfNilpotentResidual)"]},{"name" : "Tester(PrimePowerGensPcSequence)","type" : "GAP_Attribute","filters" : ["Tester(PrimePowerGensPcSequence)"]},{"name" : "Tester(NilpotentProjector)","type" : "GAP_Attribute","filters" : ["Tester(NilpotentProjector)"]},{"name" : "Tester(SupersolvableProjector)","type" : "GAP_Attribute","filters" : ["Tester(SupersolvableProjector)"]},{"name" : "Tester(SolvableSocle)","type" : "GAP_Attribute","filters" : ["Tester(SolvableSocle)"]},{"name" : "Tester(SocleComponents)","type" : "GAP_Attribute","filters" : ["Tester(SocleComponents)"]},{"name" : "Tester(SolvableSocleComponents)","type" : "GAP_Attribute","filters" : ["Tester(SolvableSocleComponents)"]},{"name" : "Tester(ComputedPSocleComponentss)","type" : "GAP_Attribute","filters" : ["Tester(ComputedPSocleComponentss)"]},{"name" : "Tester(ComputedPSocles)","type" : "GAP_Attribute","filters" : ["Tester(ComputedPSocles)"]},{"name" : "Tester(AbelianMinimalNormalSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(AbelianMinimalNormalSubgroups)"]},{"name" : "IsClassByPropertyRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByPropertyRep"]},{"name" : "IsClassByComplementRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByComplementRep"]},{"name" : "IsClassByIntersectionRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByIntersectionRep"]},{"name" : "IsClassByUnionRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByUnionRep"]},{"name" : "IsGroupClassByListRep","type" : "GAP_Representation","implied" : ["IsListOrCollection","IsClass","IsGroupClass","Tester(IsGroupClass)","IsGroupClassByListRep"]},{"name" : "IsFittingProductRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsFittingProductRep"]},{"name" : "IsFittingSetRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsClass","IsClassByPropertyRep","IsFittingSetRep"]},{"name" : "IsFormationProductRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsFormationProductRep"]},{"name" : "IsBBoxProgram","type" : "GAP_Category","implied" : ["IsBBoxProgram"]},{"name" : "IsStraightLineDecision","type" : "GAP_Category","implied" : ["IsStraightLineDecision"]},{"name" : "Tester(LinesOfStraightLineDecision)","type" : "GAP_Attribute","filters" : ["Tester(LinesOfStraightLineDecision)"]},{"name" : "Tester(NrInputsOfStraightLineDecision)","type" : "GAP_Attribute","filters" : ["Tester(NrInputsOfStraightLineDecision)"]},{"name" : "Tester(AsBBoxProgram)","type" : "GAP_Attribute","filters" : ["Tester(AsBBoxProgram)"]},{"name" : "Tester(AsStraightLineProgram)","type" : "GAP_Attribute","filters" : ["Tester(AsStraightLineProgram)"]},{"name" : "Tester(AsStraightLineDecision)","type" : "GAP_Attribute","filters" : ["Tester(AsStraightLineDecision)"]},{"name" : "Tester(Maxes)","type" : "GAP_Attribute","filters" : ["Tester(Maxes)"]},{"name" : "Tester(AtlasRepInfoRecord)","type" : "GAP_Attribute","filters" : ["Tester(AtlasRepInfoRecord)"]},{"name" : "Tester(CASInfo)","type" : "GAP_Attribute","filters" : ["Tester(CASInfo)"]},{"name" : "Tester(ConstructionInfoCharacterTable)","type" : "GAP_Attribute","filters" : ["Tester(ConstructionInfoCharacterTable)"]},{"name" : "Tester(FusionToTom)","type" : "GAP_Attribute","filters" : ["Tester(FusionToTom)"]},{"name" : "Tester(ProjectivesInfo)","type" : "GAP_Attribute","filters" : ["Tester(ProjectivesInfo)"]},{"name" : "Tester(ExtensionInfoCharacterTable)","type" : "GAP_Attribute","filters" : ["Tester(ExtensionInfoCharacterTable)"]},{"name" : "Tester(GroupInfoForCharacterTable)","type" : "GAP_Attribute","filters" : ["Tester(GroupInfoForCharacterTable)"]},{"name" : "KnowsSomeGroupInfo","type" : "GAP_Property","filters" : ["KnowsSomeGroupInfo","Tester(KnowsSomeGroupInfo)"]},{"name" : "Tester(KnowsSomeGroupInfo)","type" : "GAP_TrueProperty","implied" : ["Tester(KnowsSomeGroupInfo)"]},{"name" : "IsNontrivialDirectProduct","type" : "GAP_Property","filters" : ["IsNontrivialDirectProduct","Tester(IsNontrivialDirectProduct)"]},{"name" : "Tester(IsNontrivialDirectProduct)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNontrivialDirectProduct)"]},{"name" : "KnowsDeligneLusztigNames","type" : "GAP_Property","filters" : ["KnowsDeligneLusztigNames","Tester(KnowsDeligneLusztigNames)"]},{"name" : "Tester(KnowsDeligneLusztigNames)","type" : "GAP_TrueProperty","implied" : ["Tester(KnowsDeligneLusztigNames)"]},{"name" : "IsDuplicateTable","type" : "GAP_Property","filters" : ["IsDuplicateTable","Tester(IsDuplicateTable)"]},{"name" : "Tester(IsDuplicateTable)","type" : "GAP_TrueProperty","implied" : ["Tester(IsDuplicateTable)"]},{"name" : "Tester(IdentifierOfMainTable)","type" : "GAP_Attribute","filters" : ["Tester(IdentifierOfMainTable)"]},{"name" : "Tester(IdentifiersOfDuplicateTables)","type" : "GAP_Attribute","filters" : ["Tester(IdentifiersOfDuplicateTables)"]},{"name" : "Tester(DeligneLusztigNames)","type" : "GAP_Attribute","filters" : ["Tester(DeligneLusztigNames)"]},{"name" : "Tester(DeligneLusztigName)","type" : "GAP_Attribute","filters" : ["Tester(DeligneLusztigName)"]},{"name" : "Tester(FingerprintOfCharacterTable)","type" : "GAP_Attribute","filters" : ["Tester(FingerprintOfCharacterTable)"]},{"name" : "Tester(SpinSymIngredients)","type" : "GAP_Attribute","filters" : ["Tester(SpinSymIngredients)"]},{"name" : "IsSpinSymTable","type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable","IsSpinSymTable"]},{"name" : "IsLibTomRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLibTomRep"]},{"name" : "Tester(NamesLibTom)","type" : "GAP_Attribute","filters" : ["Tester(NamesLibTom)"]},{"name" : "Tester(NotifiedFusionsOfLibTom)","type" : "GAP_Attribute","filters" : ["Tester(NotifiedFusionsOfLibTom)"]},{"name" : "Tester(FusionsOfLibTom)","type" : "GAP_Attribute","filters" : ["Tester(FusionsOfLibTom)"]},{"name" : "Tester(NotifiedFusionsToLibTom)","type" : "GAP_Attribute","filters" : ["Tester(NotifiedFusionsToLibTom)"]},{"name" : "Tester(FusionsToLibTom)","type" : "GAP_Attribute","filters" : ["Tester(FusionsToLibTom)"]},{"name" : "Tester(StandardGeneratorsInfo)","type" : "GAP_Attribute","filters" : ["Tester(StandardGeneratorsInfo)"]},{"name" : "IsInvAutomatonCategory","type" : "GAP_Category","implied" : ["IsInvAutomatonCategory"]},{"name" : "Tester(FGA_States)","type" : "GAP_Attribute","filters" : ["Tester(FGA_States)"]},{"name" : "Tester(FGA_GeneratorsLetterRep)","type" : "GAP_Attribute","filters" : ["Tester(FGA_GeneratorsLetterRep)"]},{"name" : "Tester(FreeGeneratorsOfGroup)","type" : "GAP_Attribute","filters" : ["Tester(FreeGeneratorsOfGroup)"]},{"name" : "Tester(RankOfFreeGroup)","type" : "GAP_Attribute","filters" : ["Tester(RankOfFreeGroup)"]},{"name" : "Tester(FreeGroupAutomaton)","type" : "GAP_Attribute","filters" : ["IsListOrCollection","IsCollection","CanComputeSize","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CanEasilyTestMembership","CanComputeSizeAnySubgroup","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsSubgroupFgGroup","IsSubgroupFpGroup","IsTorsionFree","Tester(IsTorsionFree)","Tester(FreeGroupAutomaton)"]},{"name" : "Tester(FreeGroupExtendedAutomaton)","type" : "GAP_Attribute","filters" : ["Tester(FreeGroupExtendedAutomaton)"]},{"name" : "Tester(NormalizerInWholeGroup)","type" : "GAP_Attribute","filters" : ["Tester(NormalizerInWholeGroup)"]},{"name" : "Tester(FGA_Source)","type" : "GAP_Attribute","filters" : ["Tester(FGA_Source)"]},{"name" : "Tester(FGA_Image)","type" : "GAP_Attribute","filters" : ["Tester(FGA_Image)"]},{"name" : "IsAutomorphismGroupOfFreeGroup","type" : "GAP_Filter","implied" : ["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)","IsAutomorphismGroup","Tester(IsAutomorphismGroup)","IsAutomorphismGroupOfFreeGroup"]},{"name" : "Tester(FGA_WhiteheadParams)","type" : "GAP_Attribute","filters" : ["Tester(FGA_WhiteheadParams)"]},{"name" : "Tester(FGA_WhiteheadAutomorphisms)","type" : "GAP_Attribute","filters" : ["Tester(FGA_WhiteheadAutomorphisms)"]},{"name" : "Tester(FGA_NielsenAutomorphisms)","type" : "GAP_Attribute","filters" : ["Tester(FGA_NielsenAutomorphisms)"]},{"name" : "IsSimpleInvAutomatonRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsInvAutomatonCategory","IsSimpleInvAutomatonRep"]},{"name" : "IsIrreducibleMatrixGroup","type" : "GAP_Property","filters" : ["IsIrreducibleMatrixGroup","Tester(IsIrreducibleMatrixGroup)"]},{"name" : "Tester(IsIrreducibleMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIrreducibleMatrixGroup)"]},{"name" : "Tester(ComputedIsIrreducibleMatrixGroups)","type" : "GAP_Attribute","filters" : ["Tester(ComputedIsIrreducibleMatrixGroups)"]},{"name" : "IsAbsolutelyIrreducibleMatrixGroup","type" : "GAP_Property","filters" : ["IsAbsolutelyIrreducibleMatrixGroup","Tester(IsAbsolutelyIrreducibleMatrixGroup)"]},{"name" : "Tester(IsAbsolutelyIrreducibleMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAbsolutelyIrreducibleMatrixGroup)"]},{"name" : "Tester(ComputedIsPrimitiveMatrixGroups)","type" : "GAP_Attribute","filters" : ["Tester(ComputedIsPrimitiveMatrixGroups)"]},{"name" : "Tester(MinimalBlockDimensionOfMatrixGroup)","type" : "GAP_Attribute","filters" : ["Tester(MinimalBlockDimensionOfMatrixGroup)"]},{"name" : "Tester(ComputedMinimalBlockDimensionOfMatrixGroups)","type" : "GAP_Attribute","filters" : ["Tester(ComputedMinimalBlockDimensionOfMatrixGroups)"]},{"name" : "Tester(CharacteristicOfField)","type" : "GAP_Attribute","filters" : ["Tester(CharacteristicOfField)"]},{"name" : "Tester(RepresentationIsomorphism)","type" : "GAP_Attribute","filters" : ["Tester(RepresentationIsomorphism)"]},{"name" : "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup","type" : "GAP_Property","filters" : ["IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup","Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"]},{"name" : "Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"]},{"name" : "Tester(ImprimitivitySystems)","type" : "GAP_Attribute","filters" : ["Tester(ImprimitivitySystems)"]},{"name" : "Tester(ComputedImprimitivitySystemss)","type" : "GAP_Attribute","filters" : ["Tester(ComputedImprimitivitySystemss)"]},{"name" : "Tester(TraceField)","type" : "GAP_Attribute","filters" : ["Tester(TraceField)"]},{"name" : "Tester(ConjugatingMatTraceField)","type" : "GAP_Attribute","filters" : ["Tester(ConjugatingMatTraceField)"]},{"name" : "Tester(FingerprintMatrixGroup)","type" : "GAP_Attribute","filters" : ["Tester(FingerprintMatrixGroup)"]},{"name" : "Tester(IdIrreducibleSolvableMatrixGroup)","type" : "GAP_Attribute","filters" : ["Tester(IdIrreducibleSolvableMatrixGroup)"]},{"name" : "Tester(IdPrimitiveSolvableGroup)","type" : "GAP_Attribute","filters" : ["Tester(IdPrimitiveSolvableGroup)"]},{"name" : "IsNilpotentLieAutomorphismRep","type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsNilpotentLieAutomorphismRep"]},{"name" : "IsLieNilpotentOverFp","type" : "GAP_Property","filters" : ["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]},{"name" : "Tester(IsLieNilpotentOverFp)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieNilpotentOverFp)"]},{"name" : "Tester(AutomorphismGroupOfNilpotentLieAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(AutomorphismGroupOfNilpotentLieAlgebra)"]},{"name" : "Tester(MinimalGeneratorNumber)","type" : "GAP_Attribute","filters" : ["Tester(MinimalGeneratorNumber)"]},{"name" : "IsLieCover","type" : "GAP_Property","filters" : ["IsLieCover","Tester(IsLieCover)"]},{"name" : "Tester(IsLieCover)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieCover)"]},{"name" : "Tester(CoverOf)","type" : "GAP_Attribute","filters" : ["Tester(CoverOf)"]},{"name" : "Tester(CoverHomomorphism)","type" : "GAP_Attribute","filters" : ["Tester(CoverHomomorphism)"]},{"name" : "Tester(LieCover)","type" : "GAP_Attribute","filters" : ["Tester(LieCover)"]},{"name" : "Tester(LieNucleus)","type" : "GAP_Attribute","filters" : ["Tester(LieNucleus)"]},{"name" : "Tester(LieMultiplicator)","type" : "GAP_Attribute","filters" : ["Tester(LieMultiplicator)"]},{"name" : "IsLieAlgebraWithNB","type" : "GAP_Property","filters" : ["IsLieAlgebraWithNB","Tester(IsLieAlgebraWithNB)"]},{"name" : "Tester(IsLieAlgebraWithNB)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieAlgebraWithNB)"]},{"name" : "Tester(NilpotentBasis)","type" : "GAP_Attribute","filters" : ["Tester(NilpotentBasis)"]},{"name" : "IsNilpotentBasis","type" : "GAP_Property","filters" : ["IsNilpotentBasis","Tester(IsNilpotentBasis)"]},{"name" : "Tester(IsNilpotentBasis)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNilpotentBasis)"]},{"name" : "Tester(LieNBDefinitions)","type" : "GAP_Attribute","filters" : ["Tester(LieNBDefinitions)"]},{"name" : "Tester(LieNBWeights)","type" : "GAP_Attribute","filters" : ["Tester(LieNBWeights)"]},{"name" : "IsGroupAlgebra","type" : "GAP_Property","filters" : ["IsGroupAlgebra","Tester(IsGroupAlgebra)"]},{"name" : "Tester(IsGroupAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupAlgebra)"]},{"name" : "IsFModularGroupAlgebra","type" : "GAP_Property","filters" : ["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"]},{"name" : "Tester(IsFModularGroupAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFModularGroupAlgebra)"]},{"name" : "IsPModularGroupAlgebra","type" : "GAP_Property","filters" : ["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]},{"name" : "Tester(IsPModularGroupAlgebra)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPModularGroupAlgebra)"]},{"name" : "Tester(UnderlyingRing)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingRing)"]},{"name" : "Tester(UnderlyingField)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingField)"]},{"name" : "Tester(Support)","type" : "GAP_Attribute","filters" : ["Tester(Support)"]},{"name" : "Tester(CoefficientsBySupport)","type" : "GAP_Attribute","filters" : ["Tester(CoefficientsBySupport)"]},{"name" : "Tester(TraceOfMagmaRingElement)","type" : "GAP_Attribute","filters" : ["Tester(TraceOfMagmaRingElement)"]},{"name" : "Tester(Augmentation)","type" : "GAP_Attribute","filters" : ["Tester(Augmentation)"]},{"name" : "Tester(IsSymmetric)","type" : "GAP_Attribute","filters" : ["Tester(IsSymmetric)"]},{"name" : "Tester(IsUnitary)","type" : "GAP_Attribute","filters" : ["Tester(IsUnitary)"]},{"name" : "Tester(WeightedBasis)","type" : "GAP_Attribute","filters" : ["Tester(WeightedBasis)"]},{"name" : "Tester(AugmentationIdealPowerSeries)","type" : "GAP_Attribute","filters" : ["Tester(AugmentationIdealPowerSeries)"]},{"name" : "Tester(AugmentationIdealNilpotencyIndex)","type" : "GAP_Attribute","filters" : ["Tester(AugmentationIdealNilpotencyIndex)"]},{"name" : "Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)","type" : "GAP_Attribute","filters" : ["Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)"]},{"name" : "IsGroupOfUnitsOfMagmaRing","type" : "GAP_Property","filters" : ["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]},{"name" : "Tester(IsGroupOfUnitsOfMagmaRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsGroupOfUnitsOfMagmaRing)"]},{"name" : "IsUnitGroupOfGroupRing","type" : "GAP_Property","filters" : ["IsUnitGroupOfGroupRing","Tester(IsUnitGroupOfGroupRing)"]},{"name" : "Tester(IsUnitGroupOfGroupRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsUnitGroupOfGroupRing)"]},{"name" : "IsNormalizedUnitGroupOfGroupRing","type" : "GAP_Property","filters" : ["IsListOrCollection","IsCollection","CanComputeSize","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","CanComputeSizeAnySubgroup","IsSolvableGroup","Tester(IsSolvableGroup)","CanEasilyComputePcgs","IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]},{"name" : "Tester(IsNormalizedUnitGroupOfGroupRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsNormalizedUnitGroupOfGroupRing)"]},{"name" : "Tester(UnderlyingGroupRing)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingGroupRing)"]},{"name" : "Tester(NormalizedUnitGroup)","type" : "GAP_Attribute","filters" : ["Tester(NormalizedUnitGroup)"]},{"name" : "Tester(PcNormalizedUnitGroup)","type" : "GAP_Attribute","filters" : ["Tester(PcNormalizedUnitGroup)"]},{"name" : "Tester(ComputedAugmentationIdealPowerFactorGroups)","type" : "GAP_Attribute","filters" : ["Tester(ComputedAugmentationIdealPowerFactorGroups)"]},{"name" : "Tester(PcUnits)","type" : "GAP_Attribute","filters" : ["Tester(PcUnits)"]},{"name" : "Tester(NaturalBijectionToPcNormalizedUnitGroup)","type" : "GAP_Attribute","filters" : ["Tester(NaturalBijectionToPcNormalizedUnitGroup)"]},{"name" : "Tester(NaturalBijectionToNormalizedUnitGroup)","type" : "GAP_Attribute","filters" : ["Tester(NaturalBijectionToNormalizedUnitGroup)"]},{"name" : "Tester(GroupBases)","type" : "GAP_Attribute","filters" : ["Tester(GroupBases)"]},{"name" : "Tester(BicyclicUnitGroup)","type" : "GAP_Attribute","filters" : ["Tester(BicyclicUnitGroup)"]},{"name" : "Tester(UnitarySubgroup)","type" : "GAP_Attribute","filters" : ["Tester(UnitarySubgroup)"]},{"name" : "IsLieAlgebraByAssociativeAlgebra","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsAnticommutative","Tester(IsAnticommutative)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsFreeLeftModule","IsLieAlgebraByAssociativeAlgebra"]},{"name" : "Tester(UnderlyingAssociativeAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingAssociativeAlgebra)"]},{"name" : "IsLieAlgebraOfGroupRing","type" : "GAP_Property","filters" : ["IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]},{"name" : "Tester(IsLieAlgebraOfGroupRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieAlgebraOfGroupRing)"]},{"name" : "IsBasisOfLieAlgebraOfGroupRing","type" : "GAP_Property","filters" : ["IsBasisOfLieAlgebraOfGroupRing","Tester(IsBasisOfLieAlgebraOfGroupRing)"]},{"name" : "Tester(IsBasisOfLieAlgebraOfGroupRing)","type" : "GAP_TrueProperty","implied" : ["Tester(IsBasisOfLieAlgebraOfGroupRing)"]},{"name" : "Tester(NaturalBijectionToLieAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(NaturalBijectionToLieAlgebra)"]},{"name" : "Tester(NaturalBijectionToAssociativeAlgebra)","type" : "GAP_Attribute","filters" : ["Tester(NaturalBijectionToAssociativeAlgebra)"]},{"name" : "Tester(AugmentationHomomorphism)","type" : "GAP_Attribute","filters" : ["Tester(AugmentationHomomorphism)"]},{"name" : "IsLieMetabelian","type" : "GAP_Property","filters" : ["IsLieMetabelian","Tester(IsLieMetabelian)"]},{"name" : "Tester(IsLieMetabelian)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieMetabelian)"]},{"name" : "IsLieCentreByMetabelian","type" : "GAP_Property","filters" : ["IsLieCentreByMetabelian","Tester(IsLieCentreByMetabelian)"]},{"name" : "Tester(IsLieCentreByMetabelian)","type" : "GAP_TrueProperty","implied" : ["Tester(IsLieCentreByMetabelian)"]},{"name" : "Tester(LieUpperNilpotencyIndex)","type" : "GAP_Attribute","filters" : ["Tester(LieUpperNilpotencyIndex)"]},{"name" : "Tester(LieLowerNilpotencyIndex)","type" : "GAP_Attribute","filters" : ["Tester(LieLowerNilpotencyIndex)"]},{"name" : "Tester(LieDerivedLength)","type" : "GAP_Attribute","filters" : ["Tester(LieDerivedLength)"]},{"name" : "Tester(SubgroupsOfIndexTwo)","type" : "GAP_Attribute","filters" : ["Tester(SubgroupsOfIndexTwo)"]},{"name" : "Tester(DihedralDepth)","type" : "GAP_Attribute","filters" : ["Tester(DihedralDepth)"]},{"name" : "Tester(DimensionBasis)","type" : "GAP_Attribute","filters" : ["Tester(DimensionBasis)"]},{"name" : "Tester(LieDimensionSubgroups)","type" : "GAP_Attribute","filters" : ["Tester(LieDimensionSubgroups)"]},{"name" : "Tester(LieUpperCodimensionSeries)","type" : "GAP_Attribute","filters" : ["Tester(LieUpperCodimensionSeries)"]},{"name" : "Tester(RootsAsMatrices)","type" : "GAP_Attribute","filters" : ["Tester(RootsAsMatrices)"]},{"name" : "IsSolvablePolynomial","type" : "GAP_Property","filters" : ["IsSolvablePolynomial","Tester(IsSolvablePolynomial)"]},{"name" : "Tester(IsSolvablePolynomial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSolvablePolynomial)"]},{"name" : "IsSeparablePolynomial","type" : "GAP_Property","filters" : ["IsSeparablePolynomial","Tester(IsSeparablePolynomial)"]},{"name" : "Tester(IsSeparablePolynomial)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSeparablePolynomial)"]},{"name" : "Tester(IsomorphismMatrixField)","type" : "GAP_Attribute","filters" : ["Tester(IsomorphismMatrixField)"]},{"name" : "Tester(GaloisGroupOnRoots)","type" : "GAP_Attribute","filters" : ["Tester(GaloisGroupOnRoots)"]},{"name" : "IsAffineCrystGroupOnRight","type" : "GAP_Property","filters" : ["CanComputeSize","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)","IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]},{"name" : "Tester(IsAffineCrystGroupOnRight)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAffineCrystGroupOnRight)"]},{"name" : "IsAffineCrystGroupOnLeft","type" : "GAP_Property","filters" : ["CanComputeSize","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)","IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]},{"name" : "Tester(IsAffineCrystGroupOnLeft)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAffineCrystGroupOnLeft)"]},{"name" : "IsAffineCrystGroupOnLeftOrRight","type" : "GAP_Property","filters" : ["CanComputeSize","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]},{"name" : "Tester(IsAffineCrystGroupOnLeftOrRight)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAffineCrystGroupOnLeftOrRight)"]},{"name" : "IsSpaceGroup","type" : "GAP_Property","filters" : ["IsSpaceGroup","Tester(IsSpaceGroup)"]},{"name" : "Tester(IsSpaceGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSpaceGroup)"]},{"name" : "IsStandardAffineCrystGroup","type" : "GAP_Property","filters" : ["IsStandardAffineCrystGroup","Tester(IsStandardAffineCrystGroup)"]},{"name" : "Tester(IsStandardAffineCrystGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsStandardAffineCrystGroup)"]},{"name" : "IsSymmorphicSpaceGroup","type" : "GAP_Property","filters" : ["IsSymmorphicSpaceGroup","Tester(IsSymmorphicSpaceGroup)"]},{"name" : "Tester(IsSymmorphicSpaceGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsSymmorphicSpaceGroup)"]},{"name" : "IsPointGroup","type" : "GAP_Property","filters" : ["IsPointGroup","Tester(IsPointGroup)"]},{"name" : "Tester(IsPointGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPointGroup)"]},{"name" : "Tester(NormalizerPointGroupInGLnZ)","type" : "GAP_Attribute","filters" : ["Tester(NormalizerPointGroupInGLnZ)"]},{"name" : "Tester(CentralizerPointGroupInGLnZ)","type" : "GAP_Attribute","filters" : ["Tester(CentralizerPointGroupInGLnZ)"]},{"name" : "Tester(AffineCrystGroupOfPointGroup)","type" : "GAP_Attribute","filters" : ["Tester(AffineCrystGroupOfPointGroup)"]},{"name" : "Tester(PointGroup)","type" : "GAP_Attribute","filters" : ["Tester(PointGroup)"]},{"name" : "Tester(PointHomomorphism)","type" : "GAP_Attribute","filters" : ["Tester(PointHomomorphism)"]},{"name" : "Tester(TranslationBasis)","type" : "GAP_Attribute","filters" : ["Tester(TranslationBasis)"]},{"name" : "Tester(InternalBasis)","type" : "GAP_Attribute","filters" : ["Tester(InternalBasis)"]},{"name" : "Tester(TransParts)","type" : "GAP_Attribute","filters" : ["Tester(TransParts)"]},{"name" : "Tester(TranslationNormalizer)","type" : "GAP_Attribute","filters" : ["Tester(TranslationNormalizer)"]},{"name" : "Tester(AffineNormalizer)","type" : "GAP_Attribute","filters" : ["Tester(AffineNormalizer)"]},{"name" : "IsPointHomomorphism","type" : "GAP_Property","filters" : ["IsPointHomomorphism","Tester(IsPointHomomorphism)"]},{"name" : "Tester(IsPointHomomorphism)","type" : "GAP_TrueProperty","implied" : ["Tester(IsPointHomomorphism)"]},{"name" : "Tester(NiceToCryst)","type" : "GAP_Attribute","filters" : ["Tester(NiceToCryst)"]},{"name" : "IsFromAffineCrystGroupToFpGroup","type" : "GAP_Property","filters" : ["IsFromAffineCrystGroupToFpGroup","Tester(IsFromAffineCrystGroupToFpGroup)"]},{"name" : "Tester(IsFromAffineCrystGroupToFpGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFromAffineCrystGroupToFpGroup)"]},{"name" : "IsFromAffineCrystGroupToPcpGroup","type" : "GAP_Property","filters" : ["IsFromAffineCrystGroupToPcpGroup","Tester(IsFromAffineCrystGroupToPcpGroup)"]},{"name" : "Tester(IsFromAffineCrystGroupToPcpGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsFromAffineCrystGroupToPcpGroup)"]},{"name" : "IsWyckoffPosition","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsWyckoffPosition"]},{"name" : "Tester(WyckoffStabilizer)","type" : "GAP_Attribute","filters" : ["Tester(WyckoffStabilizer)"]},{"name" : "Tester(WyckoffOrbit)","type" : "GAP_Attribute","filters" : ["Tester(WyckoffOrbit)"]},{"name" : "Tester(WyckoffPositions)","type" : "GAP_Attribute","filters" : ["Tester(WyckoffPositions)"]},{"name" : "IsWyckoffGraph","type" : "GAP_Filter","implied" : ["IsWyckoffGraph"]},{"name" : "Tester(CocVecs)","type" : "GAP_Attribute","filters" : ["Tester(CocVecs)"]},{"name" : "IsColorGroup","type" : "GAP_Property","filters" : ["IsColorGroup","Tester(IsColorGroup)"]},{"name" : "Tester(IsColorGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsColorGroup)"]},{"name" : "Tester(ColorSubgroup)","type" : "GAP_Attribute","filters" : ["Tester(ColorSubgroup)"]},{"name" : "Tester(ColorCosetList)","type" : "GAP_Attribute","filters" : ["Tester(ColorCosetList)"]},{"name" : "Tester(ColorPermGroup)","type" : "GAP_Attribute","filters" : ["Tester(ColorPermGroup)"]},{"name" : "Tester(ColorHomomorphism)","type" : "GAP_Attribute","filters" : ["Tester(ColorHomomorphism)"]},{"name" : "Tester(CrystCatRecord)","type" : "GAP_Attribute","filters" : ["Tester(CrystCatRecord)"]},{"name" : "IsAlmostCrystallographic","type" : "GAP_Property","filters" : ["IsAlmostCrystallographic","Tester(IsAlmostCrystallographic)"]},{"name" : "Tester(IsAlmostCrystallographic)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAlmostCrystallographic)"]},{"name" : "IsAlmostBieberbachGroup","type" : "GAP_Property","filters" : ["IsAlmostBieberbachGroup","Tester(IsAlmostBieberbachGroup)"]},{"name" : "Tester(IsAlmostBieberbachGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsAlmostBieberbachGroup)"]},{"name" : "Tester(AlmostCrystallographicInfo)","type" : "GAP_Attribute","filters" : ["Tester(AlmostCrystallographicInfo)"]},{"name" : "Tester(NaturalHomomorphismOnHolonomyGroup)","type" : "GAP_Attribute","filters" : ["Tester(NaturalHomomorphismOnHolonomyGroup)"]},{"name" : "Tester(HolonomyGroup)","type" : "GAP_Attribute","filters" : ["Tester(HolonomyGroup)"]},{"name" : "Tester(OrientationModule)","type" : "GAP_Attribute","filters" : ["Tester(OrientationModule)"]},{"name" : "Tester(BettiNumbers)","type" : "GAP_Attribute","filters" : ["Tester(BettiNumbers)"]},{"name" : "IsIsomorphismByFinitePolycyclicMatrixGroup","type" : "GAP_Property","filters" : ["IsIsomorphismByFinitePolycyclicMatrixGroup","Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"]},{"name" : "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"]},{"name" : "IsIsomorphismByPolycyclicMatrixGroup","type" : "GAP_Property","filters" : ["IsIsomorphismByPolycyclicMatrixGroup","Tester(IsIsomorphismByPolycyclicMatrixGroup)"]},{"name" : "Tester(IsIsomorphismByPolycyclicMatrixGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsIsomorphismByPolycyclicMatrixGroup)"]},{"name" : "IsTriangularizableMatGroup","type" : "GAP_Property","filters" : ["IsTriangularizableMatGroup","Tester(IsTriangularizableMatGroup)"]},{"name" : "Tester(IsTriangularizableMatGroup)","type" : "GAP_TrueProperty","implied" : ["Tester(IsTriangularizableMatGroup)"]},{"name" : "IsZ_pi","type" : "GAP_Property","filters" : ["IsZ_pi","Tester(IsZ_pi)"]},{"name" : "Tester(IsZ_pi)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZ_pi)"]},{"name" : "Tester(NoninvertiblePrimes)","type" : "GAP_Attribute","filters" : ["Tester(NoninvertiblePrimes)"]},{"name" : "IsResidueClassUnion","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion"]},{"name" : "IsResidueClassUnionOfZ","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZ","IsResidueClassUnionOfZorZ_pi"]},{"name" : "IsResidueClassUnionOfZxZ","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZxZ"]},{"name" : "IsResidueClassUnionOfZ_pi","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZ_pi","IsResidueClassUnionOfZorZ_pi"]},{"name" : "IsResidueClassUnionOfGFqx","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfGFqx"]},{"name" : "IsResidueClassUnionOfZorZ_pi","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZorZ_pi"]},{"name" : "IsResidueClassUnionResidueListRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsResidueClassUnionResidueListRep"]},{"name" : "IsResidueClassUnionsIteratorRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsResidueClassUnionsIteratorRep"]},{"name" : "IsResidueClass","type" : "GAP_Property","filters" : ["IsResidueClass","Tester(IsResidueClass)"]},{"name" : "Tester(IsResidueClass)","type" : "GAP_TrueProperty","implied" : ["Tester(IsResidueClass)"]},{"name" : "Tester(UnderlyingIndeterminate)","type" : "GAP_Attribute","filters" : ["Tester(UnderlyingIndeterminate)"]},{"name" : "IsZxZ","type" : "GAP_Property","filters" : ["IsZxZ","Tester(IsZxZ)"]},{"name" : "Tester(IsZxZ)","type" : "GAP_TrueProperty","implied" : ["Tester(IsZxZ)"]},{"name" : "Tester(SizeOfSmallestResidueClassRing)","type" : "GAP_Attribute","filters" : ["Tester(SizeOfSmallestResidueClassRing)"]},{"name" : "Tester(Density)","type" : "GAP_Attribute","filters" : ["Tester(Density)"]},{"name" : "IsUnionOfResidueClassesWithFixedRepresentatives","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives"]},{"name" : "IsUnionOfResidueClassesOfZWithFixedRepresentatives","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfZWithFixedRepresentatives","IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"]},{"name" : "IsUnionOfResidueClassesOfZ_piWithFixedRepresentatives","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfZ_piWithFixedRepresentatives","IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"]},{"name" : "IsUnionOfResidueClassesOfGFqxWithFixedRepresentatives","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfGFqxWithFixedRepresentatives"]},{"name" : "IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives","type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"]},{"name" : "IsUnionOfResidueClassesWithFixedRepsStandardRep","type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsUnionOfResidueClassesWithFixedRepsStandardRep"]},{"name" : "IsResidueClassWithFixedRepresentative","type" : "GAP_Property","filters" : ["IsResidueClassWithFixedRepresentative","Tester(IsResidueClassWithFixedRepresentative)"]},{"name" : "Tester(IsResidueClassWithFixedRepresentative)","type" : "GAP_TrueProperty","implied" : ["Tester(IsResidueClassWithFixedRepresentative)"]},{"name" : "IsOverlappingFree","type" : "GAP_Property","filters" : ["IsOverlappingFree","Tester(IsOverlappingFree)"]},{"name" : "Tester(IsOverlappingFree)","type" : "GAP_TrueProperty","implied" : ["Tester(IsOverlappingFree)"]},{"name" : "Tester(Rho)","type" : "GAP_Attribute","filters" : ["Tester(Rho)"]},{"name" : "Name","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "InfoText","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "String","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsImpossible","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "CollectionsFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "ElementsFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "IsEmpty","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "IsTrivial","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "IsNonTrivial","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "IsFinite","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "IsWholeFamily","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "Size","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "Representative","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "RepresentativeSmallest","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "PseudoRandomSeed","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "Enumerator","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "EnumeratorSorted","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "UnderlyingCollection","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "AsList","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "AsSortedList","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "AsSSortedList","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "CanEasilyCompareElements","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "CanEasilySortElements","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "RandomizerAttr","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "CheapRandomizerAttr","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "IsSmallList","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "Length","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "ConstantTimeAccessList","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "IsSortedList","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "IsSSortedList","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "IsNSortedList","type" : "GAP_Attribute","filters" : ["IsDenseList"]},{"name" : "IsDuplicateFree","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "IsPositionsList","type" : "GAP_Attribute","filters" : ["IsDenseList"]},{"name" : "AsDuplicateFreeList","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "SortingPerm","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "NestingDepthA","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "NestingDepthM","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsZero","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithZero","IsAdditiveElement"]},{"name" : "IsOne","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElementWithOne"]},{"name" : "ZeroImmutable","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithZero","IsAdditiveElement"]},{"name" : "AdditiveInverseImmutable","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement"]},{"name" : "OneImmutable","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElementWithOne"]},{"name" : "InverseImmutable","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElementWithInverse"]},{"name" : "Int","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "Rat","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "Characteristic","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "Order","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElementWithOne"]},{"name" : "NormedRowVector","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsHomogeneousList","IsOddAdditiveNestingDepthObject","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElementWithInverse)"]},{"name" : "IsCommutativeFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "IsSkewFieldFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "IsUFDFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "AdditiveElementsAsMultiplicativeElementsFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "AdditiveElementAsMultiplicativeElement","type" : "GAP_Attribute","filters" : ["IsAdditiveElement"]},{"name" : "IsIdempotent","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElement"]},{"name" : "DegreeFFE","type" : "GAP_Attribute","filters" : ["IsFFE"]},{"name" : "IntFFE","type" : "GAP_Attribute","filters" : ["IsFFE"]},{"name" : "IntFFESymm","type" : "GAP_Attribute","filters" : ["IsFFE"]},{"name" : "AsInternalFFE","type" : "GAP_Attribute","filters" : ["IsFFE"]},{"name" : "GeneratorsOfDomain","type" : "GAP_Attribute","filters" : ["IsGeneralizedDomain","IsCollection"]},{"name" : "ParentAttr","type" : "GAP_Attribute","filters" : ["IsGeneralizedDomain","IsCollection"]},{"name" : "IsIntegralCyclotomic","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "Conductor","type" : "GAP_Attribute","filters" : ["IsCyc"]},{"name" : "RecNames","type" : "GAP_Attribute","filters" : ["IsRecord"]},{"name" : "IsRectangularTable","type" : "GAP_Attribute","filters" : ["IsList"]},{"name" : "SmallestGeneratorPerm","type" : "GAP_Attribute","filters" : ["IsPerm"]},{"name" : "SmallestMovedPoint","type" : "GAP_Attribute","filters" : ["IsPerm"]},{"name" : "LargestMovedPoint","type" : "GAP_Attribute","filters" : ["IsPerm"]},{"name" : "NrMovedPoints","type" : "GAP_Attribute","filters" : ["IsPerm"]},{"name" : "MovedPoints","type" : "GAP_Attribute","filters" : ["IsPerm"]},{"name" : "SignPerm","type" : "GAP_Attribute","filters" : ["IsPerm"]},{"name" : "CycleStructurePerm","type" : "GAP_Attribute","filters" : ["IsPerm"]},{"name" : "Cos","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Sin","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Tan","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Sec","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Csc","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Cot","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Asin","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Acos","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Atan","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Cosh","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Sinh","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Tanh","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Sech","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Csch","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Coth","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Asinh","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Acosh","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Atanh","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Log2","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Log10","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Log1p","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Exp","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Exp2","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Exp10","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Expm1","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "CubeRoot","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Square","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Ceil","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Floor","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Round","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Trunc","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "FrExp","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Argument","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "AbsoluteValue","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Frac","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "SinCos","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Erf","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Zeta","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Gamma","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "ComplexI","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "PrecisionFloat","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "SignFloat","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Sup","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Inf","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "Mid","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "AbsoluteDiameter","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "RelativeDiameter","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "IsPInfinity","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "IsNInfinity","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "IsXInfinity","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "IsNaN","type" : "GAP_Attribute","filters" : ["IsFloat"]},{"name" : "ComponentsOfDirectProductElementsFamily","type" : "GAP_Attribute","filters" : ["CategoryFamily(IsDirectProductElement)"]},{"name" : "EmptyRowVector","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "GeneratorsOfExtASet","type" : "GAP_Attribute","filters" : ["IsExtASet"]},{"name" : "AdditivelyActingDomain","type" : "GAP_Attribute","filters" : ["IsExtASet"]},{"name" : "IsLeftActedOnByDivisionRing","type" : "GAP_Attribute","filters" : ["IsExtLSet","IsLeftActedOnByRing"]},{"name" : "GeneratorsOfExtLSet","type" : "GAP_Attribute","filters" : ["IsExtLSet"]},{"name" : "LeftActingDomain","type" : "GAP_Attribute","filters" : ["IsExtLSet"]},{"name" : "GeneratorsOfExtRSet","type" : "GAP_Attribute","filters" : ["IsExtRSet"]},{"name" : "RightActingDomain","type" : "GAP_Attribute","filters" : ["IsExtRSet"]},{"name" : "GeneratorsOfExtUSet","type" : "GAP_Attribute","filters" : ["IsExtUSet"]},{"name" : "UpperActingDomain","type" : "GAP_Attribute","filters" : ["IsExtRSet"]},{"name" : "FamilyRange","type" : "GAP_Attribute","filters" : ["CategoryFamily(IsGeneralMapping)"]},{"name" : "FamilySource","type" : "GAP_Attribute","filters" : ["CategoryFamily(IsGeneralMapping)"]},{"name" : "FamiliesOfGeneralMappingsAndRanges","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "IsConstantTimeAccessGeneralMapping","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsEndoGeneralMapping","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsTotal","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsSingleValued","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsInjective","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsSurjective","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "Range","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "Source","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "UnderlyingRelation","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "UnderlyingGeneralMapping","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "IdentityMapping","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "InverseGeneralMapping","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "ImagesSource","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "PreImagesRange","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "MappingGeneratorsImages","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "RespectsMultiplication","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "RespectsOne","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "RespectsInverses","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "KernelOfMultiplicativeGeneralMapping","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "CoKernelOfMultiplicativeGeneralMapping","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "RespectsAddition","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "RespectsZero","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "RespectsAdditiveInverses","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "KernelOfAdditiveGeneralMapping","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "CoKernelOfAdditiveGeneralMapping","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "RespectsScalarMultiplication","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsFieldHomomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "TransformsMultiplicationIntoAddition","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "TranformsOneIntoZero","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "TransformsInversesIntoAdditiveInverses","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "TransformsAdditionIntoMultiplication","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "TransformsZeroIntoOne","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "TransformsAdditiveInversesIntoInverses","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "Successors","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "DegreeOfBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsReflexiveBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsSymmetricBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsTransitiveBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsAntisymmetricBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsPreOrderBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsPartialOrderBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsLatticeOrderBinaryRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsEquivalenceRelation","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "IsHasseDiagram","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "PartialOrderOfHasseDiagram","type" : "GAP_Attribute","filters" : ["IsEndoGeneralMapping"]},{"name" : "EquivalenceRelationPartition","type" : "GAP_Attribute","filters" : ["IsEquivalenceRelation"]},{"name" : "GeneratorsOfEquivalenceRelationPartition","type" : "GAP_Attribute","filters" : ["IsEquivalenceRelation"]},{"name" : "EquivalenceClassRelation","type" : "GAP_Attribute","filters" : ["IsEquivalenceClass"]},{"name" : "EquivalenceClasses","type" : "GAP_Attribute","filters" : ["IsEquivalenceRelation"]},{"name" : "AsMagma","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "GeneratorsOfMagma","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "GeneratorsOfMagmaWithOne","type" : "GAP_Attribute","filters" : ["IsMagmaWithOne"]},{"name" : "GeneratorsOfMagmaWithInverses","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses"]},{"name" : "IsGeneratorsOfMagmaWithInverses","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "TrivialSubmagmaWithOne","type" : "GAP_Attribute","filters" : ["IsMagmaWithOne"]},{"name" : "IsAssociative","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "IsCommutative","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "MultiplicativeNeutralElement","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "Centre","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "Idempotents","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "CentralizerInParent","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "MagmaGeneratorsOfFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "GeneratorsOfMagmaIdeal","type" : "GAP_Attribute","filters" : ["IsMagma","IsLeftActedOnBySuperset","IsMagma","IsRightActedOnBySuperset"]},{"name" : "MultiplicativeZero","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElementWithZero"]},{"name" : "InjectionZeroMagma","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "MagmaWithZeroAdjoined","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElementWithZero","IsMagmaWithZeroAdjoinedElementRep"]},{"name" : "UnderlyingInjectionZeroMagma","type" : "GAP_Attribute","filters" : ["IsMagmaWithZeroAdjoined"]},{"name" : "GeneratingPairsOfLeftMagmaCongruence","type" : "GAP_Attribute","filters" : ["IsLeftMagmaCongruence"]},{"name" : "PartialClosureOfCongruence","type" : "GAP_Attribute","filters" : ["IsLeftMagmaCongruence"]},{"name" : "GeneratingPairsOfRightMagmaCongruence","type" : "GAP_Attribute","filters" : ["IsRightMagmaCongruence"]},{"name" : "GeneratingPairsOfMagmaCongruence","type" : "GAP_Attribute","filters" : ["IsMagmaCongruence"]},{"name" : "IsLeftSemigroupCongruence","type" : "GAP_Attribute","filters" : ["IsLeftMagmaCongruence"]},{"name" : "IsRightSemigroupCongruence","type" : "GAP_Attribute","filters" : ["IsRightMagmaCongruence"]},{"name" : "IsSemigroupCongruence","type" : "GAP_Attribute","filters" : ["IsMagmaCongruence"]},{"name" : "IsReesCongruence","type" : "GAP_Attribute","filters" : ["IsSemigroupCongruence"]},{"name" : "AsSemigroup","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "IsGeneratorsOfSemigroup","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "CayleyGraphSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "CayleyGraphDualSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsZeroGroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsSimpleSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsZeroSimpleSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "ANonReesCongruenceOfSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsReesCongruenceSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsRegularSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsInverseSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "NilpotencyDegree","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsBand","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsBrandtSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsCliffordSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsCommutativeSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsCompletelyRegularSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsCompletelySimpleSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsGroupAsSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsIdempotentGenerated","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsLeftZeroSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsMonogenicSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsMonoidAsSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsNilpotentSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsOrthodoxSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsRectangularBand","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsRightZeroSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsSemiband","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsSemilattice","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsZeroSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsLeftSemigroupIdeal","type" : "GAP_Attribute","filters" : ["IsMagma","IsLeftActedOnBySuperset"]},{"name" : "IsRightSemigroupIdeal","type" : "GAP_Attribute","filters" : ["IsMagma","IsRightActedOnBySuperset"]},{"name" : "IsSemigroupIdeal","type" : "GAP_Attribute","filters" : ["IsMagma","IsLeftActedOnBySuperset","IsMagma","IsRightActedOnBySuperset"]},{"name" : "ReesCongruenceOfSemigroupIdeal","type" : "GAP_Attribute","filters" : ["IsMagma","IsLeftActedOnBySuperset","IsMagma","IsRightActedOnBySuperset"]},{"name" : "AsMonoid","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "NameIsomorphismClass","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsCyclic","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsElementaryAbelian","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsFinitelyGeneratedGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSubsetLocallyFiniteGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "KnowsHowToDecompose","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PrimePGroup","type" : "GAP_Attribute","filters" : ["IsPGroup"]},{"name" : "PClassPGroup","type" : "GAP_Attribute","filters" : ["IsPGroup"]},{"name" : "RankPGroup","type" : "GAP_Attribute","filters" : ["IsPGroup"]},{"name" : "IsNilpotentGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPerfectGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSporadicSimpleGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSimpleGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsAlmostSimpleGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSupersolvableGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsMonomialGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSolvableGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPolycyclicGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AbelianInvariants","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsInfiniteAbelianizationGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AsGroup","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "ChiefSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CommutatorFactorGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CompositionSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ConjugacyClasses","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ConjugacyClassesMaximalSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MaximalSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MaximalSubgroupClassReps","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PerfectResiduum","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "RepresentativesPerfectSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "RepresentativesSimpleSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ConjugacyClassesPerfectSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ConjugacyClassesSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LatticeSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DerivedLength","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "HirschLength","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DerivedSeriesOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DerivedSubgroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MaximalAbelianQuotient","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CommutatorLength","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DimensionsLoewyFactors","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ElementaryAbelianSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ElementaryAbelianSeriesLargeSteps","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Exponent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FittingSubgroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PrefrattiniSubgroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FrattiniSubgroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "InvariantForm","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "JenningsSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LowerCentralSeriesOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NilpotencyClassOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MaximalNormalSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalMaximalSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MinimalNormalSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NrConjugacyClasses","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedOmegas","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedAgemos","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "RadicalGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "RationalClasses","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "GeneratorsSmallest","type" : "GAP_Attribute","filters" : ["IsMagma"]},{"name" : "LargestElementGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MinimalGeneratingSet","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SmallGeneratingSet","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SupersolvableResiduum","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComplementSystem","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SylowSystem","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "HallSystem","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Socle","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "UpperCentralSeriesOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CoreInParent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IndexInParent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IndexInWholeGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IndependentGeneratorsOfAbelianGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","IsCommutative"]},{"name" : "IsNormalInParent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedIsPNilpotents","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedIsPSolvables","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalClosureInParent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalizerInParent","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "ComputedPCentralSeriess","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedPRumps","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedPCores","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SubnormalSeriesInParent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedSylowSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedSylowComplements","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedHallSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "GrowthFunctionOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","Tester(GeneratorsOfMagmaWithInverses)"]},{"name" : "ElementTestFunction","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "RightTransversalInParent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsomorphismTypeInfoFiniteSimpleGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsomorphismPcGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsomorphismSpecialPcGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsomorphismPermGroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsomorphismFpGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PrimePowerComponents","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElement"]},{"name" : "IsGeneratorsOfInverseSemigroup","type" : "GAP_Attribute","filters" : ["IsListOrCollection"]},{"name" : "GeneratorsOfInverseMonoid","type" : "GAP_Attribute","filters" : ["IsInverseSemigroup"]},{"name" : "GeneratorsOfInverseSemigroup","type" : "GAP_Attribute","filters" : ["IsInverseSemigroup"]},{"name" : "AsInverseSemigroup","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "AsInverseMonoid","type" : "GAP_Attribute","filters" : ["IsCollection"]},{"name" : "ReverseNaturalPartialOrder","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "NaturalPartialOrder","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsAdditivelyCommutative","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagma"]},{"name" : "GeneratorsOfNearAdditiveMagma","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagma"]},{"name" : "GeneratorsOfNearAdditiveMagmaWithZero","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagmaWithZero"]},{"name" : "GeneratorsOfNearAdditiveGroup","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup"]},{"name" : "TrivialSubnearAdditiveMagmaWithZero","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagmaWithZero"]},{"name" : "AdditiveNeutralElement","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagma"]},{"name" : "IsLDistributive","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "IsRDistributive","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "GeneratorsOfSemiring","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "GeneratorsOfSemiringWithOne","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagmaWithOne","IsLDistributive","IsRDistributive"]},{"name" : "GeneratorsOfSemiringWithZero","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagmaWithZero","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "GeneratorsOfSemiringWithOneAndZero","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagmaWithZero","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagmaWithOne","IsLDistributive","IsRDistributive"]},{"name" : "AsSemiring","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "AsSemiringWithOne","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "AsSemiringWithZero","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "AsSemiringWithOneAndZero","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "CentralIdempotentsOfSemiring","type" : "GAP_Attribute","filters" : ["IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "AsNearRing","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "AsRing","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]},{"name" : "GeneratorsOfRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "GeneratorsOfRingWithOne","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne"]},{"name" : "IsAnticommutative","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsIntegralRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsJacobianRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsZeroSquaredRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsZeroMultiplicationRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "Units","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsGeneralizedCartanMatrix","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "BaseMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "BaseOrthogonalSpaceMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "DefaultFieldOfMatrix","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "DepthOfUpperTriangularMatrix","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "DeterminantMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "DimensionsMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "NullspaceMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "TriangulizedNullspaceMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "ProjectiveOrder","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "RankMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "SemiEchelonMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "SemiEchelonMatTransformation","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "TransposedMatImmutable","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "IsMonomialMatrix","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "JordanDecomposition","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "CharacteristicPolynomial","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "BaseIntMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable","CategoryCollections(CategoryCollections(IsCyclotomic))"]},{"name" : "NullspaceIntMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable","CategoryCollections(CategoryCollections(IsCyclotomic))"]},{"name" : "AbelianInvariantsOfList","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsCyclotomic)"]},{"name" : "MatrixByBlockMatrix","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "IsTwoSidedIdealInParent","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsLeftIdealInParent","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsRightIdealInParent","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "GeneratorsOfTwoSidedIdeal","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "GeneratorsOfLeftIdeal","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "GeneratorsOfRightIdeal","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "LeftActingRingOfIdeal","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "RightActingRingOfIdeal","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsFiniteDimensional","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "IsFullRowModule","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "IsFullMatrixModule","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "Dimension","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "GeneratorsOfLeftOperatorAdditiveGroup","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum"]},{"name" : "GeneratorsOfRightOperatorAdditiveGroup","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtRSet","IsDistributiveROpDSum"]},{"name" : "IsRowModule","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "IsMatrixModule","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "DimensionOfVectors","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "IsCanonicalBasis","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IsCanonicalBasisFullRowModule","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IsCanonicalBasisFullMatrixModule","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IsIntegralBasis","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IsNormalBasis","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IsSemiEchelonized","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "BasisVectors","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "EnumeratorByBasis","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "StructureConstantsTable","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "UnderlyingLeftModule","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "Basis","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "SemiEchelonBasis","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "NiceBasis","type" : "GAP_Attribute","filters" : ["IsBasisByNiceBasis"]},{"name" : "NiceFreeLeftModule","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "NiceFreeLeftModuleInfo","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule","IsHandledByNiceBasis"]},{"name" : "CanonicalBasis","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "NormedRowVectors","type" : "GAP_Attribute","filters" : ["IsGaussianSpace"]},{"name" : "Subspaces","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne"]},{"name" : "OrthogonalSpaceInFullRowSpace","type" : "GAP_Attribute","filters" : ["IsGaussianSpace"]},{"name" : "IsVectorSpaceHomomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "AsLeftModuleGeneralMappingByImages","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsFullHomModule","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule"]},{"name" : "IsPseudoCanonicalBasisFullHomModule","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IsSimpleAlgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "GeneratorsOfLeftOperatorRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "GeneratorsOfLeftOperatorRingWithOne","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd"]},{"name" : "PowerSubalgebraSeries","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "AdjointBasis","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IndicesOfAdjointBasis","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "RadicalOfAlgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "DirectSumDecomposition","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "NullAlgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "LieAlgebraByDomain","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "LeviMalcevDecomposition","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "Grading","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "CoefficientsAndMagmaElements","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations"]},{"name" : "ZeroCoefficient","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations"]},{"name" : "IsGroupRing","type" : "GAP_Attribute","filters" : ["IsFreeMagmaRing"]},{"name" : "UnderlyingMagma","type" : "GAP_Attribute","filters" : ["IsFreeMagmaRing"]},{"name" : "AugmentationIdeal","type" : "GAP_Attribute","filters" : ["IsFreeMagmaRing"]},{"name" : "IsFullFpAlgebra","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","CategoryCollections(IsElementOfFpAlgebra)"]},{"name" : "FreeGeneratorsOfFpAlgebra","type" : "GAP_Attribute","filters" : ["IsSubalgebraFpAlgebra","IsFullFpAlgebra"]},{"name" : "RelatorsOfFpAlgebra","type" : "GAP_Attribute","filters" : ["IsSubalgebraFpAlgebra","IsFullFpAlgebra"]},{"name" : "FreeAlgebraOfFpAlgebra","type" : "GAP_Attribute","filters" : ["IsSubalgebraFpAlgebra","IsFullFpAlgebra"]},{"name" : "IsNormalForm","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "NiceNormalFormByExtRepFunction","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "NiceAlgebraMonomorphism","type" : "GAP_Attribute","filters" : ["IsSubalgebraFpAlgebra"]},{"name" : "IsLieAbelian","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "IsLieNilpotent","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "IsRestrictedLieAlgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieDerivedSubalgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieDerivedSeries","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "IsLieSolvable","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieLowerCentralSeries","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieUpperCentralSeries","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieCentre","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "RightDerivations","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "LeftDerivations","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "KillingMatrix","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "CartanSubalgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "PthPowerImages","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "NonNilpotentElement","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieNilRadical","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieSolvableRadical","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "SemiSimpleType","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieCentralizerInParent","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieNormalizerInParent","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "PowerS","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "UnderlyingLieAlgebra","type" : "GAP_Attribute","filters" : ["IsRootSystemFromLieAlgebra"]},{"name" : "RootSystem","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "PositiveRoots","type" : "GAP_Attribute","filters" : ["IsRootSystem"]},{"name" : "NegativeRoots","type" : "GAP_Attribute","filters" : ["IsRootSystem"]},{"name" : "PositiveRootVectors","type" : "GAP_Attribute","filters" : ["IsRootSystemFromLieAlgebra"]},{"name" : "NegativeRootVectors","type" : "GAP_Attribute","filters" : ["IsRootSystemFromLieAlgebra"]},{"name" : "SimpleSystem","type" : "GAP_Attribute","filters" : ["IsRootSystem"]},{"name" : "CartanMatrix","type" : "GAP_Attribute","filters" : ["IsRootSystem"]},{"name" : "BilinearFormMat","type" : "GAP_Attribute","filters" : ["IsRootSystem"]},{"name" : "CanonicalGenerators","type" : "GAP_Attribute","filters" : ["IsRootSystemFromLieAlgebra"]},{"name" : "ChevalleyBasis","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "UniversalEnvelopingAlgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "JenningsLieAlgebra","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PCentralLieAlgebra","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "IsFullSCAlgebra","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","CategoryCollections(IsSCAlgebraObj)"]},{"name" : "IsCanonicalBasisFullSCAlgebra","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "IsomorphismFpFLMLOR","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "IsomorphismMatrixFLMLOR","type" : "GAP_Attribute","filters" : ["IsFreeLeftModule","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "IsomorphismSCFLMLOR","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "LieFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "UnderlyingFamily","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "LieObject","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]},{"name" : "UnderlyingRingElement","type" : "GAP_Attribute","filters" : ["IsLieObject"]},{"name" : "IsAlgebraModule","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne"]},{"name" : "IsLeftAlgebraModule","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne"]},{"name" : "IsRightAlgebraModule","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne"]},{"name" : "LeftActingAlgebra","type" : "GAP_Attribute","filters" : ["IsAlgebraModule"]},{"name" : "RightActingAlgebra","type" : "GAP_Attribute","filters" : ["IsAlgebraModule"]},{"name" : "GeneratorsOfAlgebraModule","type" : "GAP_Attribute","filters" : ["IsAlgebraModule"]},{"name" : "AdjointModule","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "FaithfulModule","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd"]},{"name" : "IsWeylGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "WeylGroup","type" : "GAP_Attribute","filters" : ["IsRootSystem"]},{"name" : "SparseCartanMatrix","type" : "GAP_Attribute","filters" : ["IsWeylGroup"]},{"name" : "LongestWeylWordPerm","type" : "GAP_Attribute","filters" : ["IsWeylGroup"]},{"name" : "PositiveRootsAsWeights","type" : "GAP_Attribute","filters" : ["IsRootSystem"]},{"name" : "LatticeGeneratorsInUEA","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "PrimeDivisors","type" : "GAP_Attribute","filters" : ["IsInt"]},{"name" : "StandardGeneratorsSubringSCRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","CategoryCollections(IsSCRingObj)"]},{"name" : "Subrings","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "Ideals","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "DirectSumInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "RationalFunctionsFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "CoefficientsFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "NumeratorOfRationalFunction","type" : "GAP_Attribute","filters" : ["IsPolynomialFunction"]},{"name" : "DenominatorOfRationalFunction","type" : "GAP_Attribute","filters" : ["IsRationalFunction"]},{"name" : "IsPolynomial","type" : "GAP_Attribute","filters" : ["IsPolynomialFunction"]},{"name" : "AsPolynomial","type" : "GAP_Attribute","filters" : ["IsPolynomialFunction","IsPolynomial"]},{"name" : "IsUnivariateRationalFunction","type" : "GAP_Attribute","filters" : ["IsRationalFunction"]},{"name" : "IsLaurentPolynomial","type" : "GAP_Attribute","filters" : ["IsPolynomialFunction"]},{"name" : "IsConstantRationalFunction","type" : "GAP_Attribute","filters" : ["IsPolynomialFunction"]},{"name" : "ExtRepNumeratorRatFun","type" : "GAP_Attribute","filters" : ["IsPolynomialFunction"]},{"name" : "ExtRepDenominatorRatFun","type" : "GAP_Attribute","filters" : ["IsRationalFunction"]},{"name" : "ExtRepPolynomialRatFun","type" : "GAP_Attribute","filters" : ["IsPolynomialFunction","IsPolynomial"]},{"name" : "CoefficientsOfLaurentPolynomial","type" : "GAP_Attribute","filters" : ["IsLaurentPolynomial"]},{"name" : "IndeterminateNumberOfUnivariateRationalFunction","type" : "GAP_Attribute","filters" : ["IsUnivariateRationalFunction"]},{"name" : "IndeterminateOfUnivariateRationalFunction","type" : "GAP_Attribute","filters" : ["IsUnivariateRationalFunction"]},{"name" : "CoefficientsOfUnivariatePolynomial","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsUnivariateRationalFunction"]},{"name" : "DegreeOfLaurentPolynomial","type" : "GAP_Attribute","filters" : ["IsLaurentPolynomial"]},{"name" : "CoefficientsOfUnivariateRationalFunction","type" : "GAP_Attribute","filters" : ["IsUnivariateRationalFunction"]},{"name" : "Derivative","type" : "GAP_Attribute","filters" : ["IsUnivariateRationalFunction"]},{"name" : "Discriminant","type" : "GAP_Attribute","filters" : ["IsPolynomial"]},{"name" : "PrimeField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing"]},{"name" : "IsPrimeField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing"]},{"name" : "DefiningPolynomial","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "DegreeOverPrimeField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing"]},{"name" : "GeneratorsOfDivisionRing","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing"]},{"name" : "NormalBase","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "PrimitiveElement","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing"]},{"name" : "PrimitiveRoot","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative","IsFinite"]},{"name" : "RootOfDefiningPolynomial","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "Subfields","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "Conjugates","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]},{"name" : "Norm","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]},{"name" : "Trace","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]},{"name" : "GaloisGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "ComplexConjugate","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]},{"name" : "RealPart","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]},{"name" : "ImaginaryPart","type" : "GAP_Attribute","filters" : ["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]},{"name" : "FrobeniusAutomorphism","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "ModulusOfZmodnZObj","type" : "GAP_Attribute","filters" : ["IsZmodnZObj"]},{"name" : "Cyclotomic","type" : "GAP_Attribute","filters" : ["IsZmodnZepsObj"]},{"name" : "IsRingOfIntegralCyclotomics","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne"]},{"name" : "GaloisMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "RationalizedMat","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "IsNumberField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "IsAbelianNumberField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "IsCyclotomicField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInversesIfNonzero","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNonTrivial","IsAssociative","IsEuclideanRing","IsCommutative"]},{"name" : "GaloisStabilizer","type" : "GAP_Attribute","filters" : ["IsAbelianNumberField"]},{"name" : "ExponentOfPowering","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","IsTotal","IsSingleValued"]},{"name" : "CoefficientsRing","type" : "GAP_Attribute","filters" : ["IsPolynomialRing"]},{"name" : "IndeterminatesOfPolynomialRing","type" : "GAP_Attribute","filters" : ["IsPolynomialRing"]},{"name" : "SplittingField","type" : "GAP_Attribute","filters" : ["IsPolynomial"]},{"name" : "IrrFacsPol","type" : "GAP_Attribute","filters" : ["IsPolynomial"]},{"name" : "MinimizedBombieriNorm","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsRationalFunctionsFamilyElement"]},{"name" : "AlgebraicElementsFamilies","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsUnivariateRationalFunction"]},{"name" : "DefectApproximation","type" : "GAP_Attribute","filters" : ["IsAlgebraicExtension"]},{"name" : "IsFreeSemigroup","type" : "GAP_Attribute","filters" : ["CategoryCollections((IsWord and IsAssociativeElement))","IsMagma","IsAssociative"]},{"name" : "IsFreeMonoid","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","IsMagmaWithOne","IsAssociative"]},{"name" : "NumberSyllables","type" : "GAP_Attribute","filters" : ["IsWord","IsAssociativeElement"]},{"name" : "BaseDomain","type" : "GAP_Attribute","filters" : ["IsRowVectorObj"]},{"name" : "RowLength","type" : "GAP_Attribute","filters" : ["IsMatrixObj"]},{"name" : "IsBuiltFromAdditiveMagmaWithInverses","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsBuiltFromMagma","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsBuiltFromMagmaWithOne","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsBuiltFromMagmaWithInverses","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsBuiltFromGroup","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsBuiltFromSemigroup","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsBuiltFromMonoid","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "SemigroupOfRewritingSystem","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "MonoidOfRewritingSystem","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "ConfluentRws","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "GeneratorsOfRws","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "NumberGeneratorsOfRws","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "Rules","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "OrderingOfRewritingSystem","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "IsConfluent","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "IsReduced","type" : "GAP_Attribute","filters" : ["IsRewritingSystem","IsMutable"]},{"name" : "RelativeOrders","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "DefiningPcgs","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "MonomialComparisonFunction","type" : "GAP_Attribute","filters" : ["IsMonomialOrdering"]},{"name" : "MonomialExtrepComparisonFun","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "OccuringVariableIndices","type" : "GAP_Attribute","filters" : ["IsMonomialOrdering"]},{"name" : "StoredGroebnerBasis","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","CategoryCollections(IsRationalFunction)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]},{"name" : "PcGroupWithPcgs","type" : "GAP_Attribute","filters" : ["IsModuloPcgs"]},{"name" : "GroupOfPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "OneOfPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "PcSeries","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IsPcgsElementaryAbelianSeries","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "PcgsElementaryAbelianSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IndicesEANormalSteps","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "EANormalSeriesByPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IsPcgsCentralSeries","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "PcgsCentralSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IndicesCentralNormalSteps","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "CentralNormalSeriesByPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IsPcgsPCentralSeriesPGroup","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "PcgsPCentralSeriesPGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IndicesPCentralNormalStepsPGroup","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "PCentralNormalSeriesByPcgsPGroup","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IsPcgsChiefSeries","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "PcgsChiefSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IndicesChiefNormalSteps","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "ChiefNormalSeriesByPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IndicesNormalSteps","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "NormalSeriesByPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IsPrimeOrdersPcgs","type" : "GAP_Attribute","filters" : ["IsGeneralPcgs"]},{"name" : "IsFiniteOrdersPcgs","type" : "GAP_Attribute","filters" : ["IsGeneralPcgs"]},{"name" : "RefinedPcGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsomorphismRefinedPcGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LeadCoeffsIGS","type" : "GAP_Attribute","filters" : ["IsInducedPcgs"]},{"name" : "ParentPcgs","type" : "GAP_Attribute","filters" : ["IsInducedPcgs"]},{"name" : "CanonicalPcgs","type" : "GAP_Attribute","filters" : ["IsInducedPcgs"]},{"name" : "IsCanonicalPcgs","type" : "GAP_Attribute","filters" : ["IsInducedPcgs"]},{"name" : "IsParentPcgsFamilyPcgs","type" : "GAP_Attribute","filters" : ["IsInducedPcgs"]},{"name" : "ElementaryAbelianSubseries","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IsFamilyPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "DenominatorOfModuloPcgs","type" : "GAP_Attribute","filters" : ["IsModuloPcgs"]},{"name" : "NumeratorOfModuloPcgs","type" : "GAP_Attribute","filters" : ["IsModuloPcgs"]},{"name" : "IsNumeratorParentPcgsFamilyPcgs","type" : "GAP_Attribute","filters" : ["IsModuloPcgs"]},{"name" : "IsSpecialPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "SpecialPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "LGHeads","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "LGTails","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "LGWeights","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "LGLayers","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "LGFirst","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "LGLength","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "InducedPcgsWrtSpecialPcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CanonicalPcgsWrtSpecialPcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsInducedPcgsWrtSpecialPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "IsCanonicalPcgsWrtSpecialPcgs","type" : "GAP_Attribute","filters" : ["IsPcgs"]},{"name" : "CanonicalPcgsWrtFamilyPcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CanonicalPcgsWrtHomePcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FamilyPcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "HomePcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "InducedPcgsWrtFamilyPcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedInducedPcgses","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "InducedPcgsWrtHomePcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Pcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "GeneralizedPcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "OmegaSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalizerInHomePcgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","Tester(HomePcgs)"]},{"name" : "MultiplicationTable","type" : "GAP_Attribute","filters" : ["IsHomogeneousList"]},{"name" : "AllBlocks","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "TransitiveIdentification","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "PrimitiveIdentification","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "ONanScottType","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "SocleTypePrimitiveGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "TwoClosure","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "AsGroupGeneralMappingByImages","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","RespectsMultiplication","RespectsInverses"]},{"name" : "MappingOfWhichItIsAsGGMBI","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","RespectsMultiplication","RespectsInverses"]},{"name" : "NaturalHomomorphismByNormalSubgroupNCInParent","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsConjugatorIsomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","RespectsMultiplication","RespectsInverses"]},{"name" : "IsInnerAutomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","RespectsMultiplication","RespectsInverses"]},{"name" : "ConjugatorOfConjugatorIsomorphism","type" : "GAP_Attribute","filters" : ["IsConjugatorIsomorphism"]},{"name" : "ImagesSmallestGenerators","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","RespectsMultiplication","RespectsInverses"]},{"name" : "RegularActionHomomorphism","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DirectProductInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SubdirectProductInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SemidirectProductInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "WreathProductInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FreeProductInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsNaturalSymmetricGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "IsNaturalAlternatingGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "IsAlternatingGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSymmetricGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SymmetricParentGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "AlternatingSubgroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "OrbitStabilizingParentGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "DirectFactorsOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SemidirectFactorsOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DecompositionTypesOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsDihedralGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DihedralGenerators","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsQuaternionGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "QuaternionGenerators","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsQuasiDihedralGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "QuasiDihedralGenerators","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPSL","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ParametersOfGroupViewedAsPSL","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ParametersOfGroupViewedAsSL","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ParametersOfGroupViewedAsGL","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AlternatingDegree","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SymmetricDegree","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PSLDegree","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PSLUnderlyingField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SLDegree","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SLUnderlyingField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "GLDegree","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "GLUnderlyingField","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "StructureDescription","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPQuotientSystem","type" : "GAP_Attribute","filters" : ["IsQuotientSystem"]},{"name" : "IsNilpQuotientSystem","type" : "GAP_Attribute","filters" : ["IsQuotientSystem"]},{"name" : "ActingDomain","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "HomeEnumerator","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "ActionKernelExternalSet","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "LinearActionBasis","type" : "GAP_Attribute","filters" : ["IsLinearActionHomomorphism"]},{"name" : "FunctionAction","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "StabilizerOfExternalSet","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "CanonicalRepresentativeOfExternalSet","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "CanonicalRepresentativeDeterminatorOfExternalSet","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "CanEasilyDetermineCanonicalRepresentativeExternalSet","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "ActorOfExternalSet","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "ActionHomomorphismAttr","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "SurjectiveActionHomomorphismAttr","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "UnderlyingExternalSet","type" : "GAP_Attribute","filters" : ["IsActionHomomorphism"]},{"name" : "ExternalSet","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "Orbits","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "OrbitsDomain","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "OrbitLengths","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "OrbitLengthsDomain","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "ExternalOrbits","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "ExternalOrbitsStabilizers","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "Transitivity","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "BlocksAttr","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "MaximalBlocksAttr","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "RepresentativesMinimalBlocksAttr","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "Earns","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "IsTransitive","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "IsPrimitive","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "IsPrimitiveAffine","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "IsSemiRegular","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "IsRegular","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "RankAction","type" : "GAP_Attribute","filters" : ["IsExternalSet"]},{"name" : "StabChainMutable","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "StabChainImmutable","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "StabChainOptions","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "BaseOfGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "MinimalStabChain","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "DecomposedRationalClass","type" : "GAP_Attribute","filters" : ["IsRationalClassGroupRep"]},{"name" : "StoredPermliftSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedAscendingChains","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LeftActingGroup","type" : "GAP_Attribute","filters" : ["IsDoubleCoset"]},{"name" : "RightActingGroup","type" : "GAP_Attribute","filters" : ["IsDoubleCoset"]},{"name" : "RepresentativesContainedRightCosets","type" : "GAP_Attribute","filters" : ["IsDoubleCoset"]},{"name" : "NaturalHomomorphismsPool","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SocleComplement","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SocleDimensions","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ModuleOfExtension","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "OmegaAndLowerPCentralSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SchurCover","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "EpimorphismSchurCover","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AbelianInvariantsMultiplier","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Epicentre","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsCentralFactor","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Zuppos","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MaximalSubgroupsLattice","type" : "GAP_Attribute","filters" : ["IsLatticeSubgroupsRep"]},{"name" : "MinimalSupergroupsLattice","type" : "GAP_Attribute","filters" : ["IsLatticeSubgroupsRep"]},{"name" : "TomDataAlmostSimpleRecognition","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsFrattiniFree","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LinesOfStraightLineProgram","type" : "GAP_Attribute","filters" : ["IsStraightLineProgram"]},{"name" : "NrInputsOfStraightLineProgram","type" : "GAP_Attribute","filters" : ["IsStraightLineProgram"]},{"name" : "StraightLineProgElmType","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "SlotUsagePattern","type" : "GAP_Attribute","filters" : ["IsStraightLineProgram"]},{"name" : "LargestNrSlots","type" : "GAP_Attribute","filters" : ["IsStraightLineProgram"]},{"name" : "TypeOfObjWithMemory","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "FpElmEqualityMethod","type" : "GAP_Attribute","filters" : ["CategoryFamily(IsElementOfFpGroup)"]},{"name" : "FpElmComparisonMethod","type" : "GAP_Attribute","filters" : ["CategoryFamily(IsElementOfFpGroup)"]},{"name" : "FpElementNFFunction","type" : "GAP_Attribute","filters" : ["CategoryFamily(IsElementOfFpGroup)"]},{"name" : "CosetTableInWholeGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CosetTableNormalClosureInWholeGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AsSubgroupOfWholeGroupByQuotient","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup"]},{"name" : "FreeGeneratorsOfFpGroup","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup","IsGroupOfFamily"]},{"name" : "RelatorsOfFpGroup","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup","IsGroupOfFamily"]},{"name" : "FreeGroupOfFpGroup","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup","IsGroupOfFamily"]},{"name" : "IndicesInvolutaryGenerators","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup","IsGroupOfFamily"]},{"name" : "StoredExcludedOrders","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup"]},{"name" : "FPFaithHom","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "AugmentedCosetTableMtcInWholeGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AugmentedCosetTableRrsInWholeGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AugmentedCosetTableNormalClosureInWholeGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PrimaryGeneratorWords","type" : "GAP_Attribute","filters" : ["IsPresentation"]},{"name" : "TietzeOrigin","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup"]},{"name" : "TzOptions","type" : "GAP_Attribute","filters" : ["IsPresentation"]},{"name" : "IsWordDecompHomomorphism","type" : "GAP_Attribute","filters" : ["IsGroupGeneralMappingByImages"]},{"name" : "CosetTableFpHom","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "IsomorphismSimplifiedFpGroup","type" : "GAP_Attribute","filters" : ["IsSubgroupFpGroup"]},{"name" : "EpimorphismFromFreeGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NiceMonomorphism","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsCanonicalNiceMonomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","RespectsMultiplication","RespectsInverses"]},{"name" : "CanonicalNiceMonomorphism","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "NiceObject","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsHandledByNiceMonomorphism","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "SeedFaithfulAction","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AutomorphismGroup","type" : "GAP_Attribute","filters" : ["IsGeneralizedDomain","IsCollection"]},{"name" : "IsGroupOfAutomorphisms","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsGroupOfAutomorphismsFiniteGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AutomorphismDomain","type" : "GAP_Attribute","filters" : ["IsGroupOfAutomorphisms"]},{"name" : "IsAutomorphismGroup","type" : "GAP_Attribute","filters" : ["IsGroupOfAutomorphisms"]},{"name" : "InnerAutomorphismsAutomorphismGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DefaultFieldOfMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "DimensionOfMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "FieldOfMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "TransposedMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsGeneralLinearGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsNaturalGL","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSpecialLinearGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsNaturalSL","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSubgroupSL","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "InvariantBilinearForm","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsFullSubgroupGLorSLRespectingBilinearForm","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "InvariantSesquilinearForm","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsFullSubgroupGLorSLRespectingSesquilinearForm","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "InvariantQuadraticForm","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsFullSubgroupGLorSLRespectingQuadraticForm","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "FittingFreeLiftSetup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "RecogDecompinfoHomomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","IsTotal","IsSingleValued"]},{"name" : "DirectFactorsFittingFreeSocle","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ChiefSeriesTF","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsRationalMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsIntegerMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "ZClassRepsQClass","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalizerInGLnZ","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "CentralizerInGLnZ","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsBravaisGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "BravaisGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "BravaisSubgroups","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "BravaisSupergroups","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalizerInGLnZBravaisGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "InvariantLattice","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "PerfectIdentification","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DataAboutSimpleGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ImfRecord","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "OrderingsFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "IsWellFoundedOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "IsTotalOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "FamilyForOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "LessThanFunction","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "LessThanOrEqualFunction","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "IsOrderingOnFamilyOfAssocWords","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "LetterRepWordsLessFunc","type" : "GAP_Attribute","filters" : ["IsOrderingOnFamilyOfAssocWords"]},{"name" : "IsTranslationInvariantOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering","IsOrderingOnFamilyOfAssocWords"]},{"name" : "OrderingOnGenerators","type" : "GAP_Attribute","filters" : ["IsOrdering","IsOrderingOnFamilyOfAssocWords"]},{"name" : "IsShortLexOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering","IsOrderingOnFamilyOfAssocWords"]},{"name" : "WeightOfGenerators","type" : "GAP_Attribute","filters" : ["IsOrdering","IsOrderingOnFamilyOfAssocWords"]},{"name" : "IsWeightLexOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering","IsOrderingOnFamilyOfAssocWords"]},{"name" : "IsBasicWreathProductOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "IsWreathProductOrdering","type" : "GAP_Attribute","filters" : ["IsOrdering"]},{"name" : "LevelsOfGenerators","type" : "GAP_Attribute","filters" : ["IsOrdering","IsWreathProductOrdering"]},{"name" : "LargestImageOfMovedPoint","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "SmallestImageOfMovedPoint","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "RankOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "AsPermutation","type" : "GAP_Attribute","filters" : ["IsAssociativeElement"]},{"name" : "AsTransformation","type" : "GAP_Attribute","filters" : ["IsAssociativeElement"]},{"name" : "PermutationOfImage","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "DegreeOfTransformationCollection","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsTransformation)"]},{"name" : "FlatKernelOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "ImageSetOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "IndexPeriodOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "KernelOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "SmallestIdempotentPower","type" : "GAP_Attribute","filters" : ["IsAssociativeElement"]},{"name" : "ComponentRepsOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "NrComponentsOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "ComponentsOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "CyclesOfTransformation","type" : "GAP_Attribute","filters" : ["IsTransformation"]},{"name" : "LeftOne","type" : "GAP_Attribute","filters" : ["IsAssociativeElement"]},{"name" : "RightOne","type" : "GAP_Attribute","filters" : ["IsAssociativeElement"]},{"name" : "DomainOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "ImageListOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "ImageSetOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "IndexPeriodOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "ComponentRepsOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "NrComponentsOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "ComponentsOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "FixedPointsOfPartialPerm","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "NrFixedPoints","type" : "GAP_Attribute","filters" : ["IsPartialPerm"]},{"name" : "DegreeOfPartialPermCollection","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsPartialPerm)"]},{"name" : "CodegreeOfPartialPermCollection","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsPartialPerm)"]},{"name" : "RankOfPartialPermCollection","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsPartialPerm)"]},{"name" : "DomainOfPartialPermCollection","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsPartialPerm)"]},{"name" : "ImageOfPartialPermCollection","type" : "GAP_Attribute","filters" : ["CategoryCollections(IsPartialPerm)"]},{"name" : "TransformationRepresentation","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","IsTotal","IsSingleValued","IsEndoGeneralMapping"]},{"name" : "FreeGeneratorsOfFpSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsElementOfFpSemigroup)","IsWholeFamily"]},{"name" : "FreeSemigroupOfFpSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsElementOfFpSemigroup)","IsWholeFamily"]},{"name" : "RelationsOfFpSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsElementOfFpSemigroup)","IsWholeFamily"]},{"name" : "IsomorphismFpSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "FreeGeneratorsOfFpMonoid","type" : "GAP_Attribute","filters" : ["IsMagmaWithOne","IsAssociative","CategoryCollections(IsElementOfFpMonoid)","IsWholeFamily"]},{"name" : "FreeMonoidOfFpMonoid","type" : "GAP_Attribute","filters" : ["IsMagmaWithOne","IsAssociative","CategoryCollections(IsElementOfFpMonoid)","IsWholeFamily"]},{"name" : "RelationsOfFpMonoid","type" : "GAP_Attribute","filters" : ["IsMagmaWithOne","IsAssociative","CategoryCollections(IsElementOfFpMonoid)","IsWholeFamily"]},{"name" : "IsomorphismFpMonoid","type" : "GAP_Attribute","filters" : ["IsMagmaWithOne","IsAssociative"]},{"name" : "ReducedConfluentRewritingSystem","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "FreeMonoidOfRewritingSystem","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "FamilyForRewritingSystem","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "FreeSemigroupOfRewritingSystem","type" : "GAP_Attribute","filters" : ["IsRewritingSystem"]},{"name" : "TzRules","type" : "GAP_Attribute","filters" : ["IsKnuthBendixRewritingSystem"]},{"name" : "CosetTableOfFpSemigroup","type" : "GAP_Attribute","filters" : ["IsRightMagmaCongruence"]},{"name" : "AdjoinedIdentityFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "UnderlyingSemigroupFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "AdjoinedIdentityDefaultType","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "MonoidByAdjoiningIdentity","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "UnderlyingSemigroupOfMonoidByAdjoiningIdentity","type" : "GAP_Attribute","filters" : ["IsMonoidByAdjoiningIdentity"]},{"name" : "MonoidByAdjoiningIdentityElt","type" : "GAP_Attribute","filters" : ["IsMultiplicativeElement","IsAssociativeElement"]},{"name" : "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt","type" : "GAP_Attribute","filters" : ["IsMonoidByAdjoiningIdentityElt"]},{"name" : "IsFiniteSemigroupGreensRelation","type" : "GAP_Attribute","filters" : ["IsGreensRelation"]},{"name" : "GreensRRelation","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensLRelation","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensJRelation","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensDRelation","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensHRelation","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "AssociatedConcreteSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsElementOfFpSemigroup)","IsWholeFamily"]},{"name" : "AssociatedFpSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensRClasses","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensLClasses","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensJClasses","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensDClasses","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "GreensHClasses","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "RClassOfHClass","type" : "GAP_Attribute","filters" : ["IsGreensHClass"]},{"name" : "LClassOfHClass","type" : "GAP_Attribute","filters" : ["IsGreensHClass"]},{"name" : "DClassOfHClass","type" : "GAP_Attribute","filters" : ["IsGreensHClass"]},{"name" : "DClassOfLClass","type" : "GAP_Attribute","filters" : ["IsGreensLClass"]},{"name" : "DClassOfRClass","type" : "GAP_Attribute","filters" : ["IsGreensRClass"]},{"name" : "GroupHClassOfGreensDClass","type" : "GAP_Attribute","filters" : ["IsGreensDClass"]},{"name" : "IsRegularDClass","type" : "GAP_Attribute","filters" : ["IsGreensDClass"]},{"name" : "IsGroupHClass","type" : "GAP_Attribute","filters" : ["IsGreensHClass"]},{"name" : "EggBoxOfDClass","type" : "GAP_Attribute","filters" : ["IsGreensDClass"]},{"name" : "InternalRepGreensRelation","type" : "GAP_Attribute","filters" : ["IsGreensRelation"]},{"name" : "CanonicalGreensClass","type" : "GAP_Attribute","filters" : ["IsGreensClass"]},{"name" : "IsFpSemigpReducedElt","type" : "GAP_Attribute","filters" : ["IsElementOfFpSemigroup"]},{"name" : "IsFpMonoidReducedElt","type" : "GAP_Attribute","filters" : ["IsElementOfFpMonoid"]},{"name" : "IsFullTransformationSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "DegreeOfTransformationSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsTransformation)"]},{"name" : "IsomorphismTransformationSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsomorphismTransformationMonoid","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "AntiIsomorphismTransformationSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsReesMatrixSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsReesZeroMatrixSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "Matrix","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsReesMatrixSemigroupElement)"]},{"name" : "Rows","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsReesMatrixSemigroupElement)"]},{"name" : "Columns","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsReesMatrixSemigroupElement)"]},{"name" : "UnderlyingSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsReesMatrixSemigroupElement)"]},{"name" : "AssociatedReesMatrixSemigroupOfDClass","type" : "GAP_Attribute","filters" : ["IsGreensDClass"]},{"name" : "IsomorphismReesMatrixSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsomorphismReesZeroMatrixSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "ReesMatrixSemigroupOfFamily","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "TypeReesMatrixSemigroupElements","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsReesMatrixSemigroupElement)"]},{"name" : "QuotientSemigroupPreimage","type" : "GAP_Attribute","filters" : ["IsQuotientSemigroup"]},{"name" : "QuotientSemigroupCongruence","type" : "GAP_Attribute","filters" : ["IsQuotientSemigroup"]},{"name" : "QuotientSemigroupHomomorphism","type" : "GAP_Attribute","filters" : ["IsQuotientSemigroup"]},{"name" : "DegreeOfPartialPermSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsPartialPerm)"]},{"name" : "CodegreeOfPartialPermSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsPartialPerm)"]},{"name" : "RankOfPartialPermSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsPartialPerm)"]},{"name" : "IsSymmetricInverseSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative","CategoryCollections(IsPartialPerm)"]},{"name" : "IsomorphismPartialPermSemigroup","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "IsomorphismPartialPermMonoid","type" : "GAP_Attribute","filters" : ["IsMagma","IsAssociative"]},{"name" : "UnderlyingGroup","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "IdentificationOfConjugacyClasses","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "CharacterDegrees","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Irr","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LinearCharacters","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IBr","type" : "GAP_Attribute","filters" : ["IsBrauerTable"]},{"name" : "OrdinaryCharacterTable","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsAlmostSimpleCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsMonomialCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsNilpotentCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsPerfectCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsSimpleCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsSolvableCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsSporadicSimpleCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsSupersolvableCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "OrdersClassRepresentatives","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "SizesCentralizers","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "SizesConjugacyClasses","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "AutomorphismsOfTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "UnderlyingCharacteristic","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "ClassNames","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "CharacterNames","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "ClassParameters","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "CharacterParameters","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "Identifier","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "InverseClasses","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "RealClasses","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "ClassRoots","type" : "GAP_Attribute","filters" : ["IsCharacterTable"]},{"name" : "ClassPositionsOfNormalSubgroups","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfMaximalNormalSubgroups","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfMinimalNormalSubgroups","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfCentre","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfDirectProductDecompositions","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfDerivedSubgroup","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfElementaryAbelianSeries","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfFittingSubgroup","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfSolvableRadical","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfLowerCentralSeries","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfUpperCentralSeries","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfSolvableResiduum","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ClassPositionsOfSupersolvableResiduum","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ComputedPrimeBlockss","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "BlocksInfo","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "DecompositionMatrix","type" : "GAP_Attribute","filters" : ["IsBrauerTable"]},{"name" : "ComputedIsPSolvableCharacterTables","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "ComputedIndicators","type" : "GAP_Attribute","filters" : ["IsCharacterTable"]},{"name" : "ComputedBrauerTables","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "DisplayOptions","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "FactorsOfDirectProduct","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "CharacterTableIsoclinic","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "SourceOfIsoclinicTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "ClassPermutation","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "NormalSubgroupClassesInfo","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "UnderlyingCharacterTable","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "ValuesOfClassFunction","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "GlobalPartitionOfClasses","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "TrivialCharacter","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "NaturalCharacter","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "IsVirtualCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "IsIrreducibleCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "CentreOfCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "ConstituentsOfCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "DegreeOfCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "KernelOfCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "ClassPositionsOfKernel","type" : "GAP_Attribute","filters" : ["IsHomogeneousList"]},{"name" : "CentralCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "DeterminantOfCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "BrauerCharacterValue","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsTable","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsTable"]},{"name" : "ComputedPowerMaps","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "FusionConjugacyClassesOp","type" : "GAP_Attribute","filters" : ["IsGeneralMapping"]},{"name" : "ComputedClassFusions","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "NamesOfFusionSources","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "BaumClausenInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IrreducibleRepresentations","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","IsFinite"]},{"name" : "IrrBaumClausen","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IrrConlon","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MolienSeriesInfo","type" : "GAP_Attribute","filters" : ["IsRationalFunction"]},{"name" : "Alpha","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Delta","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsBergerCondition","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPrimitiveCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "TestQuasiPrimitive","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "IsQuasiPrimitive","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "IsInducedFromNormalSubgroup","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "IsMonomialCharacter","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "IsMonomialNumber","type" : "GAP_Attribute","filters" : ["IsInt","IsPosRat"]},{"name" : "TestMonomialQuick","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "TestMonomial","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "TestSubnormallyMonomial","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSubnormallyMonomial","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "TestRelativelySM","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsRelativelySM","type" : "GAP_Attribute","filters" : ["IsClassFunction"]},{"name" : "IsMinimalNonmonomial","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DixonRecord","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IrrDixonSchneider","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "TableOfMarks","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PermutationTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "MarksTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "SubsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "NrSubsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "OrdersTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "LengthsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "ClassTypesTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "ClassNamesTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "FusionsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "IdempotentsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "IdempotentsTomInfo","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "MatTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "MoebiusTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "WeightsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "IsAbelianTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "IsCyclicTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "IsNilpotentTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "IsPerfectTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "IsSolvableTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "DerivedSubgroupsTomPossible","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "DerivedSubgroupsTomUnique","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "NormalizersTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "CyclicExtensionsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "ComputedCyclicExtensionsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "MaximalSubgroupsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "GeneratorsSubgroupsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "StraightLineProgramsTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks"]},{"name" : "ProcessID","type" : "GAP_Attribute","filters" : ["IsFile"]},{"name" : "IdGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "Gap3CatalogueIdGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FrattinifactorSize","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FrattinifactorId","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "GaloisType","type" : "GAP_Attribute","filters" : ["IsRationalFunction"]},{"name" : "SimsNo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPerm)"]},{"name" : "MinimalBlockDimension","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPrimitiveMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IrrFacsAlgExtPol","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsUnivariateRationalFunction"]},{"name" : "IsUnitGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsUnitGroupIsomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","IsTotal","IsSingleValued"]},{"name" : "IsNumberFieldByMatrices","type" : "GAP_Attribute","filters" : ["IsNumberField"]},{"name" : "IsMultGroupByFieldElemsIsomorphism","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","IsTotal","IsSingleValued"]},{"name" : "IntegerDefiningPolynomial","type" : "GAP_Attribute","filters" : ["IsNumberField"]},{"name" : "IntegerPrimitiveElement","type" : "GAP_Attribute","filters" : ["IsNumberField"]},{"name" : "EquationOrderBasis","type" : "GAP_Attribute","filters" : ["IsNumberField"]},{"name" : "MaximalOrderBasis","type" : "GAP_Attribute","filters" : ["IsNumberField"]},{"name" : "UnitGroup","type" : "GAP_Attribute","filters" : ["IsNumberField"]},{"name" : "FieldOfUnitGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsWeightedCollector","type" : "GAP_Attribute","filters" : ["IsPolycyclicCollector"]},{"name" : "IsPolynomialCollector","type" : "GAP_Attribute","filters" : ["IsFromTheLeftCollectorRep"]},{"name" : "UseLibraryCollector","type" : "GAP_Attribute","filters" : ["IsFromTheLeftCollectorRep"]},{"name" : "IsPolycyclicPresentation","type" : "GAP_Attribute","filters" : ["IsFromTheLeftCollectorRep"]},{"name" : "TailOfElm","type" : "GAP_Attribute","filters" : ["IsPcpElement"]},{"name" : "RelativeOrderPcp","type" : "GAP_Attribute","filters" : ["IsPcpElement"]},{"name" : "RelativeIndex","type" : "GAP_Attribute","filters" : ["IsPcpElement"]},{"name" : "FactorOrder","type" : "GAP_Attribute","filters" : ["IsPcpElement"]},{"name" : "Igs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPcpElement)"]},{"name" : "Ngs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPcpElement)"]},{"name" : "Cgs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPcpElement)"]},{"name" : "EfaSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPcpElement)"]},{"name" : "PcpsOfEfaSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPcpElement)"]},{"name" : "IsomorphismPcpGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PcpGroupByEfaSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsHomomorphismIntoMatrixGroup","type" : "GAP_Attribute","filters" : ["IsGroupGeneralMappingByImages"]},{"name" : "SemiSimpleEfaSeries","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative","CategoryCollections(IsPcpElement)"]},{"name" : "FCCentre","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsNilpotentByFinite","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedMaximalSubgroupClassesByIndexs","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedLowIndexSubgroupClassess","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedLowIndexNormalSubgroupss","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SchurExtension","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SchurExtensionEpimorphism","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NonAbelianTensorSquare","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NonAbelianExteriorSquare","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "TorsionSubgroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalTorsionSubgroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FiniteSubgroupClasses","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsTorsionFree","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsFreeAbelian","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "MemberFunction","type" : "GAP_Attribute","filters" : ["IsClass"]},{"name" : "ComputedIsMembers","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsGroupClass","type" : "GAP_Attribute","filters" : ["IsClass"]},{"name" : "GroupClass","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "ContainsTrivialGroup","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsSubgroupClosed","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsNormalSubgroupClosed","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsQuotientClosed","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsResiduallyClosed","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsNormalProductClosed","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsDirectProductClosed","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsSchunckClass","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "IsSaturated","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "FittingClass","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "InjectorFunction","type" : "GAP_Attribute","filters" : ["IsClass"]},{"name" : "RadicalFunction","type" : "GAP_Attribute","filters" : ["IsClass"]},{"name" : "IsPrimitiveSolvableGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SchunckClass","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "Boundary","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "ProjectorFunction","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "BoundaryFunction","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "OrdinaryFormation","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "SaturatedFormation","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "FittingFormation","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "SaturatedFittingFormation","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "ResidualFunction","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "LocalDefinitionFunction","type" : "GAP_Attribute","filters" : ["IsGroupClass"]},{"name" : "ComputedProjectors","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedCoveringSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedInjectors","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedRadicals","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedResiduals","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CharacteristicSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalGeneratorsOfNilpotentResidual","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "PrimePowerGensPcSequence","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NilpotentProjector","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SupersolvableProjector","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SolvableSocle","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SocleComponents","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "SolvableSocleComponents","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedPSocleComponentss","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedPSocles","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AbelianMinimalNormalSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LinesOfStraightLineDecision","type" : "GAP_Attribute","filters" : ["IsStraightLineDecision"]},{"name" : "NrInputsOfStraightLineDecision","type" : "GAP_Attribute","filters" : ["IsStraightLineDecision"]},{"name" : "AsBBoxProgram","type" : "GAP_Attribute","filters" : ["IsStraightLineProgram"]},{"name" : "AsStraightLineProgram","type" : "GAP_Attribute","filters" : ["IsBBoxProgram"]},{"name" : "AsStraightLineDecision","type" : "GAP_Attribute","filters" : ["IsBBoxProgram"]},{"name" : "Maxes","type" : "GAP_Attribute","filters" : ["IsUnknown"]},{"name" : "AtlasRepInfoRecord","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "CASInfo","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "ConstructionInfoCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "FusionToTom","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "ProjectivesInfo","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "ExtensionInfoCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "GroupInfoForCharacterTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "KnowsSomeGroupInfo","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsNontrivialDirectProduct","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "KnowsDeligneLusztigNames","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IsDuplicateTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IdentifierOfMainTable","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "IdentifiersOfDuplicateTables","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "DeligneLusztigNames","type" : "GAP_Attribute","filters" : ["IsCharacterTable"]},{"name" : "DeligneLusztigName","type" : "GAP_Attribute","filters" : ["IsCharacter"]},{"name" : "FingerprintOfCharacterTable","type" : "GAP_Attribute","filters" : ["IsOrdinaryTable"]},{"name" : "SpinSymIngredients","type" : "GAP_Attribute","filters" : ["IsNearlyCharacterTable"]},{"name" : "NamesLibTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks","IsLibTomRep"]},{"name" : "NotifiedFusionsOfLibTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks","IsLibTomRep"]},{"name" : "FusionsOfLibTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks","IsLibTomRep"]},{"name" : "NotifiedFusionsToLibTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks","IsLibTomRep"]},{"name" : "FusionsToLibTom","type" : "GAP_Attribute","filters" : ["IsTableOfMarks","IsLibTomRep"]},{"name" : "StandardGeneratorsInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "FGA_States","type" : "GAP_Attribute","filters" : ["IsInvAutomatonCategory"]},{"name" : "FGA_GeneratorsLetterRep","type" : "GAP_Attribute","filters" : ["IsInvAutomatonCategory"]},{"name" : "FreeGeneratorsOfGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "RankOfFreeGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "FreeGroupAutomaton","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "FreeGroupExtendedAutomaton","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalizerInWholeGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "FGA_Source","type" : "GAP_Attribute","filters" : ["IsFromFpGroupGeneralMappingByImages"]},{"name" : "FGA_Image","type" : "GAP_Attribute","filters" : ["IsToFpGroupGeneralMappingByImages"]},{"name" : "FGA_WhiteheadParams","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","RespectsMultiplication","RespectsInverses","IsGeneralMapping","IsTotal","IsSingleValued"]},{"name" : "FGA_WhiteheadAutomorphisms","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "FGA_NielsenAutomorphisms","type" : "GAP_Attribute","filters" : ["CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsIrreducibleMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedIsIrreducibleMatrixGroups","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsAbsolutelyIrreducibleMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedIsPrimitiveMatrixGroups","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "MinimalBlockDimensionOfMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedMinimalBlockDimensionOfMatrixGroups","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "CharacteristicOfField","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "RepresentationIsomorphism","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "ImprimitivitySystems","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "ComputedImprimitivitySystemss","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "TraceField","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "ConjugatingMatTraceField","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "FingerprintMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IdIrreducibleSolvableMatrixGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IdPrimitiveSolvableGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsLieNilpotentOverFp","type" : "GAP_Attribute","filters" : ["IsLieNilpotent"]},{"name" : "AutomorphismGroupOfNilpotentLieAlgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "MinimalGeneratorNumber","type" : "GAP_Attribute","filters" : ["IsLieNilpotent"]},{"name" : "IsLieCover","type" : "GAP_Attribute","filters" : ["IsLieNilpotentOverFp"]},{"name" : "CoverOf","type" : "GAP_Attribute","filters" : ["IsLieCover"]},{"name" : "CoverHomomorphism","type" : "GAP_Attribute","filters" : ["IsLieCover"]},{"name" : "LieCover","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieNucleus","type" : "GAP_Attribute","filters" : ["IsLieNilpotentOverFp"]},{"name" : "LieMultiplicator","type" : "GAP_Attribute","filters" : ["IsLieNilpotentOverFp"]},{"name" : "IsLieAlgebraWithNB","type" : "GAP_Attribute","filters" : ["IsLieNilpotentOverFp"]},{"name" : "NilpotentBasis","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "IsNilpotentBasis","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "LieNBDefinitions","type" : "GAP_Attribute","filters" : ["IsNilpotentBasis"]},{"name" : "LieNBWeights","type" : "GAP_Attribute","filters" : ["IsNilpotentBasis"]},{"name" : "IsGroupAlgebra","type" : "GAP_Attribute","filters" : ["IsGroupRing"]},{"name" : "IsFModularGroupAlgebra","type" : "GAP_Attribute","filters" : ["IsGroupAlgebra"]},{"name" : "IsPModularGroupAlgebra","type" : "GAP_Attribute","filters" : ["IsFModularGroupAlgebra"]},{"name" : "UnderlyingRing","type" : "GAP_Attribute","filters" : ["IsGroupRing"]},{"name" : "UnderlyingField","type" : "GAP_Attribute","filters" : ["IsGroupAlgebra"]},{"name" : "Support","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]},{"name" : "CoefficientsBySupport","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]},{"name" : "TraceOfMagmaRingElement","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]},{"name" : "Augmentation","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]},{"name" : "IsSymmetric","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]},{"name" : "IsUnitary","type" : "GAP_Attribute","filters" : ["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]},{"name" : "WeightedBasis","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "AugmentationIdealPowerSeries","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "AugmentationIdealNilpotencyIndex","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "AugmentationIdealOfDerivedSubgroupNilpotencyIndex","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "IsGroupOfUnitsOfMagmaRing","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsUnitGroupOfGroupRing","type" : "GAP_Attribute","filters" : ["IsGroupOfUnitsOfMagmaRing"]},{"name" : "IsNormalizedUnitGroupOfGroupRing","type" : "GAP_Attribute","filters" : ["IsGroupOfUnitsOfMagmaRing"]},{"name" : "UnderlyingGroupRing","type" : "GAP_Attribute","filters" : ["IsGroupOfUnitsOfMagmaRing"]},{"name" : "NormalizedUnitGroup","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "PcNormalizedUnitGroup","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "ComputedAugmentationIdealPowerFactorGroups","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "PcUnits","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "NaturalBijectionToPcNormalizedUnitGroup","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "NaturalBijectionToNormalizedUnitGroup","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "GroupBases","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "BicyclicUnitGroup","type" : "GAP_Attribute","filters" : ["IsNormalizedUnitGroupOfGroupRing"]},{"name" : "UnitarySubgroup","type" : "GAP_Attribute","filters" : ["IsNormalizedUnitGroupOfGroupRing"]},{"name" : "UnderlyingAssociativeAlgebra","type" : "GAP_Attribute","filters" : ["IsLieAlgebraByAssociativeAlgebra"]},{"name" : "IsLieAlgebraOfGroupRing","type" : "GAP_Attribute","filters" : ["IsLieAlgebraByAssociativeAlgebra"]},{"name" : "IsBasisOfLieAlgebraOfGroupRing","type" : "GAP_Attribute","filters" : ["IsBasis"]},{"name" : "NaturalBijectionToLieAlgebra","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsAssociative"]},{"name" : "NaturalBijectionToAssociativeAlgebra","type" : "GAP_Attribute","filters" : ["IsLieAlgebraByAssociativeAlgebra"]},{"name" : "AugmentationHomomorphism","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsMagmaWithOne","IsAssociativeLOpDProd","IsGroupRing"]},{"name" : "IsLieMetabelian","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "IsLieCentreByMetabelian","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "LieUpperNilpotencyIndex","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "LieLowerNilpotencyIndex","type" : "GAP_Attribute","filters" : ["IsPModularGroupAlgebra"]},{"name" : "LieDerivedLength","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsLeftActedOnByRing","IsDistributiveLOpESum","IsAssociativeLOpEProd","IsTrivialLOpEOne","IsLeftActedOnByDivisionRing","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive","IsAssociativeLOpDProd","IsZeroSquaredRing","IsJacobianRing"]},{"name" : "SubgroupsOfIndexTwo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DihedralDepth","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "DimensionBasis","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LieDimensionSubgroups","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "LieUpperCodimensionSeries","type" : "GAP_Attribute","filters" : ["IsGroupRing"]},{"name" : "RootsAsMatrices","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsUnivariateRationalFunction"]},{"name" : "IsSolvablePolynomial","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsUnivariateRationalFunction"]},{"name" : "IsSeparablePolynomial","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsUnivariateRationalFunction"]},{"name" : "IsomorphismMatrixField","type" : "GAP_Attribute","filters" : ["IsNumberField"]},{"name" : "GaloisGroupOnRoots","type" : "GAP_Attribute","filters" : ["IsPolynomial","IsUnivariateRationalFunction"]},{"name" : "IsAffineCrystGroupOnRight","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsAffineCrystGroupOnLeft","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsAffineCrystGroupOnLeftOrRight","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSpaceGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsStandardAffineCrystGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsSymmorphicSpaceGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsPointGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "NormalizerPointGroupInGLnZ","type" : "GAP_Attribute","filters" : ["IsPointGroup"]},{"name" : "CentralizerPointGroupInGLnZ","type" : "GAP_Attribute","filters" : ["IsPointGroup"]},{"name" : "AffineCrystGroupOfPointGroup","type" : "GAP_Attribute","filters" : ["IsPointGroup"]},{"name" : "PointGroup","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "PointHomomorphism","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "TranslationBasis","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "InternalBasis","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "TransParts","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "TranslationNormalizer","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "AffineNormalizer","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "IsPointHomomorphism","type" : "GAP_Attribute","filters" : ["IsGroupGeneralMappingByImages"]},{"name" : "NiceToCryst","type" : "GAP_Attribute","filters" : ["IsPointGroup"]},{"name" : "IsFromAffineCrystGroupToFpGroup","type" : "GAP_Attribute","filters" : ["IsGroupGeneralMappingByImages"]},{"name" : "IsFromAffineCrystGroupToPcpGroup","type" : "GAP_Attribute","filters" : ["IsGroupGeneralMappingByImages"]},{"name" : "WyckoffStabilizer","type" : "GAP_Attribute","filters" : ["IsWyckoffPosition"]},{"name" : "WyckoffOrbit","type" : "GAP_Attribute","filters" : ["IsWyckoffPosition"]},{"name" : "WyckoffPositions","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "CocVecs","type" : "GAP_Attribute","filters" : ["IsAffineCrystGroupOnLeftOrRight"]},{"name" : "IsColorGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "ColorSubgroup","type" : "GAP_Attribute","filters" : ["IsColorGroup"]},{"name" : "ColorCosetList","type" : "GAP_Attribute","filters" : ["IsColorGroup"]},{"name" : "ColorPermGroup","type" : "GAP_Attribute","filters" : ["IsColorGroup"]},{"name" : "ColorHomomorphism","type" : "GAP_Attribute","filters" : ["IsColorGroup"]},{"name" : "CrystCatRecord","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsAlmostCrystallographic","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsAlmostBieberbachGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "AlmostCrystallographicInfo","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "NaturalHomomorphismOnHolonomyGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "HolonomyGroup","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "OrientationModule","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "BettiNumbers","type" : "GAP_Attribute","filters" : ["IsMagmaWithInverses","IsAssociative"]},{"name" : "IsIsomorphismByFinitePolycyclicMatrixGroup","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","IsTotal","IsSingleValued"]},{"name" : "IsIsomorphismByPolycyclicMatrixGroup","type" : "GAP_Attribute","filters" : ["IsGeneralMapping","IsTotal","IsSingleValued"]},{"name" : "IsTriangularizableMatGroup","type" : "GAP_Attribute","filters" : ["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative"]},{"name" : "IsZ_pi","type" : "GAP_Attribute","filters" : ["IsEuclideanRing"]},{"name" : "NoninvertiblePrimes","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "IsResidueClass","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "UnderlyingIndeterminate","type" : "GAP_Attribute","filters" : ["IsFamily"]},{"name" : "IsZxZ","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "SizeOfSmallestResidueClassRing","type" : "GAP_Attribute","filters" : ["IsNearAdditiveGroup","IsNearAdditiveMagma","IsAdditivelyCommutative","IsMagma","IsLDistributive","IsRDistributive"]},{"name" : "Density","type" : "GAP_Attribute","filters" : ["IsResidueClassUnion"]},{"name" : "IsResidueClassWithFixedRepresentative","type" : "GAP_Attribute","filters" : ["IsObject"]},{"name" : "IsOverlappingFree","type" : "GAP_Attribute","filters" : ["IsUnionOfResidueClassesWithFixedRepresentatives"]},{"name" : "Rho","type" : "GAP_Attribute","filters" : ["IsUnionOfResidueClassesWithFixedRepresentatives"]},{"name" : "ViewObj","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10046,"comment" : "ViewObj: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 10036,"comment" : "ViewObj: for full hom space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 10034,"comment" : "ViewObj: for groups with known structure description","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(StructureDescription)"]]},{"rank" : 10033,"comment" : "ViewObj: for a Lie matrix in default representation","filters" : [["IsPackedElementDefaultRep","IsLieMatrix"]]},{"rank" : 10023,"comment" : "ViewObj: for full ring Z\/nZ","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 10022,"comment" : "ViewObj: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 10022,"comment" : "ViewObj: for group automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]},{"rank" : 10017,"comment" : "ViewObj: for zero mapping","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"]]},{"rank" : 10017,"comment" : "ViewObj: for identity mapping","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"]]},{"rank" : 10009,"comment" : "ViewObj: for a canonical basis","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)"]]},{"rank" : 10001,"comment" : "ViewObj","filters" : [["IsPcp"]]},{"rank" : 10001,"comment" : "ViewObj: for an object with name","filters" : [["Tester(Name)"]]},{"rank" : 10000,"comment" : "ViewObj","filters" : [[]]},{"rank" : 429,"comment" : "ViewObj: for a field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 134,"comment" : "ViewObj: subgroup by property","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(ElementTestFunction)"]]},{"rank" : 129,"comment" : "ViewObj: for a two-sided ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 128,"comment" : "ViewObj: for a right ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 128,"comment" : "ViewObj: for a left ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)","Tester(LeftActingRingOfIdeal)"]]},{"rank" : 110,"comment" : "ViewObj: for a restricted mapping","filters" : [["IsGeneralRestrictedMappingRep"]]},{"rank" : 110,"comment" : "ViewObj: for a composition mapping","filters" : [["IsCompositionMappingRep"]]},{"rank" : 109,"comment" : "ViewObj: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]},{"rank" : 107,"comment" : "ViewObj: objects with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 107,"comment" : "ViewObj: straight line program elements","filters" : [["IsStraightLineProgElm"]]},{"rank" : 67,"comment" : "ViewObj: for cyclotomic field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 65,"comment" : "ViewObj: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 62,"comment" : "ViewObj: for natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 62,"comment" : "ViewObj: for natural alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 61,"comment" : "ViewObj: for function field","filters" : [["IsFunctionField"]]},{"rank" : 61,"comment" : "ViewObj: for a polynomial ring","filters" : [["IsPolynomialRing"]]},{"rank" : 56,"comment" : "ViewObj: for a matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 55,"comment" : "ViewObj: for algebraic extension","filters" : [["IsNumberField","Tester(IsNumberField)","IsAlgebraicExtension"]]},{"rank" : 48,"comment" : "ViewObj: for full matrix module","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "ViewObj: for full row module","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 45,"comment" : "ViewObj: fp group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 44,"comment" : "ViewObj: for a matrix group with stored generators","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 44,"comment" : "ViewObj: subgroup of free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 44,"comment" : "ViewObj: for GF2 matrix","filters" : [["IsTable","IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"]]},{"rank" : 44,"comment" : "ViewObj: for a Lie algebra with known dimension","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","Tester(Dimension)"]]},{"rank" : 43,"comment" : "ViewObj: for a matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "ViewObj: pc group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 43,"comment" : "ViewObj: for a Lie algebra with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 42,"comment" : "ViewObj: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : 41,"comment" : "ViewObj: for an algebra-with-one with known dimension","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(Dimension)"]]},{"rank" : 40,"comment" : "ViewObj: for an algebra-with-one with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftOperatorRingWithOne)"]]},{"rank" : 39,"comment" : "ViewObj: for an algebra-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 39,"comment" : "ViewObj: for a FLMLOR-with-one with known dimension","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(Dimension)"]]},{"rank" : 38,"comment" : "ViewObj: for an algebra with known dimension","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(Dimension)"]]},{"rank" : 38,"comment" : "ViewObj: for a FLMLOR-with-one with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorRingWithOne)"]]},{"rank" : 37,"comment" : "ViewObj: for an algebra with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 37,"comment" : "ViewObj: for a FLMLOR-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 36,"comment" : "ViewObj: for an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 36,"comment" : "ViewObj: for a FLMLOR with known dimension","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(Dimension)"]]},{"rank" : 35,"comment" : "ViewObj: for a character","filters" : [["IsClassFunction","IsCharacter","Tester(IsCharacter)"]]},{"rank" : 35,"comment" : "ViewObj: for a FLMLOR with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 34,"comment" : "ViewObj: for a FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 34,"comment" : "ViewObj: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 33,"comment" : "ViewObj: for Z_(pi) (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 33,"comment" : "ViewObj: for a virtual character","filters" : [["IsClassFunction","IsVirtualCharacter","Tester(IsVirtualCharacter)"]]},{"rank" : 33,"comment" : "ViewObj: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "ViewObj: for a semigroup Congruence with known generating pairs","filters" : [["Tester(GeneratingPairsOfMagmaCongruence)","IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 32,"comment" : "ViewObj: for a semigroup congruence","filters" : [["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 32,"comment" : "ViewObj: for ranges","filters" : [["IsList","IsRange","IsFinite","Tester(IsFinite)"]]},{"rank" : 31,"comment" : "ViewObj: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 31,"comment" : "ViewObj: for null map matrix","filters" : [["IsNullMapMatrix"]]},{"rank" : 30,"comment" : "ViewObj: for a ring-with-one with known generators","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRingWithOne)"]]},{"rank" : 29,"comment" : "ViewObj: for an alg. hom. from f. p. algebra","filters" : [["IsAlgebraHomomorphismFromFpRep"]]},{"rank" : 29,"comment" : "ViewObj: for an operation algebra homomorphism","filters" : [["IsOperationAlgebraHomomorphismDefaultRep"]]},{"rank" : 29,"comment" : "ViewObj: for a ring-with-one","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 29,"comment" : "ViewObj: for a RightSemigroupCongruence with generators","filters" : [["Tester(GeneratingPairsOfMagmaCongruence)","IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)"]]},{"rank" : 29,"comment" : "ViewObj: for a LeftSemigroupCongruence with known generating pairs","filters" : [["Tester(GeneratingPairsOfMagmaCongruence)","IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)"]]},{"rank" : 28,"comment" : "ViewObj: For a compressed MatFFE","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitMatrixRep"]]},{"rank" : 28,"comment" : "ViewObj: for an empty row vector","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 27,"comment" : "ViewObj: for algebra module","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsAlgebraModule","Tester(IsAlgebraModule)"]]},{"rank" : 27,"comment" : "ViewObj: for vector space with known dimension","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(Dimension)"]]},{"rank" : 27,"comment" : "ViewObj: for a ring with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 27,"comment" : "ViewObj: for a magma congruence with generating pairs","filters" : [["IsMagmaCongruence","Tester(GeneratingPairsOfMagmaCongruence)"]]},{"rank" : 27,"comment" : "ViewObj: for a RightMagmaCongruence with generators","filters" : [["IsRightMagmaCongruence","Tester(GeneratingPairsOfMagmaCongruence)"]]},{"rank" : 27,"comment" : "ViewObj: for a LeftMagmaCongruence with known generating pairs","filters" : [["IsLeftMagmaCongruence","Tester(GeneratingPairsOfMagmaCongruence)"]]},{"rank" : 27,"comment" : "ViewObj: for an enumerator that perhaps has its own `ViewObj' function","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"]]},{"rank" : 26,"comment" : "ViewObj: for vector space with known generators","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 26,"comment" : "ViewObj: for a ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 26,"comment" : "ViewObj: for a magma congruence","filters" : [["IsMagmaCongruence"]]},{"rank" : 25,"comment" : "ViewObj: for a fp monoid with generators","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]},{"rank" : 25,"comment" : "ViewObj: for a free monoid containing the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 25,"comment" : "ViewObj: for an algebra g.m.b.i","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 25,"comment" : "ViewObj: for vector space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 24,"comment" : "ViewObj: pcgs","filters" : [["IsPcgs","IsPcgsDefaultRep"]]},{"rank" : 24,"comment" : "ViewObj: For a compressed VecFFE","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitVectorRep"]]},{"rank" : 24,"comment" : "ViewObj: for free left module with known generators","filters" : [["IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 24,"comment" : "ViewObj: for free left module with known dimension","filters" : [["IsFreeLeftModule","Tester(Dimension)"]]},{"rank" : 24,"comment" : "ViewObj: for a RightSemigrouCongruence","filters" : [["IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)"]]},{"rank" : 24,"comment" : "ViewObj: for a LeftSemigroupCongruence","filters" : [["IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)"]]},{"rank" : 23,"comment" : "ViewObj: for saturated Fitting formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsSaturated","Tester(IsSaturated)","IsClassByPropertyRep"]]},{"rank" : 23,"comment" : "ViewObj: for GreensHRelation","filters" : [["IsGreensHRelation"]]},{"rank" : 23,"comment" : "ViewObj: for GreensDRelation","filters" : [["IsGreensDRelation"]]},{"rank" : 23,"comment" : "ViewObj: for GreensJRelation","filters" : [["IsGreensJRelation"]]},{"rank" : 23,"comment" : "ViewObj: for embedding into wreath product","filters" : [["IsEmbeddingWreathProductPermGroup"]]},{"rank" : 23,"comment" : "ViewObj: for projection from subdirect product","filters" : [["IsProjectionSubdirectProductPermGroup"]]},{"rank" : 23,"comment" : "ViewObj: for projection from a direct product","filters" : [["IsProjectionDirectProductPermGroup"]]},{"rank" : 23,"comment" : "ViewObj: for embedding into direct product","filters" : [["IsEmbeddingDirectProductPermGroup"]]},{"rank" : 23,"comment" : "ViewObj: for nat. hom. of pc group","filters" : [["IsNaturalHomomorphismPcGroupRep"]]},{"rank" : 23,"comment" : "ViewObj: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 23,"comment" : "ViewObj: for an ring g.m.b.i","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "ViewObj: for a left module m.b.m.","filters" : [["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 23,"comment" : "ViewObj: for a left module g.m.b.i","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "ViewObj: for free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 23,"comment" : "ViewObj: for a zero group","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsMagmaWithZeroAdjoined"]]},{"rank" : 23,"comment" : "ViewObj: for an iterator that perhaps has its own `ViewObj' function","filters" : [["IsIterator","IsIteratorByFunctionsRep"]]},{"rank" : 22,"comment" : "ViewObj: for a Brauer table","filters" : [["IsBrauerTable"]]},{"rank" : 22,"comment" : "ViewObj: for an ordinary table","filters" : [["IsOrdinaryTable"]]},{"rank" : 22,"comment" : "ViewObj: for action homomorphism","filters" : [["IsActionHomomorphism"]]},{"rank" : 22,"comment" : "ViewObj: for GF2 vector","filters" : [["IsHomogeneousList","IsFinite","Tester(IsFinite)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 22,"comment" : "ViewObj: for a RightMagmaCongruence","filters" : [["IsRightMagmaCongruence"]]},{"rank" : 22,"comment" : "ViewObj: for a LeftMagmaCongruence","filters" : [["IsLeftMagmaCongruence"]]},{"rank" : 21,"comment" : "ViewObj: for a free semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 21,"comment" : "ViewObj: combinatorial collector rep (32 Bits, up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 21,"comment" : "ViewObj: combinatorial collector rep (16 Bits, up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 21,"comment" : "ViewObj: combinatorial collector rep (8 Bits, up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj: for product of Fitting formations","filters" : [["IsFittingProductRep","IsFormationProductRep"]]},{"rank" : 20,"comment" : "ViewObj","filters" : [["IsUnicodeCharacter"]]},{"rank" : 20,"comment" : "ViewObj: for a fp semigroup with generators","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]},{"rank" : 20,"comment" : "ViewObj: combinatorial collector rep (32 Bits)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is32BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj: combinatorial collector rep (16 Bits)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is16BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj: combinatorial collector rep (8 Bits)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is8BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj: combinatorial collector rep (up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep"]]},{"rank" : 20,"comment" : "ViewObj: for a free semigroup containing the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 19,"comment" : "ViewObj: for Fitting formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsClassByPropertyRep"]]},{"rank" : 19,"comment" : "ViewObj: for a saturated formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsSaturated","Tester(IsSaturated)","IsClassByPropertyRep"]]},{"rank" : 19,"comment" : "ViewObj: for homomorphisms into matrix groups","filters" : [["IsHomomorphismIntoMatrixGroup","Tester(IsHomomorphismIntoMatrixGroup)"]]},{"rank" : 19,"comment" : "ViewObj: combinatorial collector rep","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsCombinatorialCollectorRep"]]},{"rank" : 19,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is32BitsSingleCollectorRep"]]},{"rank" : 19,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is16BitsSingleCollectorRep"]]},{"rank" : 19,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is8BitsSingleCollectorRep"]]},{"rank" : 19,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsSingleCollectorRep"]]},{"rank" : 19,"comment" : "ViewObj: for mapping by function with inverse","filters" : [["IsMappingByFunctionWithInverseRep"]]},{"rank" : 18,"comment" : "ViewObj: for a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 18,"comment" : "ViewObj: for a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 18,"comment" : "ViewObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 18,"comment" : "ViewObj: for a semigroup ideal with known generators","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","Tester(GeneratorsOfMagmaIdeal)","IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]]},{"rank" : 18,"comment" : "ViewObj: empty strings","filters" : [["IsString","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 17,"comment" : "ViewObj: for a Schunck class","filters" : [["IsSchunckClass","Tester(IsSchunckClass)","IsClassByPropertyRep"]]},{"rank" : 17,"comment" : "ViewObj: for a subsemigroup of a Rees 0-matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "ViewObj: for a subsemigroup of a Rees matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "ViewObj: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"]]},{"rank" : 17,"comment" : "ViewObj: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "ViewObj: for a free magma-with-one containing the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","CategoryCollections(IsWord)"]]},{"rank" : 17,"comment" : "ViewObj: For large finite field elements","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "ViewObj: for an add. magma-with-inverses with generators","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveGroup)"]]},{"rank" : 17,"comment" : "ViewObj: for a semigroup ideal","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]]},{"rank" : 16,"comment" : "ViewObj: for a Molien series","filters" : [["IsRationalFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","Tester(MolienSeriesInfo)"]]},{"rank" : 16,"comment" : "ViewObj: RightCoset","filters" : [["IsRightCoset"]]},{"rank" : 16,"comment" : "ViewObj: for a MagmaIdeal with generators","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","Tester(GeneratorsOfMagmaIdeal)"]]},{"rank" : 15,"comment" : "ViewObj: for formation product","filters" : [["IsFormationProductRep"]]},{"rank" : 15,"comment" : "ViewObj: for formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsClassByPropertyRep"]]},{"rank" : 15,"comment" : "ViewObj: for Fitting product","filters" : [["IsFittingProductRep"]]},{"rank" : 15,"comment" : "ViewObj: for Fitting class","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsClassByPropertyRep"]]},{"rank" : 15,"comment" : "ViewObj: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "ViewObj: for an add. magma-with-zero with generators","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]]},{"rank" : 15,"comment" : "ViewObj: for a MagmaIdeal","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]},{"rank" : 15,"comment" : "ViewObj: for a direct product element","filters" : [["IsDirectProductElement"]]},{"rank" : 14,"comment" : "ViewObj: for Fitting set","filters" : [["IsClassByPropertyRep","IsFittingSetRep"]]},{"rank" : 14,"comment" : "ViewObj: for a quotient semigroup with generators","filters" : [["IsQuotientSemigroup"]]},{"rank" : 14,"comment" : "ViewObj","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"]]},{"rank" : 14,"comment" : "ViewObj: for a free magma containing the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","CategoryCollections(IsWord)"]]},{"rank" : 14,"comment" : "ViewObj: for a RightMagmaIdeal with generators","filters" : [["IsRightActedOnBySuperset","Tester(GeneratorsOfExtRSet)","IsMagma"]]},{"rank" : 14,"comment" : "ViewObj: for a LeftMagmaIdeal with generators","filters" : [["IsLeftActedOnBySuperset","Tester(GeneratorsOfExtLSet)","IsMagma"]]},{"rank" : 14,"comment" : "ViewObj: for mapping by function","filters" : [["IsMappingByFunctionRep"]]},{"rank" : 13,"comment" : "ViewObj: for from-the-left collector","filters" : [["IsFromTheLeftCollectorRep"]]},{"rank" : 13,"comment" : "ViewObj: for floats","filters" : [["IsFloat"]]},{"rank" : 13,"comment" : "ViewObj: for an add. magma with generators","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagma)"]]},{"rank" : 13,"comment" : "ViewObj: for a RightMagmaIdeal","filters" : [["IsRightActedOnBySuperset","IsMagma"]]},{"rank" : 13,"comment" : "ViewObj: for a LeftMagmaIdeal","filters" : [["IsLeftActedOnBySuperset","IsMagma"]]},{"rank" : 12,"comment" : "ViewObj","filters" : [["IsPowerCommutatorCollector"]]},{"rank" : 12,"comment" : "ViewObj","filters" : [["IsPowerConjugateCollector"]]},{"rank" : 12,"comment" : "ViewObj: for an additive coset","filters" : [["IsAdditiveCoset"]]},{"rank" : 12,"comment" : "ViewObj: for an add. magma","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 11,"comment" : "ViewObj","filters" : [["IsConjugacyClassGroupRep"]]},{"rank" : 11,"comment" : "ViewObj","filters" : [["IsPolycyclicCollector"]]},{"rank" : 11,"comment" : "ViewObj: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 10,"comment" : "ViewObj: for external orbit","filters" : [["IsExternalOrbit"]]},{"rank" : 10,"comment" : "ViewObj","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]]},{"rank" : 10,"comment" : "ViewObj: for a semi-echelonized basis with basis vectors","filters" : [["IsBasis","IsSemiEchelonized","Tester(IsSemiEchelonized)","Tester(BasisVectors)"]]},{"rank" : 10,"comment" : "ViewObj: method for a weak pointer object","filters" : [["IsWeakPointerObject"]]},{"rank" : 9,"comment" : "ViewObj: for an element of an f.p. group (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpGroup"]]},{"rank" : 9,"comment" : "ViewObj: sliced perm","filters" : [["IsSlicedPermInv"]]},{"rank" : 9,"comment" : "ViewObj: sliced perm","filters" : [["IsSlicedPerm"]]},{"rank" : 9,"comment" : "ViewObj: for external subset","filters" : [["IsExternalSubset"]]},{"rank" : 9,"comment" : "ViewObj: for a semi-echelonized basis","filters" : [["IsBasis","IsSemiEchelonized","Tester(IsSemiEchelonized)"]]},{"rank" : 9,"comment" : "ViewObj: for right transversal","filters" : [["IsList","IsRightTransversalRep"]]},{"rank" : 8,"comment" : "ViewObj: IsString","filters" : [["IsString","IsFinite","Tester(IsFinite)"]]},{"rank" : 8,"comment" : "ViewObj: for a basis with basis vectors","filters" : [["IsBasis","Tester(BasisVectors)"]]},{"rank" : 8,"comment" : "ViewObj: IsString","filters" : [["IsString","IsFinite","Tester(IsFinite)"]]},{"rank" : 8,"comment" : "ViewObj: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "ViewObj: for IsGroupClass and IsClassByPropertyRep","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByPropertyRep"]]},{"rank" : 7,"comment" : "ViewObj","filters" : [["IsUnicodeString"]]},{"rank" : 7,"comment" : "ViewObj: for sparse hash tables","filters" : [["IsSparseHashRep"]]},{"rank" : 7,"comment" : "ViewObj: for dense hash tables","filters" : [["IsDenseHashRep"]]},{"rank" : 7,"comment" : "ViewObj: for a basis","filters" : [["IsBasis"]]},{"rank" : 7,"comment" : "ViewObj: for finite lists","filters" : [["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 6,"comment" : "ViewObj: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 6,"comment" : "ViewObj: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 6,"comment" : "ViewObj","filters" : [["IsMonoidByAdjoiningIdentityElt"]]},{"rank" : 6,"comment" : "ViewObj: External Set","filters" : [["IsExternalSet"]]},{"rank" : 6,"comment" : "ViewObj: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 5,"comment" : "ViewObj:  for IsGroupClassByListRep","filters" : [["IsGroupClassByListRep"]]},{"rank" : 5,"comment" : "ViewObj: for IsClassByUnionRep","filters" : [["IsClassByUnionRep"]]},{"rank" : 5,"comment" : "ViewObj: for IsClassByIntersectionRep","filters" : [["IsClassByIntersectionRep"]]},{"rank" : 5,"comment" : "ViewObj: for IsClassByComplementRep","filters" : [["IsClassByComplementRep"]]},{"rank" : 5,"comment" : "ViewObj: for IsClassByPropertyRep","filters" : [["IsClassByPropertyRep"]]},{"rank" : 5,"comment" : "ViewObj: for a Knuth Bendix rewriting system","filters" : [["IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)","IsKnuthBendixRewritingSystem"]]},{"rank" : 5,"comment" : "ViewObj: for a Knuth Bendix rewriting system","filters" : [["IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)","IsKnuthBendixRewritingSystem"]]},{"rank" : 5,"comment" : "ViewObj: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 4,"comment" : "ViewObj: for a worker farm by fork","filters" : [["IsWorkerFarmByFork"]]},{"rank" : 4,"comment" : "ViewObj: for a background job by fork","filters" : [["IsBackgroundJobByFork"]]},{"rank" : 4,"comment" : "ViewObj: for a monoid rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)"]]},{"rank" : 4,"comment" : "ViewObj: for a semigroup rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)"]]},{"rank" : 4,"comment" : "ViewObj: for an infinite list of generators","filters" : [["IsList","IsInfiniteListOfGeneratorsRep"]]},{"rank" : 4,"comment" : "ViewObj: for an infinite list of names","filters" : [["IsList","IsInfiniteListOfNamesRep"]]},{"rank" : 3,"comment" : "ViewObj: for iterators of residue class unions (ResClasses)","filters" : [["IsIterator","IsResidueClassUnionsIteratorRep"]]},{"rank" : 3,"comment" : "ViewObj: Wyckoff position","filters" : [["IsWyckoffPosition"]]},{"rank" : 3,"comment" : "ViewObj: for a tcp server","filters" : [["IsIOHub"]]},{"rank" : 3,"comment" : "ViewObj: for a real random source","filters" : [["IsRealRandomSource"]]},{"rank" : 3,"comment" : "ViewObj: lattice","filters" : [["IsLatticeSubgroupsRep"]]},{"rank" : 3,"comment" : "ViewObj: for dictionaries","filters" : [["IsDictionary"]]},{"rank" : 3,"comment" : "ViewObj: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]},{"rank" : 3,"comment" : "ViewObj: for a mutable basis of a Gaussian matrix space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianMatrixSpaceRep"]]},{"rank" : 3,"comment" : "ViewObj: for a mutable basis of a Gaussian row space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianRowSpaceRep"]]},{"rank" : 3,"comment" : "ViewObj: for mutable basis represented by a nice mutable basis","filters" : [["IsMutableBasis","IsMutableBasisViaNiceMutableBasisRep"]]},{"rank" : 3,"comment" : "ViewObj: for mutable basis represented by an immutable basis","filters" : [["IsMutableBasis","IsMutableBasisByImmutableBasisRep"]]},{"rank" : 2,"comment" : "ViewObj: for an IO_Result","filters" : [["IO_Result"]]},{"rank" : 2,"comment" : "ViewObj","filters" : [["IsRewritingSystem"]]},{"rank" : 2,"comment" : "ViewObj: for vector search tables","filters" : [["IsVectorSearchTable"]]},{"rank" : 2,"comment" : "ViewObj: default directory rep","filters" : [["IsDirectoryRep"]]},{"rank" : 2,"comment" : "ViewObj: for an operation","filters" : [["IsOperation"]]},{"rank" : 1,"comment" : "ViewObj: for a straight line decision","filters" : [["IsStraightLineDecision"]]},{"rank" : 1,"comment" : "ViewObj: for a black box program","filters" : [["IsBBoxProgram"]]},{"rank" : 1,"comment" : "ViewObj: for IsFile objects","filters" : [["IsFile"]]},{"rank" : 1,"comment" : "ViewObj","filters" : [["IsRecord"]]},{"rank" : 1,"comment" : "ViewObj: for a straight line program","filters" : [["IsStraightLineProgram"]]},{"rank" : 1,"comment" : "ViewObj","filters" : [["IsTableOfMarks"]]},{"rank" : 1,"comment" : "ViewObj: for an ordering","filters" : [["IsOrdering"]]},{"rank" : 1,"comment" : "ViewObj: stabilizer chain records","filters" : [["IsRecord"]]},{"rank" : 1,"comment" : "ViewObj: IsChar","filters" : [["IsChar"]]},{"rank" : 1,"comment" : "ViewObj: default method trying ViewString","filters" : [[]]},{"rank" : 1,"comment" : "ViewObj: record","filters" : [["IsRecord"]]},{"rank" : 1,"comment" : "ViewObj: for a function","filters" : [["IsFunction"]]},{"rank" : 0,"comment" : "ViewObj: default method using `PrintObj'","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ViewString","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10031,"comment" : "ViewString: for a symmetric inverse monoid","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)","IsSymmetricInverseSemigroup","Tester(IsSymmetricInverseSemigroup)"]]},{"rank" : 10031,"comment" : "ViewString: for a group as semigroup","filters" : [["IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]]},{"rank" : 10022,"comment" : "ViewString: for a full transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","IsFullTransformationSemigroup","Tester(IsFullTransformationSemigroup)"]]},{"rank" : 10001,"comment" : "ViewString: for an object with name","filters" : [["Tester(Name)"]]},{"rank" : 429,"comment" : "ViewString: for a field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 62,"comment" : "ViewString: for natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 62,"comment" : "ViewString: for natural alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 59,"comment" : "ViewString: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 52,"comment" : "ViewString: for a field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 48,"comment" : "ViewString: for full row modules","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 38,"comment" : "ViewString: for a group of partial perms","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 38,"comment" : "ViewString: for a group of transformations","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 36,"comment" : "ViewString: for a group with generators and size","filters" : [["Tester(Size)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 34,"comment" : "ViewString: for a group with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 34,"comment" : "ViewString: for a group with known generators (as a semigroup)","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "ViewString: for Z_(pi) (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 33,"comment" : "ViewString: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 27,"comment" : "ViewString: for a polynomial ring","filters" : [["IsPolynomialRing"]]},{"rank" : 26,"comment" : "ViewString: for a group as semigroup with known generators (as a semigroup)","filters" : [["Tester(GeneratorsOfMagma)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)"]]},{"rank" : 25,"comment" : "ViewString: for an inverse monoid with generators","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseMonoid)"]]},{"rank" : 24,"comment" : "ViewString: for a inverse monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 20,"comment" : "ViewString: for an inverse semigroup with inverse semigroup generators","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 20,"comment" : "ViewString: for an inverse semigroup with semigroup generators","filters" : [["Tester(GeneratorsOfMagma)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 19,"comment" : "ViewString: for univariate polynomial over finite field (ResClasses)","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 19,"comment" : "ViewString: for a inverse semigroup","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 19,"comment" : "ViewString: for a monoid with generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 18,"comment" : "ViewString: for a monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 18,"comment" : "ViewString: for integer","filters" : [["IsInt"]]},{"rank" : 17,"comment" : "ViewString: for a finite field element (ResClasses)","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 17,"comment" : "ViewString: for rationals","filters" : [["IsRat"]]},{"rank" : 17,"comment" : "ViewString: For large finite field elements","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "ViewString: for an internal FFE delegating to String","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 17,"comment" : "ViewString: for a magma-with-inverses with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 16,"comment" : "ViewString: RightCoset","filters" : [["IsRightCoset"]]},{"rank" : 15,"comment" : "ViewString: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 14,"comment" : "ViewString: for a semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 14,"comment" : "ViewString: for a magma-with-one with generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 13,"comment" : "ViewString: for floats","filters" : [["IsFloat"]]},{"rank" : 13,"comment" : "ViewString: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 12,"comment" : "ViewString: for a magma with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)"]]},{"rank" : 11,"comment" : "ViewString: for a magma","filters" : [["IsMagma"]]},{"rank" : 9,"comment" : "ViewString: for residue classes of Z^2 (ResClasses)","filters" : [["IsResidueClassUnionOfZxZ","IsResidueClass","Tester(IsResidueClass)"]]},{"rank" : 8,"comment" : "ViewString: DoubleCoset","filters" : [["IsDoubleCoset"]]},{"rank" : 8,"comment" : "ViewString: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "ViewString: for a Green's class","filters" : [["IsGreensClass"]]},{"rank" : 7,"comment" : "ViewString: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "ViewString: for a transformation","filters" : [["IsTransformation"]]},{"rank" : 7,"comment" : "ViewString: call ViewString and incorporate hints","filters" : [["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 5,"comment" : "ViewString: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 5,"comment" : "ViewString: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"]]},{"rank" : 2,"comment" : "ViewString: for residue classes with fixed rep's (ResClasses)","filters" : [["IsResidueClassWithFixedRepresentative","Tester(IsResidueClassWithFixedRepresentative)"]]},{"rank" : 2,"comment" : "ViewString: for residue classes (ResClasses)","filters" : [["IsResidueClass","Tester(IsResidueClass)"]]},{"rank" : 1,"comment" : "ViewString: IsChar","filters" : [["IsChar"]]},{"rank" : 1,"comment" : "ViewString: generic default method","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NameFunction","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetNameFunction","type" : "GAP_Operation","filters" : [[[],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumberArgumentsFunction","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CallFuncList","type" : "GAP_Operation","filters" : [[[],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "=","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10019,"comment" : "=: for two lists, the second being empty","filters" : [["IsList"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 10019,"comment" : "=: for two lists, the first being empty","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"]]},{"rank" : 10011,"comment" : "=: for a list and a residue class union (ResClasses)","filters" : [["IsList"],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 10011,"comment" : "=: for a residue class union and a list (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsList"]]},{"rank" : 734,"comment" : "=: handled by nice monomorphism: attribute CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 222,"comment" : "=: for 32 bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is32BitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is32BitsPcWordRep"]]},{"rank" : 222,"comment" : "=: for 16 bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is16BitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is16BitsPcWordRep"]]},{"rank" : 222,"comment" : "=: for 8 bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is8BitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is8BitsPcWordRep"]]},{"rank" : 220,"comment" : "=: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"],["IsPerm","IsStraightLineProgElm"]]},{"rank" : 214,"comment" : "=: two objects with memory","filters" : [["IsObjWithMemory"],["IsObjWithMemory"]]},{"rank" : 118,"comment" : "=: perm with straight line program element","filters" : [["IsPerm"],["IsPerm","IsStraightLineProgElm"]]},{"rank" : 118,"comment" : "=: straight line program element with perm","filters" : [["IsPerm","IsStraightLineProgElm"],["IsPerm"]]},{"rank" : 114,"comment" : "=: for two abelian number fields","filters" : [["IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 112,"comment" : "=: for two finite fields in the same family","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 110,"comment" : "=: objects with memory with x","filters" : [["IsObjWithMemory"],["IsMultiplicativeElement"]]},{"rank" : 110,"comment" : "=: x with straight line program element","filters" : [["IsMultiplicativeElement"],["IsStraightLineProgElm"]]},{"rank" : 110,"comment" : "=: straight line program element with x","filters" : [["IsStraightLineProgElm"],["IsMultiplicativeElement"]]},{"rank" : 110,"comment" : "=: for two compressed 8 bit matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 100,"comment" : "=: for subgroups of free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 100,"comment" : "=: for two division rings","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 96,"comment" : "=: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 90,"comment" : "=: for GF2 matrix and GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 82,"comment" : "=: for certain cyclotomic semirings","filters" : [["CategoryCollections(IsCyclotomic)","IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsCyclotomic)","IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 70,"comment" : "=: subgroups of fp group","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 70,"comment" : "=: pcgs computable groups using family pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(CanonicalPcgsWrtFamilyPcgs)","Tester(FamilyPcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(CanonicalPcgsWrtFamilyPcgs)","Tester(FamilyPcgs)"]]},{"rank" : 70,"comment" : "=: pcgs computable groups using home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(CanonicalPcgsWrtHomePcgs)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(CanonicalPcgsWrtHomePcgs)","Tester(HomePcgs)"]]},{"rank" : 68,"comment" : "=: for two ordinary block matrices","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 66,"comment" : "=: for Z_(pi)'s (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 66,"comment" : "=: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 62,"comment" : "=: for two class functions","filters" : [["IsClassFunction"],["IsClassFunction"]]},{"rank" : 54,"comment" : "=: for two rings with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 52,"comment" : "=: for two ANF automorphisms","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"]]},{"rank" : 52,"comment" : "=: for two Frobenius automorphisms","filters" : [["IsFrobeniusAutomorphism"],["IsFrobeniusAutomorphism"]]},{"rank" : 50,"comment" : "=: For 2 8 bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 47,"comment" : "=: pc group homomorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcGroupGeneralMappingByImages"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcGroupGeneralMappingByImages"]]},{"rank" : 46,"comment" : "=: for two field homomorphisms","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"],["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]]},{"rank" : 46,"comment" : "=: for two free left modules (at least one fin. dim.)","filters" : [["IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 46,"comment" : "=: method for two s.v. gen. mappings that is a field homomorphism","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]]},{"rank" : 44,"comment" : "=: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 44,"comment" : "=: for group automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]},{"rank" : 44,"comment" : "=: for GreensRelation","filters" : [["IsGreensRelation"],["IsGreensRelation"]]},{"rank" : 44,"comment" : "=: for GF2 vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 43,"comment" : "=: for ANF automorphism and identity mapping","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 43,"comment" : "=: for identity mapping and ANF automorphism","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"]]},{"rank" : 43,"comment" : "=: for Frobenius automorphism and identity mapping","filters" : [["IsFrobeniusAutomorphism"],["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 43,"comment" : "=: for identity mapping and Frobenius automorphism","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsFrobeniusAutomorphism"]]},{"rank" : 42,"comment" : "=: for eqivalence relations","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]},{"rank" : 42,"comment" : "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,one,scal. mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 40,"comment" : "=","filters" : [["IsUnicodeCharacter"],["IsUnicodeCharacter"]]},{"rank" : 40,"comment" : "=: for an inverse semigroups with generators","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"],["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 40,"comment" : "=: for two underlying relations of general mappings","filters" : [["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"],["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"]]},{"rank" : 39,"comment" : "=: homomorphism by images with homomorphism: compare generator images","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 38,"comment" : "=: homomorphism with general mapping: test b=a","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages"]]},{"rank" : 38,"comment" : "=: for ring ring general mapping and ring g.m.b.i.","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 38,"comment" : "=: for ring g.m.b.i. and ring general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 38,"comment" : "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,scal. mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 38,"comment" : "=: method for two s.v. gen. mappings that respect mult.,one,add.,add.inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 36,"comment" : "=: for two unknowns in default representation","filters" : [["IsUnknown","IsUnknownDefaultRep"],["IsUnknown","IsUnknownDefaultRep"]]},{"rank" : 35,"comment" : "=: for internal FFE and element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 35,"comment" : "=: for element in Z\/pZ (ModulusRep) and internal FFE","filters" : [["IsFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsInternalRep"]]},{"rank" : 34,"comment" : "=: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"],["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"]]},{"rank" : 34,"comment" : "=","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 34,"comment" : "=: BFElm=BFElm","filters" : [["IsAlgBFRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "=: BFElm<AlgElm","filters" : [["IsAlgBFRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "=: AlgElm=BFElm","filters" : [["IsKroneckerConstRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "=: AlgElm=AlgElm","filters" : [["IsKroneckerConstRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "=: laurent","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 34,"comment" : "=: method for two s.v. gen. mappings that respect add.,add.inv.,scal. mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 34,"comment" : "=: method for two s.v. gen. mappings that respect mult.,add.,add.inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 33,"comment" : "=: for a list and a class function","filters" : [["IsList"],["IsClassFunction"]]},{"rank" : 33,"comment" : "=: for a class function and a list","filters" : [["IsClassFunction"],["IsList"]]},{"rank" : 32,"comment" : "=: IsTransformationRepOfEndo, IsTransformationRepOfEndo","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"]]},{"rank" : 32,"comment" : "=: RightCosets","filters" : [["IsRightCoset"],["IsRightCoset"]]},{"rank" : 32,"comment" : "=","filters" : [["IsFFE"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 32,"comment" : "=","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE"]]},{"rank" : 32,"comment" : "=: for two elements in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 32,"comment" : "=: for cyclotomic and unknown","filters" : [["IsCyc"],["IsUnknown"]]},{"rank" : 32,"comment" : "=: for unknown and cyclotomic","filters" : [["IsUnknown"],["IsCyc"]]},{"rank" : 31,"comment" : "=: for `-infinity' and cyclotomic","filters" : [["IsNegInfinity"],["IsCyclotomic"]]},{"rank" : 31,"comment" : "=: for cyclotomic and `-infinity'","filters" : [["IsCyclotomic"],["IsNegInfinity"]]},{"rank" : 31,"comment" : "=: for `infinity' and cyclotomic","filters" : [["IsInfinity"],["IsCyclotomic"]]},{"rank" : 31,"comment" : "=: for cyclotomic and `infinity'","filters" : [["IsCyclotomic"],["IsInfinity"]]},{"rank" : 30,"comment" : "=: for two plist matrices","filters" : [["IsPlistMatrixRep"],["IsPlistMatrixRep"]]},{"rank" : 30,"comment" : "=: univariate = univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 30,"comment" : "=: method for two s.v. gen. mappings that respect add. and add. inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 30,"comment" : "=: method for two s.v. gen. mappings that respect mult. and inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 30,"comment" : "=: for two direct product elements","filters" : [["IsDirectProductElement"],["IsDirectProductElement"]]},{"rank" : 30,"comment" : "=: for a collection, and an empty row vector in the same family","filters" : [["IsCollection"],["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 30,"comment" : "=: for an empty row vector, and a collection in the same family","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"],["IsCollection"]]},{"rank" : 29,"comment" : "=: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "=: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 29,"comment" : "=: IsEndoMapping, IsTransformationRepOfEndo","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"]]},{"rank" : 29,"comment" : "=: IsTransformationRepOfEndo, IsEndoMapping","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 28,"comment" : "=","filters" : [["IsPadicExtensionNumber"],["IsPadicExtensionNumber"]]},{"rank" : 28,"comment" : "=","filters" : [["IsPurePadicNumber"],["IsPurePadicNumber"]]},{"rank" : 28,"comment" : "=: polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 28,"comment" : "=: for additive group and additive coset","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsAdditiveCoset"]]},{"rank" : 28,"comment" : "=: for additive coset and additive group","filters" : [["IsAdditiveCoset"],["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 28,"comment" : "=: for semigroup with generators and semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"],["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 26,"comment" : "=: classes for perm group","filters" : [["IsConjugacyClassPermGroupRep"],["IsConjugacyClassPermGroupRep"]]},{"rank" : 26,"comment" : "=: compare source generator images","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 26,"comment" : "=: zmodnze : for two elements in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 26,"comment" : "=: rational functions","filters" : [["IsRationalFunction"],["IsRationalFunction"]]},{"rank" : 26,"comment" : "=: for s. c. ring elements in dense vector rep.","filters" : [["IsSCRingObj","IsDenseCoeffVectorRep"],["IsSCRingObj","IsDenseCoeffVectorRep"]]},{"rank" : 26,"comment" : "=: for two Lie objects in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 26,"comment" : "=: for s. c. algebra elements in dense vector rep.","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 26,"comment" : "=: method for two s.v. gen. mappings that respect add. and zero","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 26,"comment" : "=: method for two s.v. gen. mappings that respect mult. and one","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)"]]},{"rank" : 25,"comment" : "=: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 25,"comment" : "=: FElm=BFElm","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsAlgBFRep"]]},{"rank" : 25,"comment" : "=: BFElm=FElm","filters" : [["IsAlgBFRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "=: FElm=AlgElm","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsKroneckerConstRep"]]},{"rank" : 25,"comment" : "=: AlgElm=FElm","filters" : [["IsKroneckerConstRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 24,"comment" : "=","filters" : [["IsRationalClassPermGroupRep"],["IsRationalClassPermGroupRep"]]},{"rank" : 24,"comment" : "=: xorbs which know their size","filters" : [["Tester(Size)","IsExternalOrbit"],["Tester(Size)","IsExternalOrbit"]]},{"rank" : 24,"comment" : "=: for two UEALattice elements","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"],["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 24,"comment" : "=: for two additive cosets","filters" : [["IsAdditiveCoset"],["IsAdditiveCoset"]]},{"rank" : 24,"comment" : "=: for binary relss over [1..n] with images list","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 22,"comment" : "=","filters" : [["IsConjugacyClassSubgroupsRep"],["IsConjugacyClassSubgroupsRep"]]},{"rank" : 22,"comment" : "=","filters" : [["IsRationalClassGroupRep"],["IsRationalClassGroupRep"]]},{"rank" : 22,"comment" : "=: xorbs with canonicalRepresentativeDeterminator","filters" : [["IsExternalOrbit","Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"],["IsExternalOrbit","Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]]},{"rank" : 22,"comment" : "=: for two plist vectors","filters" : [["IsPlistVectorRep"],["IsPlistVectorRep"]]},{"rank" : 22,"comment" : "=: for s. c. algebra elements","filters" : [["IsSCAlgebraObj"],["IsSCAlgebraObj"]]},{"rank" : 22,"comment" : "=: for two normalized f.p. algebra elements","filters" : [["IsElementOfFpAlgebra","IsNormalForm","Tester(IsNormalForm)"],["IsElementOfFpAlgebra","IsNormalForm","Tester(IsNormalForm)"]]},{"rank" : 22,"comment" : "=: for two free magma ring elements","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 22,"comment" : "=: method for two s.v. gen. mappings that respect add.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)"]]},{"rank" : 22,"comment" : "=: method for two s.v. gen. mappings that respect mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)"]]},{"rank" : 20,"comment" : "=: xorbs","filters" : [["IsExternalOrbit"],["IsExternalOrbit"]]},{"rank" : 20,"comment" : "=: for two weight rep elements","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"],["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 20,"comment" : "=: for two cochains","filters" : [["IsPackedElementDefaultRep","IsCochain"],["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 20,"comment" : "=: for direct sum elements","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"],["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 20,"comment" : "=: for sparse rowspace elements","filters" : [["IsPackedElementDefaultRep","IsSparseRowSpaceElement"],["IsPackedElementDefaultRep","IsSparseRowSpaceElement"]]},{"rank" : 20,"comment" : "=: for monomial elements","filters" : [["IsMonomialElement","IsMonomialElementRep"],["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 20,"comment" : "=: for two algebra module elements in packed representation","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"],["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 18,"comment" : "=: for two residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 18,"comment" : "=: for two f.p. algebra elements (try nice monomorphism)","filters" : [["IsElementOfFpAlgebra"],["IsElementOfFpAlgebra"]]},{"rank" : 18,"comment" : "=: method for two s.v. gen. mappings","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 18,"comment" : "=: for two small lists","filters" : [["IsList","IsSmallList","Tester(IsSmallList)"],["IsList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 16,"comment" : "=: for fp monoid elts produced by the Froidure-Pin algorithm","filters" : [["IsFpMonoidReducedElt","Tester(IsFpMonoidReducedElt)"],["IsFpMonoidReducedElt","Tester(IsFpMonoidReducedElt)"]]},{"rank" : 16,"comment" : "=: DoubleCosets","filters" : [["IsDoubleCoset"],["IsDoubleCoset"]]},{"rank" : 16,"comment" : "=: for two inf. bits assoc. words","filters" : [["IsInfBitsAssocWord"],["IsInfBitsAssocWord"]]},{"rank" : 16,"comment" : "=: for two 32 bits assoc. words","filters" : [["Is32BitsAssocWord"],["Is32BitsAssocWord"]]},{"rank" : 16,"comment" : "=: for two 16 bits assoc. words","filters" : [["Is16BitsAssocWord"],["Is16BitsAssocWord"]]},{"rank" : 16,"comment" : "=: for two 8 bits assoc. words","filters" : [["Is8BitsAssocWord"],["Is8BitsAssocWord"]]},{"rank" : 14,"comment" : "=","filters" : [["IsUnicodeString"],["IsUnicodeString"]]},{"rank" : 14,"comment" : "=: for fp semigp elts produced by the Froidure-Pin algorithm","filters" : [["IsFpSemigpReducedElt","Tester(IsFpSemigpReducedElt)"],["IsFpSemigpReducedElt","Tester(IsFpSemigpReducedElt)"]]},{"rank" : 14,"comment" : "=: for Green's classes","filters" : [["IsGreensClass"],["IsGreensClass"]]},{"rank" : 14,"comment" : "=: for two f.p. group elements","filters" : [["IsElementOfFpGroup"],["IsElementOfFpGroup"]]},{"rank" : 14,"comment" : "=: wreath elements","filters" : [["IsWreathProductElement"],["IsWreathProductElement"]]},{"rank" : 14,"comment" : "=: for two elements of magma by mult. table","filters" : [["IsMagmaByMultiplicationTableObj"],["IsMagmaByMultiplicationTableObj"]]},{"rank" : 14,"comment" : "=: for two elements of a magma with zero adjoined","filters" : [["IsMagmaWithZeroAdjoinedElementRep"],["IsMagmaWithZeroAdjoinedElementRep"]]},{"rank" : 14,"comment" : "=: for two general mappings","filters" : [["IsGeneralMapping"],["IsGeneralMapping"]]},{"rank" : 14,"comment" : "=: for two finite lists (not necessarily small)","filters" : [["IsList","IsFinite","Tester(IsFinite)"],["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 12,"comment" : "=: for two unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 12,"comment" : "=: for a list of elements and an infinite domain (ResClasses)","filters" : [["IsList","IsFinite","Tester(IsFinite)"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 12,"comment" : "=: for an infinite domain and a list of elements (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 12,"comment" : "=: for pcp elements","filters" : [["IsPcpElement"],["IsPcpElement"]]},{"rank" : 12,"comment" : "=","filters" : [["IsMonoidByAdjoiningIdentityElt"],["IsMonoidByAdjoiningIdentityElt"]]},{"rank" : 12,"comment" : "=: for two elements of a f.p. monoid","filters" : [["IsElementOfFpMonoid"],["IsElementOfFpMonoid"]]},{"rank" : 12,"comment" : "=","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 12,"comment" : "=: assoc words in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]},{"rank" : 12,"comment" : "=: for two equivalence classes","filters" : [["IsEquivalenceClass"],["IsEquivalenceClass"]]},{"rank" : 10,"comment" : "=: for elements of a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroupElement"],["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 10,"comment" : "=: for elements of a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroupElement"],["IsReesMatrixSemigroupElement"]]},{"rank" : 10,"comment" : "=: for two Knuth-Bendix rewriting systems","filters" : [["IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"],["IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]},{"rank" : 10,"comment" : "=: for two elements of a f.p. semigroup","filters" : [["IsElementOfFpSemigroup"],["IsElementOfFpSemigroup"]]},{"rank" : 10,"comment" : "=: for two domains","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 10,"comment" : "=: for a domain and a list","filters" : [["IsCollection","IsGeneralizedDomain"],["IsList","IsCollection"]]},{"rank" : 10,"comment" : "=: for a list and a domain","filters" : [["IsList","IsCollection"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 10,"comment" : "=: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"],["IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 8,"comment" : "=: for two words","filters" : [["IsWord"],["IsWord"]]},{"rank" : 6,"comment" : "=","filters" : [["IsWyckoffPosition"],["IsWyckoffPosition"]]},{"rank" : 6,"comment" : "=: for two lists with length - last resort","filters" : [["IsList","Tester(LENGTH)"],["IsList","Tester(LENGTH)"]]},{"rank" : 4,"comment" : "=: for classes","filters" : [["IsClass"],["IsClass"]]},{"rank" : 4,"comment" : "=: for two IO_Results","filters" : [["IO_Result"],["IO_Result"]]},{"rank" : 4,"comment" : "=: for two lists - last resort","filters" : [["IsList"],["IsList"]]},{"rank" : 4,"comment" : "=: for two info classes","filters" : [["IsInfoClassListRep"],["IsInfoClassListRep"]]},{"rank" : 2,"comment" : "=: for two IsFile objects","filters" : [["IsFile"],["IsFile"]]},{"rank" : 2,"comment" : "=: for another object and an IO_Result","filters" : [[],["IO_Result"]]},{"rank" : 2,"comment" : "=: for an IO_Result and another object","filters" : [["IO_Result"],[]]},{"rank" : 2,"comment" : "=: for two directories","filters" : [["IsDirectory"],["IsDirectory"]]},{"rank" : 2,"comment" : "=: for two families: delegate to `IsIdenticalObj'","filters" : [["IsFamily"],["IsFamily"]]},{"rank" : 2,"comment" : "=: record = record","filters" : [["IsRecord"],["IsRecord"]]},{"rank" : 0,"comment" : "=:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "=: for two objects in different families","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "<","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 222,"comment" : "<: for 32 bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is32BitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is32BitsPcWordRep"]]},{"rank" : 222,"comment" : "<: for 16 bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is16BitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is16BitsPcWordRep"]]},{"rank" : 222,"comment" : "<: method for 8 bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is8BitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","Is8BitsPcWordRep"]]},{"rank" : 220,"comment" : "<: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"],["IsPerm","IsStraightLineProgElm"]]},{"rank" : 214,"comment" : "<: two objects with memory","filters" : [["IsObjWithMemory"],["IsObjWithMemory"]]},{"rank" : 134,"comment" : "<: RightCosets of perm group","filters" : [["CategoryCollections(IsPerm)","IsRightCoset"],["CategoryCollections(IsPerm)","IsRightCoset"]]},{"rank" : 116,"comment" : "<: for two inf. bits assoc. words","filters" : [["IsInfBitsAssocWord"],["IsInfBitsAssocWord"]]},{"rank" : 114,"comment" : "<: for two abelian number fields","filters" : [["IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 110,"comment" : "<: x with objects with memory","filters" : [["IsObjWithMemory"],["IsMultiplicativeElement"]]},{"rank" : 110,"comment" : "<: objects with memory with x","filters" : [["IsObjWithMemory"],["IsMultiplicativeElement"]]},{"rank" : 110,"comment" : "<: x with straight line program element","filters" : [["IsMultiplicativeElement"],["IsStraightLineProgElm"]]},{"rank" : 110,"comment" : "<: straight line program element with x","filters" : [["IsStraightLineProgElm"],["IsMultiplicativeElement"]]},{"rank" : 110,"comment" : "<: for two compressed 8 bit matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 100,"comment" : "<: two AffineCrystGroupOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 100,"comment" : "<: two AffineCrystGroupOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 90,"comment" : "<: for GF2 matrix and GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 86,"comment" : "<: cgs comparison","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 66,"comment" : "<: groups by smallest generating sets","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 62,"comment" : "<: for two class functions","filters" : [["IsClassFunction"],["IsClassFunction"]]},{"rank" : 52,"comment" : "<: for two ANF automorphisms","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"]]},{"rank" : 52,"comment" : "<: for two Frobenius automorphisms","filters" : [["IsFrobeniusAutomorphism"],["IsFrobeniusAutomorphism"]]},{"rank" : 50,"comment" : "<: For 2 8 bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 46,"comment" : "<: for two free left modules","filters" : [["IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 44,"comment" : "<: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 44,"comment" : "<: for GF2 vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 43,"comment" : "<: for ANF automorphism and identity mapping","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 43,"comment" : "<: for identity mapping and ANF automorphism","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"]]},{"rank" : 43,"comment" : "<: for a Frobenius automorphism, and an identity mapping","filters" : [["IsFrobeniusAutomorphism"],["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 43,"comment" : "<: for an identity mapping, and a Frobenius automorphism","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsFrobeniusAutomorphism"]]},{"rank" : 40,"comment" : "<: for two underlying relations of general mappings","filters" : [["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"],["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"]]},{"rank" : 38,"comment" : "<: for transformation semigroups","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 38,"comment" : "<: for two elements in Z\/pZ (ModulusRep, small)","filters" : [["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 38,"comment" : "<: for two elements in Z\/pZ (ModulusRep, large)","filters" : [["IsFFE","IsLexOrderedFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsLexOrderedFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 36,"comment" : "<","filters" : [["IsLexOrderedFFE","IsCoeffsModConwayPolRep"],["IsLexOrderedFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 36,"comment" : "<: for internal FFE and element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 36,"comment" : "<: for element in Z\/pZ (ModulusRep) and internal FFE","filters" : [["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsInternalRep"]]},{"rank" : 36,"comment" : "<: for two unknowns in default representation","filters" : [["IsUnknown","IsUnknownDefaultRep"],["IsUnknown","IsUnknownDefaultRep"]]},{"rank" : 34,"comment" : "<: group homomorphisms: Images of smallest generators","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 34,"comment" : "<: for two elements in Z\/nZ (ModulusRep, nonprime)","filters" : [["IsZmodnZObjNonprime","IsModulusRep"],["IsZmodnZObjNonprime","IsModulusRep"]]},{"rank" : 34,"comment" : "<: BFElm<BFElm","filters" : [["IsAlgBFRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "<: BFElm<AlgElm","filters" : [["IsAlgBFRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "<: AlgElm<BFElm","filters" : [["IsKroneckerConstRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "<: AlgElm<AlgElm","filters" : [["IsKroneckerConstRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "<: Univariate Polynomials","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 33,"comment" : "<: for a module and a residue class union (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsResidueClassUnion"]]},{"rank" : 33,"comment" : "<: for a residue class union and a module (ResClasses)","filters" : [["IsResidueClassUnion"],["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 33,"comment" : "<: for a list and a class function","filters" : [["IsClassFunction"],["IsList"]]},{"rank" : 33,"comment" : "<: for a class function and a list","filters" : [["IsClassFunction"],["IsList"]]},{"rank" : 32,"comment" : "<: for a ring and a residue class union (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsResidueClassUnion"]]},{"rank" : 32,"comment" : "<: for a residue class union and a ring (ResClasses)","filters" : [["IsResidueClassUnion"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 32,"comment" : "<: IsTransformationRepOfEndo, IsTransformationRepOfEndo","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"]]},{"rank" : 32,"comment" : "<: for cyclotomic and unknown","filters" : [["IsCyc"],["IsUnknown"]]},{"rank" : 32,"comment" : "<: for unknown and cyclotomic","filters" : [["IsUnknown"],["IsCyc"]]},{"rank" : 31,"comment" : "<: for `-infinity' and cyclotomic","filters" : [["IsNegInfinity"],["IsCyclotomic"]]},{"rank" : 31,"comment" : "<: for cyclotomic and `-infinity'","filters" : [["IsCyclotomic"],["IsNegInfinity"]]},{"rank" : 31,"comment" : "<: for `infinity' and cyclotomic","filters" : [["IsInfinity"],["IsCyclotomic"]]},{"rank" : 31,"comment" : "<: for cyclotomic and `infinity'","filters" : [["IsCyclotomic"],["IsInfinity"]]},{"rank" : 30,"comment" : "<: for two plist matrices","filters" : [["IsPlistMatrixRep"],["IsPlistMatrixRep"]]},{"rank" : 30,"comment" : "<: for two direct product elements","filters" : [["IsDirectProductElement"],["IsDirectProductElement"]]},{"rank" : 30,"comment" : "<: for two finite field elements in different characteristic","filters" : [["IsFFE"],["IsFFE"]]},{"rank" : 30,"comment" : "<: for a finite field element, and a cyclotomic","filters" : [["IsFFE"],["IsCyclotomic"]]},{"rank" : 30,"comment" : "<: for a cyclotomic, and a finite field element","filters" : [["IsCyclotomic"],["IsFFE"]]},{"rank" : 29,"comment" : "<: for a module and a list of elements (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsList"]]},{"rank" : 29,"comment" : "<: for a list of elements and a module (ResClasses)","filters" : [["IsList"],["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 29,"comment" : "<: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "<: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 29,"comment" : "<: IsTransformationRepOfEndo, IsEndoMapping","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 29,"comment" : "<: IsEndoMapping, IsTransformationRepOfEndo","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"]]},{"rank" : 28,"comment" : "<: for a ring and a list of elements (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]},{"rank" : 28,"comment" : "<: for a list of elements and a ring (ResClasses)","filters" : [["IsList"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 28,"comment" : "<","filters" : [["IsPadicExtensionNumber"],["IsPadicExtensionNumber"]]},{"rank" : 28,"comment" : "<","filters" : [["IsPurePadicNumber"],["IsPurePadicNumber"]]},{"rank" : 26,"comment" : "<: zmodnze : for two elements in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 26,"comment" : "<: for s. c. ring elements in dense vector rep.","filters" : [["IsSCRingObj","IsDenseCoeffVectorRep"],["IsSCRingObj","IsDenseCoeffVectorRep"]]},{"rank" : 26,"comment" : "<: for two Lie objects in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 26,"comment" : "<: for s. c. algebra elements in dense vector rep.","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 25,"comment" : "<: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 25,"comment" : "<: FElm<BFElm","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsAlgBFRep"]]},{"rank" : 25,"comment" : "<: BFElm<FElm","filters" : [["IsAlgBFRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "<: FElm<AlgElm","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsKroneckerConstRep"]]},{"rank" : 25,"comment" : "<: AlgElm<FElm","filters" : [["IsKroneckerConstRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 24,"comment" : "<: rational functions","filters" : [["IsPolynomialFunction"],["IsPolynomialFunction"]]},{"rank" : 24,"comment" : "<: for two UEALattice elements","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"],["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 24,"comment" : "<: for binary rels over [1..n] with images list","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 23,"comment" : "<: for a permutation, and a finite field element","filters" : [["IsPerm"],["IsFFE"]]},{"rank" : 23,"comment" : "<: for a permutation, and a cyclotomic","filters" : [["IsPerm"],["IsCyclotomic"]]},{"rank" : 23,"comment" : "<: for a finite field element, and a permutation","filters" : [["IsFFE"],["IsPerm"]]},{"rank" : 23,"comment" : "<: for a cyclotomic, and a permutation","filters" : [["IsCyclotomic"],["IsPerm"]]},{"rank" : 22,"comment" : "<: for a transformation and finite field element","filters" : [["IsTransformation"],["IsFFE"]]},{"rank" : 22,"comment" : "<: for a finite field element and transformation","filters" : [["IsFFE"],["IsTransformation"]]},{"rank" : 22,"comment" : "<: for a cyclotomic and transformation","filters" : [["IsCyclotomic"],["IsTransformation"]]},{"rank" : 22,"comment" : "<: for a transformation and cyclotomic","filters" : [["IsTransformation"],["IsCyclotomic"]]},{"rank" : 22,"comment" : "<: for two plist vectors","filters" : [["IsPlistVectorRep"],["IsPlistVectorRep"]]},{"rank" : 22,"comment" : "<: for s. c. algebra elements","filters" : [["IsSCAlgebraObj"],["IsSCAlgebraObj"]]},{"rank" : 22,"comment" : "<: for two normalized f.p. algebra elements","filters" : [["IsElementOfFpAlgebra","IsNormalForm","Tester(IsNormalForm)"],["IsElementOfFpAlgebra","IsNormalForm","Tester(IsNormalForm)"]]},{"rank" : 22,"comment" : "<: for two free magma ring elements","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 20,"comment" : "<: xorbs, via AsSSortedList","filters" : [["IsExternalOrbit"],["IsExternalOrbit"]]},{"rank" : 20,"comment" : "<: for two weight rep elements","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"],["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 20,"comment" : "<: for two cochains","filters" : [["IsPackedElementDefaultRep","IsCochain"],["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 20,"comment" : "<: for direct sum elements","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"],["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 20,"comment" : "<: for sparse rowspace elements","filters" : [["IsPackedElementDefaultRep","IsSparseRowSpaceElement"],["IsPackedElementDefaultRep","IsSparseRowSpaceElement"]]},{"rank" : 20,"comment" : "<: for monomial elements","filters" : [["IsMonomialElement","IsMonomialElementRep"],["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 20,"comment" : "<: for two algebra module elements in packed representation","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"],["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 19,"comment" : "<","filters" : [["IsFFE","IsModulusRep"],["IsCoeffsModConwayPolRep"]]},{"rank" : 19,"comment" : "<","filters" : [["IsCoeffsModConwayPolRep"],["IsFFE","IsModulusRep"]]},{"rank" : 19,"comment" : "<","filters" : [["IsFFE","IsInternalRep"],["IsCoeffsModConwayPolRep"]]},{"rank" : 19,"comment" : "<","filters" : [["IsCoeffsModConwayPolRep"],["IsFFE","IsInternalRep"]]},{"rank" : 18,"comment" : "<: for two residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 18,"comment" : "<: for two f.p. algebra elements (try nice monomorphism)","filters" : [["IsElementOfFpAlgebra"],["IsElementOfFpAlgebra"]]},{"rank" : 18,"comment" : "<: for two small homogeneous lists","filters" : [["IsHomogeneousList","IsSmallList","Tester(IsSmallList)"],["IsHomogeneousList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 18,"comment" : "<: for two small lists, possibly in different families","filters" : [["IsList","IsSmallList","Tester(IsSmallList)"],["IsList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 17,"comment" : "<: for a list, and a finite field element","filters" : [["IsList"],["IsFFE"]]},{"rank" : 17,"comment" : "<: for a list, and a cyclotomic","filters" : [["IsList"],["IsCyclotomic"]]},{"rank" : 17,"comment" : "<: for a finite field element, and a list","filters" : [["IsFFE"],["IsList"]]},{"rank" : 17,"comment" : "<: for a cyclotomic, and a list","filters" : [["IsCyclotomic"],["IsList"]]},{"rank" : 16,"comment" : "<: for fp monoid elts produced by the Froidure-Pin algorithm","filters" : [["IsFpMonoidReducedElt","Tester(IsFpMonoidReducedElt)"],["IsFpMonoidReducedElt","Tester(IsFpMonoidReducedElt)"]]},{"rank" : 16,"comment" : "<: for two 32 bits assoc. words","filters" : [["Is32BitsAssocWord"],["Is32BitsAssocWord"]]},{"rank" : 16,"comment" : "<: for two 16 bits assoc. words","filters" : [["Is16BitsAssocWord"],["Is16BitsAssocWord"]]},{"rank" : 16,"comment" : "<: for two 8 bits assoc. words","filters" : [["Is8BitsAssocWord"],["Is8BitsAssocWord"]]},{"rank" : 16,"comment" : "<: for a character, and a finite field element","filters" : [["IsChar"],["IsFFE"]]},{"rank" : 16,"comment" : "<: for a character, and a cyclotomic","filters" : [["IsChar"],["IsCyclotomic"]]},{"rank" : 16,"comment" : "<: for a boolean, and a finite field element","filters" : [["IsBool"],["IsFFE"]]},{"rank" : 16,"comment" : "<: for a boolean, and a cyclotomic","filters" : [["IsBool"],["IsCyclotomic"]]},{"rank" : 16,"comment" : "<: for a finite field element, and a character","filters" : [["IsFFE"],["IsChar"]]},{"rank" : 16,"comment" : "<: for a finite field element, and a boolean","filters" : [["IsFFE"],["IsBool"]]},{"rank" : 16,"comment" : "<: for a cyclotomic, and a character","filters" : [["IsCyclotomic"],["IsChar"]]},{"rank" : 16,"comment" : "<: for a cyclotomic, and a boolean","filters" : [["IsCyclotomic"],["IsBool"]]},{"rank" : 14,"comment" : "<: for fp semigp elts produced by the Froidure-Pin algorithm","filters" : [["IsFpSemigpReducedElt","Tester(IsFpSemigpReducedElt)"],["IsFpSemigpReducedElt","Tester(IsFpSemigpReducedElt)"]]},{"rank" : 14,"comment" : "<: for two f.p. group elements","filters" : [["IsElementOfFpGroup"],["IsElementOfFpGroup"]]},{"rank" : 14,"comment" : "<: wreath elements","filters" : [["IsWreathProductElement"],["IsWreathProductElement"]]},{"rank" : 14,"comment" : "<: for two elements of magma by mult. table","filters" : [["IsMagmaByMultiplicationTableObj"],["IsMagmaByMultiplicationTableObj"]]},{"rank" : 14,"comment" : "<: for two elements of magmas with zero adjoined","filters" : [["IsMagmaWithZeroAdjoinedElementRep"],["IsMagmaWithZeroAdjoinedElementRep"]]},{"rank" : 14,"comment" : "<: for two general mappings","filters" : [["IsGeneralMapping"],["IsGeneralMapping"]]},{"rank" : 14,"comment" : "<: for two finite homogeneous lists (not necessarily small)","filters" : [["IsHomogeneousList","IsFinite","Tester(IsFinite)"],["IsHomogeneousList","IsFinite","Tester(IsFinite)"]]},{"rank" : 12,"comment" : "<: for two unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 12,"comment" : "<: for pcp elements","filters" : [["IsPcpElement"],["IsPcpElement"]]},{"rank" : 12,"comment" : "<","filters" : [["IsMonoidByAdjoiningIdentityElt"],["IsMonoidByAdjoiningIdentityElt"]]},{"rank" : 12,"comment" : "<: for two elements of a f.p. monoid","filters" : [["IsElementOfFpMonoid"],["IsElementOfFpMonoid"]]},{"rank" : 12,"comment" : "<","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 12,"comment" : "<: assoc words in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]},{"rank" : 12,"comment" : "<: for two equivalence classes","filters" : [["IsEquivalenceClass"],["IsEquivalenceClass"]]},{"rank" : 10,"comment" : "<: for elements of a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroupElement"],["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 10,"comment" : "<: for elements of a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroupElement"],["IsReesMatrixSemigroupElement"]]},{"rank" : 10,"comment" : "<: for two elements of a f.p. semigroup","filters" : [["IsElementOfFpSemigroup"],["IsElementOfFpSemigroup"]]},{"rank" : 10,"comment" : "<: assoc words","filters" : [["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]},{"rank" : 10,"comment" : "<: for a domain and a list","filters" : [["IsCollection","IsGeneralizedDomain"],["IsList","IsCollection"]]},{"rank" : 10,"comment" : "<: for a list and a domain","filters" : [["IsList","IsCollection"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 10,"comment" : "<: for a list, and a permutation","filters" : [["IsList"],["IsPerm"]]},{"rank" : 10,"comment" : "<: for a permutation, and a list","filters" : [["IsPerm"],["IsList"]]},{"rank" : 10,"comment" : "<: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"],["IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 9,"comment" : "<: for a character, and a permutation","filters" : [["IsChar"],["IsPerm"]]},{"rank" : 9,"comment" : "<: for a boolean, and a permutation","filters" : [["IsBool"],["IsPerm"]]},{"rank" : 9,"comment" : "<: for a permutation, and a character","filters" : [["IsPerm"],["IsChar"]]},{"rank" : 9,"comment" : "<: for a permutation, and a boolean","filters" : [["IsPerm"],["IsBool"]]},{"rank" : 8,"comment" : "<: for a residue class union and a list (ResClasses)","filters" : [["IsResidueClassUnion"],["IsList"]]},{"rank" : 8,"comment" : "<: for a list and a residue class union (ResClasses)","filters" : [["IsList"],["IsResidueClassUnion"]]},{"rank" : 8,"comment" : "<: nonassoc words","filters" : [["IsWord"],["IsWord"]]},{"rank" : 6,"comment" : "<","filters" : [["IsWyckoffPosition"],["IsWyckoffPosition"]]},{"rank" : 4,"comment" : "<: for classes","filters" : [["IsClass"],["IsClass"]]},{"rank" : 4,"comment" : "<: for two info classes","filters" : [["IsInfoClassListRep"],["IsInfoClassListRep"]]},{"rank" : 4,"comment" : "<: for two finite lists, possibly in different families","filters" : [["IsList"],["IsList"]]},{"rank" : 3,"comment" : "<: for a list, and a character","filters" : [["IsList"],["IsChar"]]},{"rank" : 3,"comment" : "<: for a list, and a boolean","filters" : [["IsList"],["IsBool"]]},{"rank" : 3,"comment" : "<: for a character, and a list","filters" : [["IsChar"],["IsList"]]},{"rank" : 3,"comment" : "<: for a boolean, and a list","filters" : [["IsBool"],["IsList"]]},{"rank" : 2,"comment" : "<: for two IsFile objects","filters" : [["IsFile"],["IsFile"]]},{"rank" : 2,"comment" : "<: for a character, and a boolean","filters" : [["IsChar"],["IsBool"]]},{"rank" : 2,"comment" : "<: for a boolean, and a character","filters" : [["IsBool"],["IsChar"]]},{"rank" : 2,"comment" : "<: record < record","filters" : [["IsRecord"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "in","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10014,"comment" : "in: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 10004,"comment" : "in: for an object, and a collection that contains the whole family","filters" : [[],["IsCollection","IsWholeFamily","Tester(IsWholeFamily)"]]},{"rank" : 10002,"comment" : "in: for wrong family relation","filters" : [[],["IsCollection"]]},{"rank" : 434,"comment" : "in: TF method, use tree","filters" : [["IsMultiplicativeElementWithInverse"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingFreeLiftSetup)"]]},{"rank" : 434,"comment" : "in: for a FFE, and a field of FFEs","filters" : [["IsFFE"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 427,"comment" : "in: special linear group","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalSL","Tester(IsNaturalSL)"]]},{"rank" : 425,"comment" : "in: general linear group","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalGL","Tester(IsNaturalGL)"]]},{"rank" : 410,"comment" : "in: for groups of FFE","filters" : [["IsFFE"],["CategoryCollections(IsFFE)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 408,"comment" : "in: respecting sesquilinear form","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFullSubgroupGLorSLRespectingSesquilinearForm","Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]]},{"rank" : 408,"comment" : "in: respecting bilinear form","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFullSubgroupGLorSLRespectingBilinearForm","Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"]]},{"rank" : 372,"comment" : "in: by nice monomorphism","filters" : [["IsMultiplicativeElementWithInverse"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 134,"comment" : "in: subgroup by property","filters" : [[],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(ElementTestFunction)"]]},{"rank" : 86,"comment" : "in: for matrix and SL(n,Z)","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNaturalSL","Tester(IsNaturalSL)","IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"]]},{"rank" : 84,"comment" : "in: for matrix and GL(n,Z)","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNaturalGL","Tester(IsNaturalGL)","IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"]]},{"rank" : 84,"comment" : "in: for cyclotomic and Rationals","filters" : [["IsCyclotomic"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 84,"comment" : "in: for subgroups of Z\/p^aZ, p<>2","filters" : [["IsZmodnZObjNonprime"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 83,"comment" : "in: for cyclotomic and cyclotomic field","filters" : [["IsCyc"],["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 81,"comment" : "in: for cyclotomic and abelian number field","filters" : [["IsCyc"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 78,"comment" : "in: for CrystGroup","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 70,"comment" : "in: perm in natsymmetric group","filters" : [["IsPerm"],["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 70,"comment" : "in: alternating","filters" : [["IsPerm"],["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 68,"comment" : "in: Alg in Ext","filters" : [["IsAlgebraicElement"],["IsAlgebraicExtension"]]},{"rank" : 67,"comment" : "in: for a permutation, and a permutation group","filters" : [["IsPerm"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 61,"comment" : "in: FElm in Ext","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsAlgebraicExtension"]]},{"rank" : 60,"comment" : "in: for full row module","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 58,"comment" : "in: for Gaussian integers","filters" : [["IsCyc"],["IsGaussianIntegers"]]},{"rank" : 57,"comment" : "in: for a subgroup of a free group","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 54,"comment" : "in: LAGUNA: for a Lie algebra that comes from an associative algebra and a Lie object","filters" : [["IsLieObject"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 54,"comment" : "in: for integers","filters" : [["IsCyclotomic"],["IsIntegers"]]},{"rank" : 53,"comment" : "in","filters" : [["IsIEEE754FloatRep"],["IsIEEE754PseudoField"]]},{"rank" : 52,"comment" : "in: for a pcp element and a pcp group","filters" : [["IsPcpElement"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 52,"comment" : "in: for s. c. algebra element, and full s. c. algebra","filters" : [["IsSCAlgebraObj"],["IsFullSCAlgebra","Tester(IsFullSCAlgebra)"]]},{"rank" : 51,"comment" : "in: for automorphism groups of free groups","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsAutomorphismGroupOfFreeGroup"]]},{"rank" : 49,"comment" : "in: generic wreath product","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)","CategoryCollections(IsWreathProductElement)"],["IsWreathProductElement"]]},{"rank" : 49,"comment" : "in: generic direct product","filters" : [["IsDirectProductElement"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 48,"comment" : "in: for full matrix module","filters" : [[],["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 47,"comment" : "in: polynomial ideal","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"]]},{"rank" : 46,"comment" : "in: for ring element, and magma ring","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsMagmaRingModuloRelations"]]},{"rank" : 44,"comment" : "in","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsConjugacyClassSubgroupsRep"]]},{"rank" : 43,"comment" : "in: for full hom space of linear mappings","filters" : [["IsGeneralMapping"],["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 43,"comment" : "in: for nonnegative integers","filters" : [["IsCyclotomic"],["IsNonnegativeIntegers"]]},{"rank" : 42,"comment" : "in: for pc group","filters" : [["IsMultiplicativeElementWithInverse"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FamilyPcgs)","CanEasilyComputePcgs"]]},{"rank" : 42,"comment" : "in: for row vector and Gaussian row space","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]},{"rank" : 42,"comment" : "in: for positive integers","filters" : [["IsCyclotomic"],["IsPositiveIntegers"]]},{"rank" : 41,"comment" : "in: subgroup of fp group by quotient rep","filters" : [["IsMultiplicativeElementWithInverse"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 41,"comment" : "in: for pcgs computable groups with home pcgs","filters" : [["IsMultiplicativeElementWithInverse"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(InducedPcgsWrtHomePcgs)","CanEasilyComputePcgs"]]},{"rank" : 41,"comment" : "in: SC Rings","filters" : [["IsSCRingObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)","CategoryCollections(IsSCRingObj)"]]},{"rank" : 40,"comment" : "in: subgroup of fp group","filters" : [["IsMultiplicativeElementWithInverse"],["IsSubgroupFpGroup"]]},{"rank" : 40,"comment" : "in: for pcgs computable groups with induced pcgs","filters" : [["IsMultiplicativeElementWithInverse"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(ComputedInducedPcgses)","CanEasilyComputePcgs"]]},{"rank" : 40,"comment" : "in: ratfun in fctfield","filters" : [["IsRationalFunction"],["IsFunctionField"]]},{"rank" : 39,"comment" : "in: polynomial in polynomial ring","filters" : [["IsPolynomialFunction"],["IsPolynomialRing"]]},{"rank" : 39,"comment" : "in: default method, checking for <g> being among the generators","filters" : [["IsMultiplicativeElementWithInverse"],["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 35,"comment" : "in: for an element and an underlying relation of a general mapping","filters" : [["IsDirectProductElement"],["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"]]},{"rank" : 33,"comment" : "in: for object and Z_(pi) (ResClasses)","filters" : [[],["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 33,"comment" : "in: for vector and free left module that is handled by a nice basis","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsFreeLeftModule","IsHandledByNiceBasis"]]},{"rank" : 32,"comment" : "in: for vector and fin. dim. free left module","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsFreeLeftModule","IsFiniteDimensional","Tester(IsFiniteDimensional)"]]},{"rank" : 25,"comment" : "in: for eq relation with partition","filters" : [["IsList"],["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","Tester(EquivalenceRelationPartition)"]]},{"rank" : 22,"comment" : "in: for a transformation and a full transformation semigroup","filters" : [["IsTransformation"],["IsFullTransformationSemigroup","Tester(IsFullTransformationSemigroup)"]]},{"rank" : 21,"comment" : "in: perm class rep","filters" : [["IsPerm"],["IsConjugacyClassPermGroupRep"]]},{"rank" : 20,"comment" : "in: for a right coset with representative","filters" : [[],["Tester(Representative)","Tester(ActingDomain)","Tester(FunctionAction)","IsRightCosetDefaultRep"]]},{"rank" : 20,"comment" : "in","filters" : [["IsPerm"],["IsRationalClassPermGroupRep"]]},{"rank" : 17,"comment" : "in: xset: Test representative equal","filters" : [[],["Tester(Representative)","IsExternalSet"]]},{"rank" : 17,"comment" : "in: for an object, and an empty list","filters" : [[],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "in: for additive element and additive coset","filters" : [["IsAdditiveElement"],["IsAdditiveCoset"]]},{"rank" : 14,"comment" : "in: for binary rels over [1..n] with images list","filters" : [["IsList"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 13,"comment" : "in: for a simple inverse automaton","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsSimpleInvAutomatonRep"]]},{"rank" : 13,"comment" : "in: double coset","filters" : [["IsMultiplicativeElementWithInverse"],["IsDoubleCoset"]]},{"rank" : 13,"comment" : "in: by CanonicalRepresentativeDeterminator","filters" : [[],["IsExternalOrbit","Tester(CanonicalRepresentativeDeterminatorOfExternalSet)"]]},{"rank" : 13,"comment" : "in: xorb HasAsSSortedList","filters" : [[],["Tester(AsSSortedList)","IsExternalOrbit"]]},{"rank" : 12,"comment" : "in: for a res.-cl. and a union of res.-cl. with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 12,"comment" : "in: xorb HasAsList","filters" : [[],["Tester(AsList)","IsExternalOrbit"]]},{"rank" : 12,"comment" : "in: very small xorbs: test in AsList","filters" : [[],["Tester(Size)","IsExternalOrbit"]]},{"rank" : 11,"comment" : "in","filters" : [[],["IsRationalClassGroupRep"]]},{"rank" : 11,"comment" : "in: xorb: HasEnumerator","filters" : [[],["Tester(Enumerator)","IsExternalOrbit"]]},{"rank" : 10,"comment" : "in: xorb: RepresentativeAction","filters" : [[],["IsExternalOrbit"]]},{"rank" : 10,"comment" : "in: for a magma congruence class","filters" : [[],["IsCongruenceClass"]]},{"rank" : 9,"comment" : "in: for a ring element and a residue class union (ResClasses)","filters" : [[],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 9,"comment" : "in: for an object, and a small list","filters" : [[],["IsList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 7,"comment" : "in: membership test of Green's class","filters" : [[],["IsGreensClass"]]},{"rank" : 7,"comment" : "in: for an enumerator that perhaps has its own membership test function","filters" : [[],["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"]]},{"rank" : 6,"comment" : "in: empty class","filters" : [[],["IsEmpty","Tester(IsEmpty)","IsClass"]]},{"rank" : 6,"comment" : "in: for element and equivalence class","filters" : [[],["IsEquivalenceClass"]]},{"rank" : 5,"comment" : "in: for a domain, and an element","filters" : [[],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 4,"comment" : "in: for group class","filters" : [[],["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 2,"comment" : "in: for class, delegate to IsMember","filters" : [[],["IsClass"]]},{"rank" : 2,"comment" : "in: for an object, and a list","filters" : [[],["IsList"]]},{"rank" : 0,"comment" : "in:  fallback method to test conditions","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ShallowCopy","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 44,"comment" : "ShallowCopy: for GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"]]},{"rank" : 31,"comment" : "ShallowCopy: for class function","filters" : [["IsClassFunction"]]},{"rank" : 28,"comment" : "ShallowCopy: For a compressed MatFFE","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitMatrixRep"]]},{"rank" : 28,"comment" : "ShallowCopy: for an empty row vector","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 24,"comment" : "ShallowCopy: For a compressed VecFFE","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitVectorRep"]]},{"rank" : 22,"comment" : "ShallowCopy: for GF2 vectors","filters" : [["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 19,"comment" : "ShallowCopy: combinatorial collector rep","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsCombinatorialCollectorRep"]]},{"rank" : 18,"comment" : "ShallowCopy","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 15,"comment" : "ShallowCopy: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 11,"comment" : "ShallowCopy","filters" : [["IsCopyable","IsSortLookupDictionary"]]},{"rank" : 11,"comment" : "ShallowCopy: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 10,"comment" : "ShallowCopy: method for a weak pointer object","filters" : [["IsWeakPointerObject"]]},{"rank" : 9,"comment" : "ShallowCopy","filters" : [["IsCopyable","TableHasIntKeyFun","IsSparseHashRep"]]},{"rank" : 9,"comment" : "ShallowCopy","filters" : [["IsCopyable","IsPositionDictionary"]]},{"rank" : 9,"comment" : "ShallowCopy","filters" : [["IsCopyable","IsListLookupDictionary"]]},{"rank" : 9,"comment" : "ShallowCopy: for a strictly sorted dense list","filters" : [["IsList","IsDenseList","IsSSortedList","Tester(IS_SSORT_LIST)"]]},{"rank" : 8,"comment" : "ShallowCopy","filters" : [["IsCopyable","IsSparseHashRep"]]},{"rank" : 8,"comment" : "ShallowCopy","filters" : [["IsCopyable","IsSortDictionary"]]},{"rank" : 8,"comment" : "ShallowCopy: for a strictly sorted list","filters" : [["IsList","IsSSortedList","Tester(IS_SSORT_LIST)"]]},{"rank" : 7,"comment" : "ShallowCopy","filters" : [["IsUnicodeString"]]},{"rank" : 7,"comment" : "ShallowCopy","filters" : [["IsCopyable","IsPositionDictionary"]]},{"rank" : 7,"comment" : "ShallowCopy","filters" : [["IsCopyable","IsListDictionary"]]},{"rank" : 5,"comment" : "ShallowCopy: for a Knuth Bendix rewriting system","filters" : [["IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]},{"rank" : 5,"comment" : "ShallowCopy: for a presentation in default representation","filters" : [["IsPresentation","IsPresentationDefaultRep"]]},{"rank" : 3,"comment" : "ShallowCopy: for iterators of residue class unions (ResClasses)","filters" : [["IsIterator","IsResidueClassUnionsIteratorRep"]]},{"rank" : 3,"comment" : "ShallowCopy: for a dense list","filters" : [["IsList","IsDenseList"]]},{"rank" : 3,"comment" : "ShallowCopy: for `IsIteratorByFunctions'","filters" : [["IsIterator","IsIteratorByFunctionsRep"]]},{"rank" : 2,"comment" : "ShallowCopy: for a list","filters" : [["IsList"]]},{"rank" : 1,"comment" : "ShallowCopy: generic method for mutable basis","filters" : [["IsMutableBasis"]]},{"rank" : 0,"comment" : "ShallowCopy: for a (not copyable) object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Name","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "Name: system getter","filters" : [["IsAttributeStoringRep","Tester(Name)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Name)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10001,"comment" : "Setter(Name): generic test routine","filters" : [[],[]]},{"rank" : 22,"comment" : "Setter(Name): set name of indeterminate","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsString"]]},{"rank" : 2,"comment" : "Setter(Name): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Name): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Name)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InfoText","type" : "GAP_Operation","filters" : [[[]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "InfoText: system getter","filters" : [["IsAttributeStoringRep","Tester(InfoText)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InfoText)","type" : "GAP_Operation","filters" : [[[],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InfoText): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InfoText): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InfoText)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "String","type" : "GAP_Operation","filters" : [[[]],[[],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "String: system getter","filters" : [["IsAttributeStoringRep","Tester(String)"]]},{"rank" : 10000,"comment" : "String","filters" : [[]]},{"rank" : 429,"comment" : "String: for a field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 67,"comment" : "String: for cyclotomic field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 65,"comment" : "String: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 62,"comment" : "String: for natural alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 62,"comment" : "String: for natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 61,"comment" : "String: for a polynomial ring","filters" : [["IsPolynomialRing"]]},{"rank" : 48,"comment" : "String: for full row modules","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 34,"comment" : "String: for a group with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "String: for Z_(pi) (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 33,"comment" : "String: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 30,"comment" : "String: for a range","filters" : [["IsRange"]]},{"rank" : 25,"comment" : "String: for a inverse monoid with known generators","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseMonoid)"]]},{"rank" : 24,"comment" : "String: for a inverse monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 23,"comment" : "String: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 20,"comment" : "String: for a inverse semigroup with known generators","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 19,"comment" : "String: for a inverse semigroup","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 19,"comment" : "String: for monoid with known generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 18,"comment" : "String: for element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 18,"comment" : "String: for an unknown in default representation","filters" : [["IsUnknown","IsUnknownDefaultRep"]]},{"rank" : 18,"comment" : "String: for monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 18,"comment" : "String: for an integer","filters" : [["IsInt"]]},{"rank" : 17,"comment" : "String: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "String: For large finite field elements","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "String: for an internal FFE","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 17,"comment" : "String: AlgElm","filters" : [["IsKroneckerConstRep"]]},{"rank" : 17,"comment" : "String: BFElm","filters" : [["IsAlgBFRep"]]},{"rank" : 17,"comment" : "String: laurent polynomial","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 17,"comment" : "String: for a rational","filters" : [["IsRat"]]},{"rank" : 16,"comment" : "String: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"]]},{"rank" : 16,"comment" : "String: for -infinity","filters" : [["IsNegInfinity"]]},{"rank" : 16,"comment" : "String: for infinity","filters" : [["IsInfinity"]]},{"rank" : 16,"comment" : "String: for a cyclotomic","filters" : [["IsCyc"]]},{"rank" : 15,"comment" : "String: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 15,"comment" : "String: for plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "String: univar","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 14,"comment" : "String: polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 14,"comment" : "String: for a semigroup with known generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "String: from-the-left collector","filters" : [["IsFromTheLeftCollectorRep"]]},{"rank" : 13,"comment" : "String: rational function","filters" : [["IsRationalFunction"]]},{"rank" : 13,"comment" : "String: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 11,"comment" : "String: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "String: for s. c. ring element","filters" : [["IsSCRingObj"]]},{"rank" : 11,"comment" : "String: for s. c. algebra element","filters" : [["IsSCAlgebraObj"]]},{"rank" : 11,"comment" : "String: for magma ring element","filters" : [["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 10,"comment" : "String: pcword","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 9,"comment" : "String: for an element of an f.p. group (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpGroup"]]},{"rank" : 8,"comment" : "String: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "String: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "String: for a transformation","filters" : [["IsTransformation"]]},{"rank" : 6,"comment" : "String: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 6,"comment" : "String: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 6,"comment" : "String: for pcp elements","filters" : [["IsPcpElement"]]},{"rank" : 6,"comment" : "String: for an fp monoid element","filters" : [["IsElementOfFpMonoid"]]},{"rank" : 5,"comment" : "String: for an f.p. semigroup element","filters" : [["IsElementOfFpSemigroup"]]},{"rank" : 5,"comment" : "String: for an associative word","filters" : [["IsAssociativeElement","IsWord"]]},{"rank" : 5,"comment" : "String: for a nonassociative word","filters" : [["IsNonassocWord"]]},{"rank" : 5,"comment" : "String: for a string (do nothing)","filters" : [["IsString"]]},{"rank" : 2,"comment" : "String: for a (finite) list","filters" : [["IsList"]]},{"rank" : 1,"comment" : "String: for a boolean","filters" : [["IsBool"]]},{"rank" : 1,"comment" : "String: record","filters" : [["IsRecord"]]},{"rank" : 1,"comment" : "String: for a character","filters" : [["IsChar"]]},{"rank" : 0,"comment" : "String","filters" : [[]]}],"2args" : [{"rank" : 21,"comment" : "String: for an object, and zero","filters" : [[],["IsZeroCyc"]]},{"rank" : 19,"comment" : "String: for an object, and a negative integer","filters" : [[],["IsInt","IsNegRat"]]},{"rank" : 19,"comment" : "String: for an object, and a positive integer","filters" : [[],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(String)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(String): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(String): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(String)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrintObj","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10036,"comment" : "PrintObj: for full hom space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 10023,"comment" : "PrintObj: for full ring Z\/nZ","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 10022,"comment" : "PrintObj: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 10022,"comment" : "PrintObj: for group automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]},{"rank" : 10017,"comment" : "PrintObj: for zero mapping","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"]]},{"rank" : 10017,"comment" : "PrintObj: for identity mapping","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"]]},{"rank" : 10013,"comment" : "PrintObj: for a Lie object in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 10009,"comment" : "PrintObj: for a canonical basis","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)"]]},{"rank" : 10001,"comment" : "PrintObj: for an object with name","filters" : [["Tester(Name)"]]},{"rank" : 429,"comment" : "PrintObj: for a field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 134,"comment" : "PrintObj: subgroup by property","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(ElementTestFunction)"]]},{"rank" : 110,"comment" : "PrintObj: for a restricted mapping","filters" : [["IsGeneralRestrictedMappingRep"]]},{"rank" : 110,"comment" : "PrintObj: for a composition mapping","filters" : [["IsCompositionMappingRep"]]},{"rank" : 109,"comment" : "PrintObj: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]},{"rank" : 107,"comment" : "PrintObj: objects with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 67,"comment" : "PrintObj: for cyclotomic field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 65,"comment" : "PrintObj: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 62,"comment" : "PrintObj: for natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 62,"comment" : "PrintObj: for natural alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 61,"comment" : "PrintObj: for a function field","filters" : [["IsFunctionField"]]},{"rank" : 61,"comment" : "PrintObj: for a polynomial ring","filters" : [["IsPolynomialRing"]]},{"rank" : 56,"comment" : "PrintObj: for a matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 55,"comment" : "PrintObj: for algebraic extension","filters" : [["IsNumberField","Tester(IsNumberField)","IsAlgebraicExtension"]]},{"rank" : 53,"comment" : "PrintObj: for a field with known generators","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","Tester(GeneratorsOfDivisionRing)"]]},{"rank" : 52,"comment" : "PrintObj: for a field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 48,"comment" : "PrintObj: for full matrix module","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "PrintObj: for full row module","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 46,"comment" : "PrintObj: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 43,"comment" : "PrintObj: for a matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 40,"comment" : "PrintObj: for a semigroup with known generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsMagmaWithInverses","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 40,"comment" : "PrintObj: for an algebra-with-one with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 39,"comment" : "PrintObj: for an algebra-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 38,"comment" : "PrintObj: for a semigroup with known generators","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsMagmaWithInverses","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 38,"comment" : "PrintObj: for a FLMLOR-with-one with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 37,"comment" : "PrintObj: for an algebra with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 37,"comment" : "PrintObj: for a FLMLOR-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 36,"comment" : "PrintObj: for an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 36,"comment" : "PrintObj: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 35,"comment" : "PrintObj: for a character","filters" : [["IsClassFunction","IsCharacter","Tester(IsCharacter)"]]},{"rank" : 35,"comment" : "PrintObj: for a FLMLOR with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 34,"comment" : "PrintObj: for a FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 34,"comment" : "PrintObj: for a group with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 34,"comment" : "PrintObj: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 33,"comment" : "PrintObj: for Z_(pi) (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 33,"comment" : "PrintObj: for a virtual character","filters" : [["IsClassFunction","IsVirtualCharacter","Tester(IsVirtualCharacter)"]]},{"rank" : 33,"comment" : "PrintObj: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "PrintObj: for a semigroup Congruence with known generating pairs","filters" : [["Tester(GeneratingPairsOfMagmaCongruence)","IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 32,"comment" : "PrintObj: for a semigroup congruence","filters" : [["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 31,"comment" : "PrintObj: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 31,"comment" : "PrintObj: for an algebra-with-one hom. b.i","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsOne","Tester(RespectsOne)","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 31,"comment" : "PrintObj: for null map matrix","filters" : [["IsNullMapMatrix"]]},{"rank" : 30,"comment" : "PrintObj: for a ring-with-one with generators","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRingWithOne)"]]},{"rank" : 29,"comment" : "PrintObj: for an alg. hom. from f. p. algebra","filters" : [["IsAlgebraHomomorphismFromFpRep"]]},{"rank" : 29,"comment" : "PrintObj: for an operation algebra homomorphism","filters" : [["IsOperationAlgebraHomomorphismDefaultRep"]]},{"rank" : 29,"comment" : "PrintObj: for an algebra hom. b.i.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 29,"comment" : "PrintObj: for a two-sided ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 29,"comment" : "PrintObj: for a ring-with-one","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 29,"comment" : "PrintObj: for a right semigroup congruence with known generating pairs","filters" : [["Tester(GeneratingPairsOfMagmaCongruence)","IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)"]]},{"rank" : 29,"comment" : "PrintObj: for a left semigroup congruence with known generating pairs","filters" : [["Tester(GeneratingPairsOfMagmaCongruence)","IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)"]]},{"rank" : 28,"comment" : "PrintObj: For a compressed MatFFE","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitMatrixRep"]]},{"rank" : 28,"comment" : "PrintObj: for a right ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 28,"comment" : "PrintObj: for a left ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)","Tester(LeftActingRingOfIdeal)"]]},{"rank" : 27,"comment" : "PrintObj: for inner automorphism","filters" : [["IsInnerAutomorphism","Tester(IsInnerAutomorphism)"]]},{"rank" : 27,"comment" : "PrintObj: for an ring hom. b.i.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 27,"comment" : "PrintObj: for algebra module","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsAlgebraModule","Tester(IsAlgebraModule)"]]},{"rank" : 27,"comment" : "PrintObj: for an algebra-with-one g.m.b.i","filters" : [["IsGeneralMapping","RespectsOne","Tester(RespectsOne)","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 27,"comment" : "PrintObj: for a left module hom. b.i","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 27,"comment" : "PrintObj: for a ring with generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 27,"comment" : "PrintObj: for a magma Congruence with known generating pairs","filters" : [["IsMagmaCongruence","Tester(GeneratingPairsOfMagmaCongruence)"]]},{"rank" : 27,"comment" : "PrintObj: for a right magma congruence with known generating pairs","filters" : [["IsRightMagmaCongruence","Tester(GeneratingPairsOfMagmaCongruence)"]]},{"rank" : 27,"comment" : "PrintObj: for a left magma congruence with known generating pairs","filters" : [["IsLeftMagmaCongruence","Tester(GeneratingPairsOfMagmaCongruence)"]]},{"rank" : 26,"comment" : "PrintObj: for ANF automorphism","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"]]},{"rank" : 26,"comment" : "PrintObj: for a Frobenius automorphism","filters" : [["IsFrobeniusAutomorphism"]]},{"rank" : 26,"comment" : "PrintObj: method for vector space with left module generators","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 26,"comment" : "PrintObj: for a ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 26,"comment" : "PrintObj: for a magma congruence","filters" : [["IsMagmaCongruence"]]},{"rank" : 25,"comment" : "PrintObj: for an algebra g.m.b.i","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 25,"comment" : "PrintObj: method for vector space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 25,"comment" : "PrintObj: for a inverse monoid with known generators","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseMonoid)"]]},{"rank" : 24,"comment" : "PrintObj: pcgs","filters" : [["IsPcgs","IsPcgsDefaultRep"]]},{"rank" : 24,"comment" : "PrintObj: For a compressed VecFFE","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitVectorRep"]]},{"rank" : 24,"comment" : "PrintObj: for free left module with known generators","filters" : [["IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 24,"comment" : "PrintObj: for a right semigroup congruence","filters" : [["IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)"]]},{"rank" : 24,"comment" : "PrintObj: for a left semigroup congruence","filters" : [["IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)"]]},{"rank" : 23,"comment" : "PrintObj: for saturated Fitting formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsSaturated","Tester(IsSaturated)","IsClassByPropertyRep"]]},{"rank" : 23,"comment" : "PrintObj: for embedding into wreath product","filters" : [["IsEmbeddingImprimitiveWreathProductMatrixGroup"]]},{"rank" : 23,"comment" : "PrintObj: for projection from a direct product","filters" : [["IsProjectionDirectProductMatrixGroup"]]},{"rank" : 23,"comment" : "PrintObj: for embedding into direct product","filters" : [["IsEmbeddingDirectProductMatrixGroup"]]},{"rank" : 23,"comment" : "PrintObj: for embedding into wreath product","filters" : [["IsEmbeddingWreathProductPermGroup"]]},{"rank" : 23,"comment" : "PrintObj: for projection from subdirect product","filters" : [["IsProjectionSubdirectProductPermGroup"]]},{"rank" : 23,"comment" : "PrintObj: for projection from a direct product","filters" : [["IsProjectionDirectProductPermGroup"]]},{"rank" : 23,"comment" : "PrintObj: for embedding into direct product","filters" : [["IsEmbeddingDirectProductPermGroup"]]},{"rank" : 23,"comment" : "PrintObj: method for a PcGroupHomomorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcGroupGeneralMappingByImages"]]},{"rank" : 23,"comment" : "PrintObj: for nat. hom. of pc group","filters" : [["IsNaturalHomomorphismPcGroupRep"]]},{"rank" : 23,"comment" : "PrintObj: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 23,"comment" : "PrintObj: for an ring g.m.b.i","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "PrintObj: for a left module m.b.m.","filters" : [["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 23,"comment" : "PrintObj: for a left module g.m.b.i","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "PrintObj: for free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 23,"comment" : "PrintObj: for a magma with zero adjoined","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsMagmaWithZeroAdjoined"]]},{"rank" : 22,"comment" : "PrintObj: for a Brauer table","filters" : [["IsBrauerTable"]]},{"rank" : 22,"comment" : "PrintObj: for an ordinary table","filters" : [["IsOrdinaryTable"]]},{"rank" : 22,"comment" : "PrintObj: for action homomorphism","filters" : [["IsActionHomomorphism"]]},{"rank" : 22,"comment" : "PrintObj: for a right magma congruence","filters" : [["IsRightMagmaCongruence"]]},{"rank" : 22,"comment" : "PrintObj: for a left magma congruence","filters" : [["IsLeftMagmaCongruence"]]},{"rank" : 21,"comment" : "PrintObj: for GHBI","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsGroupGeneralMappingByImages"]]},{"rank" : 21,"comment" : "PrintObj: combinatorial collector rep (32 Bits, up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 21,"comment" : "PrintObj: combinatorial collector rep (16 Bits, up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 21,"comment" : "PrintObj: combinatorial collector rep (8 Bits, up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 21,"comment" : "PrintObj: for an equivalence relation","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]},{"rank" : 20,"comment" : "PrintObj: for product of Fitting formations","filters" : [["IsFittingProductRep","IsFormationProductRep"]]},{"rank" : 20,"comment" : "PrintObj","filters" : [["IsUnicodeCharacter"]]},{"rank" : 20,"comment" : "PrintObj: modulo pcgs","filters" : [["IsModuloPcgs"]]},{"rank" : 20,"comment" : "PrintObj: combinatorial collector rep (32 Bits)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is32BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "PrintObj: combinatorial collector rep (16 Bits)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is16BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "PrintObj: combinatorial collector rep (8 Bits)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is8BitsSingleCollectorRep","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "PrintObj: combinatorial collector (up to date)","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsCombinatorialCollectorRep"]]},{"rank" : 20,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep"]]},{"rank" : 20,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep"]]},{"rank" : 20,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep"]]},{"rank" : 20,"comment" : "PrintObj: for a inverse semigroup with known generators","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 19,"comment" : "PrintObj: for Fitting formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsClassByPropertyRep"]]},{"rank" : 19,"comment" : "PrintObj: for a saturated formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsSaturated","Tester(IsSaturated)","IsClassByPropertyRep"]]},{"rank" : 19,"comment" : "PrintObj: for a Rees 0-matrix semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 19,"comment" : "PrintObj: for a Rees matrix semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 19,"comment" : "PrintObj: combinatorial collector","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsCombinatorialCollectorRep"]]},{"rank" : 19,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is32BitsSingleCollectorRep"]]},{"rank" : 19,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is16BitsSingleCollectorRep"]]},{"rank" : 19,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","Is8BitsSingleCollectorRep"]]},{"rank" : 19,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsSingleCollectorRep"]]},{"rank" : 19,"comment" : "PrintObj: for monoid with known generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 19,"comment" : "PrintObj: for mapping by function with inverse","filters" : [["IsMappingByFunctionWithInverseRep"]]},{"rank" : 18,"comment" : "PrintObj: for a subsemigroup of a Rees 0-matrix semigroup","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 18,"comment" : "PrintObj: for a subsemigroup of a Rees matrix semigroup","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 18,"comment" : "PrintObj","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 18,"comment" : "PrintObj: zmodnze : for full collection Z\/nZ(m)","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZepsObj)"]]},{"rank" : 18,"comment" : "PrintObj: for element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 18,"comment" : "PrintObj: for unknown in default representation","filters" : [["IsUnknown","IsUnknownDefaultRep"]]},{"rank" : 18,"comment" : "PrintObj: for a semigroup ideal with known generators","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","Tester(GeneratorsOfMagmaIdeal)","IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]]},{"rank" : 17,"comment" : "PrintObj: for a Schunck class","filters" : [["IsSchunckClass","Tester(IsSchunckClass)","IsClassByPropertyRep"]]},{"rank" : 17,"comment" : "PrintObj: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"]]},{"rank" : 17,"comment" : "PrintObj: for group general mapping b.i.","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "PrintObj: for large finite field elements (use String)","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "PrintObj: AlgElm","filters" : [["IsKroneckerConstRep"]]},{"rank" : 17,"comment" : "PrintObj: BFElm","filters" : [["IsAlgBFRep"]]},{"rank" : 17,"comment" : "PrintObj: laurent polynomial","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 17,"comment" : "PrintObj: for an add. magma-with-inverses with generators","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveGroup)"]]},{"rank" : 17,"comment" : "PrintObj: for a semigroup ideal","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]]},{"rank" : 16,"comment" : "PrintObj: for a Molien series","filters" : [["IsRationalFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","Tester(MolienSeriesInfo)"]]},{"rank" : 16,"comment" : "PrintObj: RightCoset","filters" : [["IsRightCoset"]]},{"rank" : 16,"comment" : "PrintObj: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"]]},{"rank" : 16,"comment" : "PrintObj: for a magma ideal with known generators","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","Tester(GeneratorsOfMagmaIdeal)"]]},{"rank" : 16,"comment" : "PrintObj: for -infinity","filters" : [["IsNegInfinity"]]},{"rank" : 16,"comment" : "PrintObj: for infinity","filters" : [["IsInfinity"]]},{"rank" : 15,"comment" : "PrintObj: for formation product","filters" : [["IsFormationProductRep"]]},{"rank" : 15,"comment" : "PrintObj: for formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsClassByPropertyRep"]]},{"rank" : 15,"comment" : "PrintObj: for Fitting product","filters" : [["IsFittingProductRep"]]},{"rank" : 15,"comment" : "PrintObj: for Fitting class","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsClassByPropertyRep"]]},{"rank" : 15,"comment" : "PrintObj: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "PrintObj: for GF2 matrix","filters" : [["IsGF2MatrixRep"]]},{"rank" : 15,"comment" : "PrintObj: univar","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "PrintObj: for an add. magma-with-zero with generators","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]]},{"rank" : 15,"comment" : "PrintObj: for a magma ideal","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]},{"rank" : 15,"comment" : "PrintObj: for a direct product element","filters" : [["IsDirectProductElement"]]},{"rank" : 14,"comment" : "PrintObj: for Fitting set","filters" : [["IsClassByPropertyRep","IsFittingSetRep"]]},{"rank" : 14,"comment" : "PrintObj","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"]]},{"rank" : 14,"comment" : "PrintObj","filters" : [["IsPadicExtensionNumber"]]},{"rank" : 14,"comment" : "PrintObj","filters" : [["IsPurePadicNumber"]]},{"rank" : 14,"comment" : "PrintObj: polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 14,"comment" : "PrintObj: for a semigroup with known generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 14,"comment" : "PrintObj: for a right magma ideal with known generators","filters" : [["IsRightActedOnBySuperset","Tester(GeneratorsOfExtRSet)","IsMagma"]]},{"rank" : 14,"comment" : "PrintObj: for a left magma ideal with known generators","filters" : [["IsLeftActedOnBySuperset","Tester(GeneratorsOfExtLSet)","IsMagma"]]},{"rank" : 14,"comment" : "PrintObj: for mapping by function","filters" : [["IsMappingByFunctionRep"]]},{"rank" : 13,"comment" : "PrintObj: for from-the-left collector","filters" : [["IsFromTheLeftCollectorRep"]]},{"rank" : 13,"comment" : "PrintObj: for floats","filters" : [["IsFloat"]]},{"rank" : 13,"comment" : "PrintObj: zmodnze : for element in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 13,"comment" : "PrintObj: rational function","filters" : [["IsRationalFunction"]]},{"rank" : 13,"comment" : "PrintObj: for an add. magma with generators","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagma)"]]},{"rank" : 13,"comment" : "PrintObj: for a right magma ideal","filters" : [["IsRightActedOnBySuperset","IsMagma"]]},{"rank" : 13,"comment" : "PrintObj: for a left magma ideal","filters" : [["IsLeftActedOnBySuperset","IsMagma"]]},{"rank" : 12,"comment" : "PrintObj","filters" : [["IsPowerCommutatorCollector"]]},{"rank" : 12,"comment" : "PrintObj","filters" : [["IsPowerConjugateCollector"]]},{"rank" : 12,"comment" : "PrintObj: for UEALattice element","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 12,"comment" : "PrintObj: for an additive coset","filters" : [["IsAdditiveCoset"]]},{"rank" : 12,"comment" : "PrintObj: for an add. magma","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 12,"comment" : "PrintObj: for a binary relation on  n points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 11,"comment" : "PrintObj","filters" : [["IsConjugacyClassSubgroupsRep"]]},{"rank" : 11,"comment" : "PrintObj","filters" : [["IsRationalClassGroupRep"]]},{"rank" : 11,"comment" : "PrintObj","filters" : [["IsConjugacyClassGroupRep"]]},{"rank" : 11,"comment" : "PrintObj","filters" : [["IsPolycyclicCollector"]]},{"rank" : 11,"comment" : "PrintObj: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "PrintObj: for GF2 vector","filters" : [["IsGF2VectorRep"]]},{"rank" : 11,"comment" : "PrintObj: for s. c. ring element","filters" : [["IsSCRingObj"]]},{"rank" : 11,"comment" : "PrintObj: for symmetric elements","filters" : [["IsSymmetricPowerElement","IsMonomialElementRep"]]},{"rank" : 11,"comment" : "PrintObj: for wedge elements","filters" : [["IsWedgeElement","IsMonomialElementRep"]]},{"rank" : 11,"comment" : "PrintObj: for tensor elements","filters" : [["IsTensorElement","IsMonomialElementRep"]]},{"rank" : 11,"comment" : "PrintObj: for s. c. algebra element","filters" : [["IsSCAlgebraObj"]]},{"rank" : 11,"comment" : "PrintObj: fp algebra elements","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 11,"comment" : "PrintObj: for magma ring element","filters" : [["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 11,"comment" : "PrintObj: for a mapping","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 10,"comment" : "PrintObj: for external orbit","filters" : [["IsExternalOrbit"]]},{"rank" : 10,"comment" : "PrintObj: pcword","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 10,"comment" : "PrintObj","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]]},{"rank" : 10,"comment" : "PrintObj: for weight rep element","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 10,"comment" : "PrintObj: for direct sum elements","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 10,"comment" : "PrintObj: for algebra module element in packed representation","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 10,"comment" : "PrintObj: method for a subspaces domain","filters" : [["IsSubspacesVectorSpace","IsSubspacesVectorSpaceDefaultRep"]]},{"rank" : 10,"comment" : "PrintObj: for a semi-echelonized basis with basis vectors","filters" : [["IsBasis","IsSemiEchelonized","Tester(IsSemiEchelonized)","Tester(BasisVectors)"]]},{"rank" : 10,"comment" : "PrintObj: method for a weak pointer object","filters" : [["IsWeakPointerObject"]]},{"rank" : 9,"comment" : "PrintObj: for an element of an f.p. group (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpGroup"]]},{"rank" : 9,"comment" : "PrintObj: sliced perm","filters" : [["IsSlicedPermInv"]]},{"rank" : 9,"comment" : "PrintObj: sliced perm","filters" : [["IsSlicedPerm"]]},{"rank" : 9,"comment" : "PrintObj: for external subset","filters" : [["IsExternalSubset"]]},{"rank" : 9,"comment" : "PrintObj: for a semi-echelonized basis","filters" : [["IsBasis","IsSemiEchelonized","Tester(IsSemiEchelonized)"]]},{"rank" : 9,"comment" : "PrintObj: for right transversal","filters" : [["IsList","IsRightTransversalRep"]]},{"rank" : 8,"comment" : "PrintObj","filters" : [["IsPackedElementDefaultRep","IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 8,"comment" : "PrintObj: for a cochain","filters" : [["IsCochain"]]},{"rank" : 8,"comment" : "PrintObj: for a sparse rowspace element","filters" : [["IsSparseRowSpaceElement"]]},{"rank" : 8,"comment" : "PrintObj: for a basis with basis vectors","filters" : [["IsBasis","Tester(BasisVectors)"]]},{"rank" : 7,"comment" : "PrintObj: for IsGroupClass and IsClassByPropertyRep","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByPropertyRep"]]},{"rank" : 7,"comment" : "PrintObj","filters" : [["IsUnicodeString"]]},{"rank" : 7,"comment" : "PrintObj: for a Green's class","filters" : [["IsGreensClass"]]},{"rank" : 7,"comment" : "PrintObj: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "PrintObj: wreath elements","filters" : [["IsWreathProductElement"]]},{"rank" : 7,"comment" : "PrintObj: for element of magma by mult. table","filters" : [["IsMagmaByMultiplicationTableObj"]]},{"rank" : 7,"comment" : "PrintObj: for sparse hash tables","filters" : [["IsSparseHashRep"]]},{"rank" : 7,"comment" : "PrintObj: for dense hash tables","filters" : [["IsDenseHashRep"]]},{"rank" : 7,"comment" : "PrintObj: for a basis","filters" : [["IsBasis"]]},{"rank" : 7,"comment" : "PrintObj: for an element of a magma with zero adjoined","filters" : [["IsMagmaWithZeroAdjoinedElementRep"]]},{"rank" : 7,"comment" : "PrintObj: for a general mapping","filters" : [["IsGeneralMapping"]]},{"rank" : 7,"comment" : "PrintObj: for an enumerator that perhaps has its own `PrintObj' function","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"]]},{"rank" : 6,"comment" : "PrintObj: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 6,"comment" : "PrintObj: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 6,"comment" : "PrintObj","filters" : [["IsSimpleInvAutomatonRep"]]},{"rank" : 6,"comment" : "PrintObj: for pcp elements","filters" : [["IsPcpElement"]]},{"rank" : 6,"comment" : "PrintObj","filters" : [["IsMonoidByAdjoiningIdentityElt"]]},{"rank" : 6,"comment" : "PrintObj: for an fp monoid element","filters" : [["IsElementOfFpMonoid"]]},{"rank" : 6,"comment" : "PrintObj: External Set","filters" : [["IsExternalSet"]]},{"rank" : 6,"comment" : "PrintObj: assoc word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]},{"rank" : 6,"comment" : "PrintObj: for an eq. class","filters" : [["IsEquivalenceClass"]]},{"rank" : 6,"comment" : "PrintObj: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 5,"comment" : "PrintObj:  for IsGroupClassByListRep","filters" : [["IsGroupClassByListRep"]]},{"rank" : 5,"comment" : "PrintObj: for IsClassByUnionRep","filters" : [["IsClassByUnionRep"]]},{"rank" : 5,"comment" : "PrintObj: for IsClassByIntersectionRep","filters" : [["IsClassByIntersectionRep"]]},{"rank" : 5,"comment" : "PrintObj: for IsClassByComplementRep","filters" : [["IsClassByComplementRep"]]},{"rank" : 5,"comment" : "PrintObj: for IsClassByPropertyRep","filters" : [["IsClassByPropertyRep"]]},{"rank" : 5,"comment" : "PrintObj: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 5,"comment" : "PrintObj: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"]]},{"rank" : 5,"comment" : "PrintObj: for an f.p. semigroup element","filters" : [["IsElementOfFpSemigroup"]]},{"rank" : 5,"comment" : "PrintObj: for a presentation in default representation","filters" : [["IsPresentation","IsPresentationDefaultRep"]]},{"rank" : 5,"comment" : "PrintObj: for an associative word","filters" : [["IsAssociativeElement","IsWord"]]},{"rank" : 5,"comment" : "PrintObj: for a nonassociative word","filters" : [["IsNonassocWord"]]},{"rank" : 5,"comment" : "PrintObj: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 4,"comment" : "PrintObj: for an infinite list of generators","filters" : [["IsList","IsInfiniteListOfGeneratorsRep"]]},{"rank" : 4,"comment" : "PrintObj: for an infinite list of names","filters" : [["IsList","IsInfiniteListOfNamesRep"]]},{"rank" : 4,"comment" : "PrintObj: for an enumerator","filters" : [["IsList","IsAttributeStoringRep"]]},{"rank" : 3,"comment" : "PrintObj: Wyckoff position","filters" : [["IsWyckoffPosition"]]},{"rank" : 3,"comment" : "PrintObj: lattice","filters" : [["IsLatticeSubgroupsRep"]]},{"rank" : 3,"comment" : "PrintObj: for mutable basis with underlying mutable basis","filters" : [["IsMutableBasis","IsMutableBasisViaUnderlyingMutableBasisRep"]]},{"rank" : 3,"comment" : "PrintObj: for a mutable basis of a Gaussian matrix space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianMatrixSpaceRep"]]},{"rank" : 3,"comment" : "PrintObj: for a mutable basis of a Gaussian row space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianRowSpaceRep"]]},{"rank" : 3,"comment" : "PrintObj: for mutable basis represented by a nice mutable basis","filters" : [["IsMutableBasis","IsMutableBasisViaNiceMutableBasisRep"]]},{"rank" : 3,"comment" : "PrintObj: for mutable basis represented by an immutable basis","filters" : [["IsMutableBasis","IsMutableBasisByImmutableBasisRep"]]},{"rank" : 3,"comment" : "PrintObj: for an iterator that perhaps has its own `PrintObj' function","filters" : [["IsIterator","IsIteratorByFunctionsRep"]]},{"rank" : 2,"comment" : "PrintObj","filters" : [["IsRewritingSystem"]]},{"rank" : 2,"comment" : "PrintObj","filters" : [["IsRandomSource"]]},{"rank" : 2,"comment" : "PrintObj: output text none","filters" : [["IsOutputTextNoneRep"]]},{"rank" : 2,"comment" : "PrintObj: output text file","filters" : [["IsOutputTextFileRep"]]},{"rank" : 2,"comment" : "PrintObj: output text string","filters" : [["IsOutputTextStringRep"]]},{"rank" : 2,"comment" : "PrintObj: input text none","filters" : [["IsInputTextNoneRep"]]},{"rank" : 2,"comment" : "PrintObj: input text file","filters" : [["IsInputTextFileRep"]]},{"rank" : 2,"comment" : "PrintObj: input text string","filters" : [["IsInputTextStringRep"]]},{"rank" : 2,"comment" : "PrintObj: default directory rep","filters" : [["IsDirectoryRep"]]},{"rank" : 2,"comment" : "PrintObj: for an info class","filters" : [["IsInfoClassListRep"]]},{"rank" : 2,"comment" : "PrintObj: for an operation","filters" : [["IsOperation"]]},{"rank" : 1,"comment" : "PrintObj: for a straight line decision","filters" : [["IsStraightLineDecision"]]},{"rank" : 1,"comment" : "PrintObj: for a black box program","filters" : [["IsBBoxProgram"]]},{"rank" : 1,"comment" : "PrintObj: for pcp","filters" : [["IsPcp"]]},{"rank" : 1,"comment" : "PrintObj","filters" : [["IsRecord"]]},{"rank" : 1,"comment" : "PrintObj: IsObjToBePrinted","filters" : [["IsObjToBePrinted"]]},{"rank" : 1,"comment" : "PrintObj: for a straight line program","filters" : [["IsStraightLineProgram"]]},{"rank" : 1,"comment" : "PrintObj","filters" : [["IsTableOfMarks"]]},{"rank" : 1,"comment" : "PrintObj: for a root system","filters" : [["IsRootSystem"]]},{"rank" : 1,"comment" : "PrintObj: closed stream","filters" : [["IsClosedStream"]]},{"rank" : 1,"comment" : "PrintObj: for an iterator","filters" : [["IsIterator"]]},{"rank" : 1,"comment" : "PrintObj: record","filters" : [["IsRecord"]]},{"rank" : 1,"comment" : "PrintObj: for 'to be defined' objects","filters" : [["IsToBeDefinedObj"]]},{"rank" : 1,"comment" : "PRINT_OBJ: for a type","filters" : [["IsType"]]},{"rank" : 1,"comment" : "PRINT_OBJ: for a family","filters" : [["IsFamily"]]},{"rank" : 0,"comment" : "PrintObj: default method delegating to PrintString","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrintString","type" : "GAP_Operation","filters" : [[[]],[[],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 34,"comment" : "PrintString: for a group with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 25,"comment" : "PrintString: for a inverse monoid with known generators","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseMonoid)"]]},{"rank" : 20,"comment" : "PrintString: for a inverse semigroup with known generators","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 19,"comment" : "PrintString: for monoid with known generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "PrintString: for a magma-with-inverses with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 16,"comment" : "PrintString: RightCoset","filters" : [["IsRightCoset"]]},{"rank" : 14,"comment" : "PrintString: for a semigroup with known generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 14,"comment" : "PrintString: for a magma-with-one with generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 12,"comment" : "PrintString: for a magma with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)"]]},{"rank" : 11,"comment" : "PrintString: for a magma","filters" : [["IsMagma"]]},{"rank" : 9,"comment" : "PrintString: for right transversal","filters" : [["IsList","IsRightTransversalRep"]]},{"rank" : 7,"comment" : "PrintString: for a Green's class","filters" : [["IsGreensClass"]]},{"rank" : 7,"comment" : "PrintString: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "PrintString: for a transformation","filters" : [["IsTransformation"]]},{"rank" : -1,"comment" : "PrintString: default method delegating to String","filters" : [[]]}],"2args" : [{"rank" : 21,"comment" : "PrintString: for an object, and zero","filters" : [[],["IsZeroCyc"]]},{"rank" : 19,"comment" : "PrintString: for an object, and a negative integer","filters" : [[],["IsInt","IsNegRat"]]},{"rank" : 19,"comment" : "PrintString: for an object, and a positive integer","filters" : [[],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Display","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10002,"comment" : "Display: for partitions of Z^2 into residue class unions (ResClasses)","filters" : [["IsList"]]},{"rank" : 52,"comment" : "Display: for matrix of FFEs (for larger fields)","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 42,"comment" : "Display: for matrix of FFEs","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 41,"comment" : "Display: for matrix over Integers mod n","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]]},{"rank" : 36,"comment" : "Display: for finitely presented groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 31,"comment" : "Display: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 30,"comment" : "Display: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 20,"comment" : "Display: for a nearly character table","filters" : [["IsNearlyCharacterTable"]]},{"rank" : 17,"comment" : "Display: For large finite field elements","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 15,"comment" : "Display: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 13,"comment" : "Display: for floats","filters" : [["IsFloat"]]},{"rank" : 11,"comment" : "Display: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 6,"comment" : "Display: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 6,"comment" : "Display: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 5,"comment" : "Display: for vector search tables in default representation","filters" : [["IsVectorSearchTableDefaultRep"]]},{"rank" : 2,"comment" : "Display: for a (finite) list","filters" : [["IsList"]]},{"rank" : 1,"comment" : "Display: for a straight line decision","filters" : [["IsStraightLineDecision"]]},{"rank" : 1,"comment" : "Display: for a black box program","filters" : [["IsBBoxProgram"]]},{"rank" : 1,"comment" : "Display: for a straight line program","filters" : [["IsStraightLineProgram"]]},{"rank" : 1,"comment" : "Display: for a table of marks (add empty options record)","filters" : [["IsTableOfMarks"]]},{"rank" : 0,"comment" : "Display: generic: use DisplayString or otherwise PrintObj","filters" : [[]]}],"2args" : [{"rank" : 32,"comment" : "Display: for a class function, and a record","filters" : [["IsClassFunction"],["IsRecord"]]},{"rank" : 22,"comment" : "Display: for a nearly character table, and a list","filters" : [["IsNearlyCharacterTable"],["IsList"]]},{"rank" : 21,"comment" : "Display: for a nearly character table, and a record","filters" : [["IsNearlyCharacterTable"],["IsRecord"]]},{"rank" : 2,"comment" : "Display: for a straight line decision, and a record","filters" : [["IsStraightLineDecision"],["IsRecord"]]},{"rank" : 2,"comment" : "Display: for a straight line program, and a record","filters" : [["IsStraightLineProgram"],["IsRecord"]]},{"rank" : 2,"comment" : "Display: for a table of marks and an options record","filters" : [["IsTableOfMarks"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DisplayString","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "DisplayString: for a partial perm semigroup with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "DisplayString: for a transformation semigroup with generators","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "DisplayString: For large finite field elements","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "DisplayString: for an internal FFE via String","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 13,"comment" : "DisplayString: for floats","filters" : [["IsFloat"]]},{"rank" : 7,"comment" : "DisplayString: for a transformation","filters" : [["IsTransformation"]]},{"rank" : 7,"comment" : "DisplayString: IsList","filters" : [["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 6,"comment" : "DisplayString: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 1,"comment" : "DisplayString: IsChar","filters" : [["IsChar"]]},{"rank" : -1,"comment" : "DisplayString: generic: return default string","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInternallyConsistent","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "IsInternallyConsistent: for a Brauer table","filters" : [["IsBrauerTable"]]},{"rank" : 22,"comment" : "IsInternallyConsistent: for an ordinary character table","filters" : [["IsOrdinaryTable"]]},{"rank" : 1,"comment" : "IsInternallyConsistent: for a straight line decision","filters" : [["IsStraightLineDecision"]]},{"rank" : 1,"comment" : "IsInternallyConsistent: for a straight line program","filters" : [["IsStraightLineProgram"]]},{"rank" : 1,"comment" : "IsInternallyConsistent: for a table of marks, decomposition test","filters" : [["IsTableOfMarks"]]},{"rank" : 0,"comment" : "IsInternallyConsistent: default method 'ReturnTrue'","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsImpossible","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsImpossible: system getter","filters" : [["IsAttributeStoringRep","Tester(IsImpossible)"]]},{"rank" : 33,"comment" : "IsImpossible","filters" : [["IsOrdinaryMatrix","IsLieMatrix"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsImpossible)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsImpossible): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsImpossible): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsImpossible)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtRepOfObj","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 109,"comment" : "ExtRepOfObj: for a straight line program word","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"]]},{"rank" : 103,"comment" : "ExtRepOfObj: using 32Bits_ExtRepOfObj","filters" : [["Is32BitsPcWordRep"]]},{"rank" : 103,"comment" : "ExtRepOfObj: using 16Bits_ExtRepOfObj","filters" : [["Is16BitsPcWordRep"]]},{"rank" : 103,"comment" : "ExtRepOfObj: using 8Bits_ExtRepOfObj","filters" : [["Is8BitsPcWordRep"]]},{"rank" : 17,"comment" : "ExtRepOfObj: for an internal cyclotomic","filters" : [["IsCyc","IsInternalRep"]]},{"rank" : 17,"comment" : "ExtRepOfObj: for element in Z\/nZ (ModulusRep, nonprime)","filters" : [["IsZmodnZObjNonprime","IsModulusRep"]]},{"rank" : 17,"comment" : "ExtRepOfObj: ExtElm","filters" : [["IsAlgebraicElement","IsKroneckerConstRep"]]},{"rank" : 17,"comment" : "ExtRepOfObj: baseFieldElm","filters" : [["IsAlgebraicElement","IsAlgBFRep"]]},{"rank" : 13,"comment" : "ExtRepOfObj: for s. c. ring element in dense coeff. vector rep.","filters" : [["IsSCRingObj","IsDenseCoeffVectorRep"]]},{"rank" : 13,"comment" : "ExtRepOfObj: for s. c. algebra element in dense coeff. vector rep.","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 12,"comment" : "ExtRepOfObj: for floats","filters" : [["IsFloat"]]},{"rank" : 11,"comment" : "ExtRepOfObj: for f.p. algebra element","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 11,"comment" : "ExtRepOfObj: for magma ring element","filters" : [["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 10,"comment" : "ExtRepOfObj: for weight rep element","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 10,"comment" : "ExtRepOfObj: for an UEALattice element","filters" : [["IsUEALatticeElement"]]},{"rank" : 10,"comment" : "ExtRepOfObj: for a cochain","filters" : [["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 10,"comment" : "ExtRepOfObj: for a direct sum element","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 10,"comment" : "ExtRepOfObj: for a sparse rowspace element","filters" : [["IsPackedElementDefaultRep","IsSparseRowSpaceElement"]]},{"rank" : 10,"comment" : "ExtRepOfObj: for a monomial element","filters" : [["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 10,"comment" : "ExtRepOfObj: for algebra module element in packed element rep","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 9,"comment" : "ExtRepOfObj: for an element of an f.p. group (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpGroup"]]},{"rank" : 8,"comment" : "ExtRepOfObj: for a inf. bits assoc. word","filters" : [["IsInfBitsAssocWord"]]},{"rank" : 8,"comment" : "ExtRepOfObj: for a 32 bits assoc. word","filters" : [["Is32BitsAssocWord"]]},{"rank" : 8,"comment" : "ExtRepOfObj: for a 16 bits assoc. word","filters" : [["Is16BitsAssocWord"]]},{"rank" : 8,"comment" : "ExtRepOfObj: for an 8 bits assoc. word","filters" : [["Is8BitsAssocWord"]]},{"rank" : 7,"comment" : "ExtRepOfObj: for a nonassoc. word","filters" : [["IsNonassocWord","IsBracketRep"]]},{"rank" : 6,"comment" : "ExtRepOfObj: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 6,"comment" : "ExtRepOfObj","filters" : [["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 6,"comment" : "ExtRepOfObj: assoc word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ObjByExtRep","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 25,"comment" : "ObjByExtRep: for floats","filters" : [["CategoryFamily(IsFloat)"],["CategoryCollections(IsCyclotomic)"]]},{"rank" : 23,"comment" : "ObjByExtRep: for family of elements in Z\/nZ (nonprime), and integer","filters" : [["CategoryFamily(IsZmodnZObjNonprime)"],["IsInt"]]},{"rank" : 20,"comment" : "ObjByExtRep: for a family of nonassociative words, and an integer","filters" : [["CategoryFamily(IsNonassocWord)"],["IsInt"]]},{"rank" : 13,"comment" : "ObjByExtRep: baseFieldElm","filters" : [["CategoryFamily(IsAlgebraicElement)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 9,"comment" : "ObjByExtRep: for s. c. alg. elms. family with coefficients family","filters" : [["IsFamilyOverFullCoefficientsFamily","CategoryFamily(IsSCAlgebraObj)"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "ObjByExtRep: for a InfBits-family of associative words, and a homogeneous list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","IsInfBitsFamily"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "ObjByExtRep: for a 32Bits-family of associative words, and a homogeneous list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","Is32BitsFamily"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "ObjByExtRep: for a 16Bits-family of associative words, and a homogeneous list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","Is16BitsFamily"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "ObjByExtRep: for a 8Bits-family of associative words, and a homogeneous list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","Is8BitsFamily"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "ObjByExtRep: for s. c. ring elements family","filters" : [["CategoryFamily(IsSCRingObj)"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "ObjByExtRep: for s. c. algebra elements family","filters" : [["CategoryFamily(IsSCAlgebraObj)"],["IsHomogeneousList"]]},{"rank" : 7,"comment" : "ObjByExtRep: letter rep family","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily"],["IsHomogeneousList"]]},{"rank" : 7,"comment" : "ObjByExtRep: for a family of associative words, and a homogeneous list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily"],["IsHomogeneousList"]]},{"rank" : 7,"comment" : "ObjByExtRep: ExtElm","filters" : [["CategoryFamily(IsAlgebraicElement)"],["IsList"]]},{"rank" : 7,"comment" : "ObjByExtRep: for family of f.p. algebra elements with normal form","filters" : [["CategoryFamily(IsElementOfFpAlgebra)","Tester(NiceNormalFormByExtRepFunction)"],["IsList"]]},{"rank" : 6,"comment" : "ObjByExtRep: for family of UEALattice elements, and list","filters" : [["CategoryFamily(IsUEALatticeElement)"],["IsList"]]},{"rank" : 6,"comment" : "ObjByExtRep: for magma ring elements family, and list","filters" : [["CategoryFamily(IsElementOfMagmaRingModuloRelations)"],["IsList"]]},{"rank" : 5,"comment" : "ObjByExtRep: using 32Bits_AssocWord","filters" : [["IsElementsFamilyBy32BitsSingleCollector"],["IsList"]]},{"rank" : 5,"comment" : "ObjByExtRep: using 16Bits_AssocWord","filters" : [["IsElementsFamilyBy16BitsSingleCollector"],["IsList"]]},{"rank" : 5,"comment" : "ObjByExtRep: using 8Bits_AssocWord","filters" : [["IsElementsFamilyBy8BitsSingleCollector"],["IsList"]]},{"rank" : 4,"comment" : "ObjByExtRep: for a family of nonassociative words, and a list","filters" : [["CategoryFamily(IsNonassocWord)"],["IsList"]]},{"rank" : 4,"comment" : "ObjByExtRep: for a family of weight rep elements and a list","filters" : [["CategoryFamily(IsWeightRepElement)"],["IsList"]]},{"rank" : 4,"comment" : "ObjByExtRep: for a family of direct sum elements and a list","filters" : [["CategoryFamily(IsDirectSumElement)"],["IsList"]]},{"rank" : 4,"comment" : "ObjByExtRep: for a sparse rowspace element family and a list","filters" : [["CategoryFamily(IsSparseRowSpaceElement)"],["IsList"]]},{"rank" : 4,"comment" : "ObjByExtRep: for a family of monomial elements and a list","filters" : [["CategoryFamily(IsMonomialElement)"],["IsList"]]},{"rank" : 3,"comment" : "ObjByExtRep: reconstruct a residue class union (ResClasses)","filters" : [["IsFamily"],["IsList"]]},{"rank" : 2,"comment" : "ObjByExtRep: for algebra module elements family, object","filters" : [["CategoryFamily(IsAlgebraModuleElement)"],[]]}],"3args" : [],"4args" : [{"rank" : 44,"comment" : "ObjByExtRep: for a 32 bits assoc. words family, two integers, and a list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","Is32BitsFamily"],["IsInt"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 44,"comment" : "ObjByExtRep: for a 16 bits assoc. words family, two integers, and a list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","Is16BitsFamily"],["IsInt"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 44,"comment" : "ObjByExtRep: for an 8 bits assoc. words family, two integers, and a list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","Is8BitsFamily"],["IsInt"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 43,"comment" : "ObjByExtRep: letter rep family,integers (ignored)","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily"],["IsInt"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 41,"comment" : "ObjByExtRep: for an inf. bits assoc. words family, two integers, and a list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","IsInfBitsFamily"],["IsCyclotomic"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 40,"comment" : "ObjByExtRep: for a fam. of assoc. words, a cyclotomic, an int., and a homog. list","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily"],["IsCyclotomic"],["IsInt"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "KnownAttributesOfObject","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 0,"comment" : "KnownAttributesOfObject: for an object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KnownPropertiesOfObject","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 0,"comment" : "KnownPropertiesOfObject: for an object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KnownTruePropertiesOfObject","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 0,"comment" : "KnownTruePropertiesOfObject: for an object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CategoriesOfObject","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 0,"comment" : "CategoriesOfObject: for an object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentationsOfObject","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 0,"comment" : "RepresentationsOfObject: for an object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PostMakeImmutable","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "PostMakeImmutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "PostMakeImmutable","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "PostMakeImmutable","filters" : [["IsGF2MatrixRep"]]},{"rank" : 11,"comment" : "PostMakeImmutable: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 0,"comment" : "PostMakeImmutable: unless otherwise directed, do nothing","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MemoryUsage","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "MemoryUsage: for a plist","filters" : [["IsList","IsPlistRep"]]},{"rank" : 17,"comment" : "MemoryUsage: for a rational","filters" : [["IsRat"]]},{"rank" : 1,"comment" : "MemoryUsage: for a type","filters" : [["IsType"]]},{"rank" : 1,"comment" : "MemoryUsage: for a family","filters" : [["IsFamily"]]},{"rank" : 1,"comment" : "MemoryUsage: for a function","filters" : [["IsFunction"]]},{"rank" : 1,"comment" : "MemoryUsage: for a component object","filters" : [["IsComponentObjectRep"]]},{"rank" : 1,"comment" : "MemoryUsage: for a positional object","filters" : [["IsPositionalObjectRep"]]},{"rank" : 1,"comment" : "MemoryUsage: for a record","filters" : [["IsRecord"]]},{"rank" : 0,"comment" : "MemoryUsage: fallback method for objs without subobjs","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FlushCaches","type" : "GAP_Operation","filters" : [[]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CollectionsFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "CollectionsFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(CollectionsFamily)"]]},{"rank" : 91,"comment" : "CollectionsFamily: for a family","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CollectionsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CollectionsFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CollectionsFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CollectionsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementsFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "ElementsFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(ElementsFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ElementsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 4,"comment" : "Setter(ElementsFamily): method to inherit `Characteristic' to collections families","filters" : [["IsAttributeStoringRep","IsFamily"],["IsFamily"]]},{"rank" : 2,"comment" : "Setter(ElementsFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ElementsFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ElementsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UseSubsetRelation","type" : "GAP_Operation","filters" : [[["IsCollection"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 0,"comment" : "UseSubsetRelation: default method that checks maintenances and then returns `true'","filters" : [["IsCollection"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UseIsomorphismRelation","type" : "GAP_Operation","filters" : [[["IsCollection"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 0,"comment" : "UseIsomorphismRelation: default method that checks maintenances and then returns `true'","filters" : [["IsCollection"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UseFactorRelation","type" : "GAP_Operation","filters" : [[["IsCollection"],[],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 93,"comment" : "UseFactorRelation","filters" : [["Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "UseFactorRelation: default method that checks maintenances and then returns `true'","filters" : [["IsCollection"],[],["IsCollection"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Iterator","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10006,"comment" : "Iterator: for a trivial collection","filters" : [["IsCollection","IsTrivial","Tester(IsTrivial)"]]},{"rank" : 432,"comment" : "Iterator","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 86,"comment" : "Iterator: for a trivial permutation group","filters" : [["IsTrivial","Tester(IsTrivial)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 69,"comment" : "Iterator: for `Rationals'","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 58,"comment" : "Iterator: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 47,"comment" : "Iterator: for a free group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 39,"comment" : "Iterator: for `Integers'","filters" : [["IsIntegers"]]},{"rank" : 27,"comment" : "Iterator: for `PositiveIntegers'","filters" : [["IsPositiveIntegers"]]},{"rank" : 23,"comment" : "Iterator: for free left module (delegate to 'IteratorByBasis')","filters" : [["IsFreeLeftModule"]]},{"rank" : 19,"comment" : "Iterator: more helpful error for integers","filters" : [["IsInt","IsPosRat"]]},{"rank" : 16,"comment" : "Iterator: for a free monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 14,"comment" : "Iterator: for a free semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 11,"comment" : "Iterator: for subspaces collection of a (finite) full row module","filters" : [["IsSubspacesVectorSpace","IsSubspacesFullRowSpaceDefaultRep"]]},{"rank" : 10,"comment" : "Iterator: for a subspaces domain","filters" : [["IsSubspacesVectorSpace","IsSubspacesVectorSpaceDefaultRep"]]},{"rank" : 9,"comment" : "Iterator: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 5,"comment" : "Iterator: for a collection that is a list","filters" : [["IsList","IsCollection"]]},{"rank" : 3,"comment" : "Iterator: for a mutable iterator","filters" : [["IsMutable","IsIterator"]]},{"rank" : 2,"comment" : "Iterator: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "Iterator: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IteratorSorted","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "IteratorSorted: for a collection that is a list","filters" : [["IsList","IsCollection"]]},{"rank" : 2,"comment" : "IteratorSorted: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "IteratorSorted: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsDoneIterator","type" : "GAP_Operation","filters" : [[["IsIterator"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "IsDoneIterator: primitive groups iterator","filters" : [["IsMutable","IsIterator","IsPrimGrpIterRep"]]},{"rank" : 3,"comment" : "IsDoneIterator: for iterators of residue class unions (ResClasses)","filters" : [["IsIterator","IsResidueClassUnionsIteratorRep"]]},{"rank" : 3,"comment" : "IsDoneIterator: for `IsIteratorByFunctions'","filters" : [["IsIterator","IsIteratorByFunctionsRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NextIterator","type" : "GAP_Operation","filters" : [[["IsMutable","IsIterator"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "NextIterator: for iterators of residue class unions (ResClasses)","filters" : [["IsMutable","IsIterator","IsResidueClassUnionsIteratorRep"]]},{"rank" : 5,"comment" : "NextIterator: primitive groups iterator","filters" : [["IsMutable","IsIterator","IsPrimGrpIterRep"]]},{"rank" : 5,"comment" : "NextIterator: for `IsIteratorByFunctions'","filters" : [["IsMutable","IsIterator","IsIteratorByFunctionsRep"]]},{"rank" : 1,"comment" : "NextIterator: for an immutable iterator (print a reasonable error message)","filters" : [["IsIterator"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsEmpty","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsEmpty: system getter","filters" : [["IsAttributeStoringRep","Tester(IsEmpty)"]]},{"rank" : 5,"comment" : "IsEmpty","filters" : [["IsGroupClass","Tester(IsGroupClass)","Tester(ContainsTrivialGroup)"]]},{"rank" : 5,"comment" : "IsEmpty","filters" : [["IsClassByUnionRep"]]},{"rank" : 5,"comment" : "IsEmpty","filters" : [["IsClassByIntersectionRep"]]},{"rank" : 5,"comment" : "IsEmpty","filters" : [["IsClassByComplementRep"]]},{"rank" : 4,"comment" : "IsEmpty","filters" : [["IsCollection","Tester(Size)"]]},{"rank" : 2,"comment" : "IsEmpty: for generic class","filters" : [["IsClass"]]},{"rank" : 2,"comment" : "IsEmpty: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "IsEmpty: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsEmpty)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsEmpty): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsEmpty): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsEmpty)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTrivial","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsTrivial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTrivial)"]]},{"rank" : 50,"comment" : "IsTrivial: for a division ring","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 37,"comment" : "IsTrivial: for a FLMLOR-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 36,"comment" : "IsTrivial: for finitely presented groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 34,"comment" : "IsTrivial: for a FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 33,"comment" : "IsTrivial","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 24,"comment" : "IsTrivial","filters" : [["IsFreeLeftModule","Tester(Dimension)"]]},{"rank" : 23,"comment" : "IsTrivial: for a free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 17,"comment" : "IsTrivial","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveGroup)"]]},{"rank" : 17,"comment" : "IsTrivial","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 15,"comment" : "IsTrivial","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]]},{"rank" : 14,"comment" : "IsTrivial","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 4,"comment" : "IsTrivial","filters" : [["IsCollection","Tester(Size)"]]},{"rank" : 3,"comment" : "IsTrivial","filters" : [["IsCollection","Tester(IsNonTrivial)"]]},{"rank" : 2,"comment" : "IsTrivial: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTrivial)","type" : "GAP_Operation","filters" : [[["IsCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTrivial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTrivial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTrivial)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNonTrivial","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsNonTrivial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNonTrivial)"]]},{"rank" : 3,"comment" : "IsNonTrivial","filters" : [["IsCollection","Tester(IsTrivial)"]]},{"rank" : 2,"comment" : "IsNonTrivial: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNonTrivial)","type" : "GAP_Operation","filters" : [[["IsCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNonTrivial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNonTrivial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNonTrivial)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFinite","type" : "GAP_Operation","filters" : [[["IsCollection"]],[["IsFloat"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsFinite: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFinite)"]]},{"rank" : 50,"comment" : "IsFinite: via Minkowski kernel (short but not too efficient)","filters" : [["IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"]]},{"rank" : 48,"comment" : "IsFinite: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 46,"comment" : "IsFinite: cyclotomic matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "IsFinite: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 38,"comment" : "IsFinite: pcgs computable groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 36,"comment" : "IsFinite: for a magma ring modulo the span of ``zero''","filters" : [["IsMagmaRingModuloSpanOfZero"]]},{"rank" : 36,"comment" : "IsFinite: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 24,"comment" : "IsFinite","filters" : [["IsFreeLeftModule","Tester(IsFiniteDimensional)"]]},{"rank" : 23,"comment" : "IsFinite: for a free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 22,"comment" : "IsFinite: for an ordinary character table","filters" : [["IsOrdinaryTable"]]},{"rank" : 20,"comment" : "IsFinite: for an underlying relation of a general mapping","filters" : [["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"]]},{"rank" : 18,"comment" : "IsFinite: for a semigroup of assoc. words","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 17,"comment" : "IsFinite: for a Rees 0-matrix subsemigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "IsFinite: for a Rees matrix subsemigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "IsFinite","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 13,"comment" : "IsFinite: for a magma of nonassoc. words","filters" : [["IsMagma","CategoryCollections(IsNonassocWord)"]]},{"rank" : 12,"comment" : "IsFinite: for floats","filters" : [["IsFloat"]]},{"rank" : 12,"comment" : "IsFinite: for an additive coset","filters" : [["IsAdditiveCoset"]]},{"rank" : 11,"comment" : "IsFinite: for a conjugacy class","filters" : [["IsConjugacyClassGroupRep"]]},{"rank" : 11,"comment" : "IsFinite: method for an ext. orbit by stabilizer","filters" : [["IsExternalOrbitByStabilizerRep"]]},{"rank" : 5,"comment" : "IsFinite","filters" : [["IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsFinite","filters" : [["IsCollection","Tester(Size)"]]},{"rank" : 2,"comment" : "IsFinite: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFinite)","type" : "GAP_Operation","filters" : [[["IsCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFinite): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFinite): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFinite)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsWholeFamily","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsWholeFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(IsWholeFamily)"]]},{"rank" : 50,"comment" : "IsWholeFamily: for a finitely generated free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 44,"comment" : "IsWholeFamily: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 36,"comment" : "IsWholeFamily: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 33,"comment" : "IsWholeFamily: for s. c. algebra elements collection","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)"]]},{"rank" : 24,"comment" : "IsWholeFamily: for a free monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 18,"comment" : "IsWholeFamily: for a free semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 17,"comment" : "IsWholeFamily: for a subsemigroup of a Rees 0-matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "IsWholeFamily: for a subsemigroup of a Rees matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 13,"comment" : "IsWholeFamily: for a free magma","filters" : [["IsMagma","CategoryCollections(IsNonassocWord)"]]},{"rank" : 2,"comment" : "IsWholeFamily: default for a collection, print an error message","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsWholeFamily)","type" : "GAP_Operation","filters" : [[["IsCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsWholeFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsWholeFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsWholeFamily)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Size","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "Size: system getter","filters" : [["IsAttributeStoringRep","Tester(Size)"]]},{"rank" : 397,"comment" : "Size: natural SL","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalSL","Tester(IsNaturalSL)"]]},{"rank" : 395,"comment" : "Size: general linear group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalGL","Tester(IsNaturalGL)"]]},{"rank" : 395,"comment" : "Size: for groups of FFE","filters" : [["CategoryCollections(IsFFE)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 368,"comment" : "Size: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 62,"comment" : "Size","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 62,"comment" : "Size","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 59,"comment" : "Size: for a permutation group that knows to be a direct product","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 58,"comment" : "Size: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 48,"comment" : "Size: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 46,"comment" : "Size","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 46,"comment" : "Size: cyclotomic matrix group not known to be finite","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 44,"comment" : "Size: for a matrix group that knows to be a wreath product","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)"]]},{"rank" : 44,"comment" : "Size: for a matrix group that knows to be a direct product","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 44,"comment" : "Size: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 43,"comment" : "Size: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 38,"comment" : "Size: pcgs computable groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 36,"comment" : "Size: infinite abelianization","filters" : [["Tester(AbelianInvariants)","IsSubgroupFpGroup"]]},{"rank" : 36,"comment" : "Size: for finitely presented groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 35,"comment" : "Size: subgroups of finitely presented groups","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 34,"comment" : "Size: for a group with known ordinary character table","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(OrdinaryCharacterTable)"]]},{"rank" : 34,"comment" : "Size: subdirect product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SubdirectProductInfo)"]]},{"rank" : 34,"comment" : "Size: group direct product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 30,"comment" : "Size: for sc rings and their subrings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)","CategoryCollections(IsSCRingObj)"]]},{"rank" : 28,"comment" : "Size: characteristic zero ring is infinite","filters" : [["Tester(Characteristic)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 24,"comment" : "Size: for a free monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 23,"comment" : "Size: for a free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 20,"comment" : "Size: for a character table","filters" : [["IsNearlyCharacterTable"]]},{"rank" : 20,"comment" : "Size: for a free semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 20,"comment" : "Size: for a free semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 20,"comment" : "Size: for an underlying relation of a general mapping","filters" : [["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"]]},{"rank" : 19,"comment" : "Size","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 18,"comment" : "Size: zmodnze : for full ring Z\/nZ(m)","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZepsObj)"]]},{"rank" : 15,"comment" : "Size: for a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 15,"comment" : "Size: for a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 13,"comment" : "Size: for a free magma","filters" : [["IsMagma","CategoryCollections(IsNonassocWord)"]]},{"rank" : 12,"comment" : "Size: for an additive coset","filters" : [["IsAdditiveCoset"]]},{"rank" : 12,"comment" : "Size: for a magma with a zero adjoined","filters" : [["IsMagmaWithZeroAdjoined"]]},{"rank" : 11,"comment" : "Size: method for a rational class","filters" : [["IsRationalClassGroupRep"]]},{"rank" : 11,"comment" : "Size: for a conjugacy class","filters" : [["IsConjugacyClassGroupRep"]]},{"rank" : 11,"comment" : "Size: method for an ext. orbit by stabilizer","filters" : [["IsExternalOrbitByStabilizerRep"]]},{"rank" : 10,"comment" : "Size: method for a subspaces domain","filters" : [["IsSubspacesVectorSpace","IsSubspacesVectorSpaceDefaultRep"]]},{"rank" : 10,"comment" : "Size: for a trivial domain","filters" : [["IsCollection","IsTrivial","Tester(IsTrivial)","IsGeneralizedDomain"]]},{"rank" : 8,"comment" : "Size: double coset","filters" : [["IsDoubleCoset"]]},{"rank" : 7,"comment" : "Size: for Green's classes","filters" : [["IsGreensClass"]]},{"rank" : 7,"comment" : "Size: for sparse hash tables","filters" : [["IsHash","IsSparseHashRep"]]},{"rank" : 7,"comment" : "Size: for dense hash tables","filters" : [["IsDenseHashRep"]]},{"rank" : 5,"comment" : "Size: for a list that is a collection","filters" : [["IsList","IsCollection"]]},{"rank" : 5,"comment" : "Size","filters" : [["IsAttributeStoringRep","IsCollection","Tester(AsList)"]]},{"rank" : 5,"comment" : "Size","filters" : [["IsAttributeStoringRep","IsCollection","Tester(IsFinite)"]]},{"rank" : 2,"comment" : "Size: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "Size: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Size)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Size): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Size): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Size)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Representative","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "Representative: system getter","filters" : [["IsAttributeStoringRep","Tester(Representative)"]]},{"rank" : 10018,"comment" : "Representative: for additive-magma-with-zero with known zero","filters" : [["Tester(ZeroImmutable)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 10016,"comment" : "Representative: for magma-with-one with known one","filters" : [["Tester(OneImmutable)","IsMagmaWithOne"]]},{"rank" : 10014,"comment" : "Representative: for additive coset in default repres.","filters" : [["IsAdditiveCoset","IsAdditiveCosetDefaultRep"]]},{"rank" : 59,"comment" : "Representative","filters" : [["IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 51,"comment" : "Representative: for a division ring with known generators","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","Tester(GeneratorsOfDivisionRing)"]]},{"rank" : 48,"comment" : "Representative: for full matrix module","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "Representative: for full row module","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 43,"comment" : "Representative: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 36,"comment" : "Representative: for full hom space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 33,"comment" : "Representative: for left operator ring-with-one with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftOperatorRingWithOne)"]]},{"rank" : 30,"comment" : "Representative: for left operator ring with known generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 30,"comment" : "Representative: for a ring-with-one with generators","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRingWithOne)"]]},{"rank" : 27,"comment" : "Representative: for a ring with generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 20,"comment" : "Representative: for a subsemigroup of Rees 0-matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 20,"comment" : "Representative: for a subsemigroup of Rees matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 19,"comment" : "Representative: for right operator additive group with known generators","filters" : [["IsExtRSet","IsDistributiveROpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfRightOperatorAdditiveGroup)"]]},{"rank" : 19,"comment" : "Representative: for left operator additive group with known generators","filters" : [["IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 17,"comment" : "Representative: for additive-magma-with-inverses with known generators","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveGroup)"]]},{"rank" : 17,"comment" : "Representative: for magma-with-inverses with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 15,"comment" : "Representative: for a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 15,"comment" : "Representative: for a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 15,"comment" : "Representative: for additive-magma-with-zero with stored parent","filters" : [["Tester(ParentAttr)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 15,"comment" : "Representative: for additive-magma-with-zero with known generators","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]]},{"rank" : 14,"comment" : "Representative: for magma-with-one with stored parent","filters" : [["Tester(ParentAttr)","IsMagmaWithOne"]]},{"rank" : 14,"comment" : "Representative: for magma-with-one with generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 13,"comment" : "Representative: for additive magma with known generators","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagma)"]]},{"rank" : 12,"comment" : "Representative: for magma with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)"]]},{"rank" : 6,"comment" : "Representative: External Set","filters" : [["IsExternalSet"]]},{"rank" : 6,"comment" : "Representative: for a domain with known domain generators","filters" : [["IsCollection","IsGeneralizedDomain","Tester(GeneratorsOfDomain)"]]},{"rank" : 6,"comment" : "Representative: for a domain with known elements list","filters" : [["IsCollection","Tester(AsList)","IsGeneralizedDomain"]]},{"rank" : 5,"comment" : "Representative: for a collection that is a list","filters" : [["IsList","IsCollection"]]},{"rank" : 2,"comment" : "Representative: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Representative)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Representative): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Representative): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Representative)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativeSmallest","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "RepresentativeSmallest: system getter","filters" : [["IsAttributeStoringRep","Tester(RepresentativeSmallest)"]]},{"rank" : 17,"comment" : "RepresentativeSmallest: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 8,"comment" : "RepresentativeSmallest: for a strictly sorted list","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)"]]},{"rank" : 5,"comment" : "RepresentativeSmallest","filters" : [["IsAttributeStoringRep","IsCollection","Tester(AsSSortedList)"]]},{"rank" : 5,"comment" : "RepresentativeSmallest","filters" : [["IsAttributeStoringRep","IsCollection","Tester(EnumeratorSorted)"]]},{"rank" : 2,"comment" : "RepresentativeSmallest: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "RepresentativeSmallest: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RepresentativeSmallest)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RepresentativeSmallest): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RepresentativeSmallest): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RepresentativeSmallest)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Random","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]],[["IsInt"],["IsInt"]],[["IsRandomSource"],["IsList"]],[["IsRandomSource"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 432,"comment" : "Random","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 397,"comment" : "Random: for natural SL","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalSL","Tester(IsNaturalSL)"]]},{"rank" : 395,"comment" : "Random: for natural GL","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalGL","Tester(IsNaturalGL)"]]},{"rank" : 368,"comment" : "Random: handled by nice monomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 119,"comment" : "Random: for an internal list","filters" : [["IsList","IsInternalRep"]]},{"rank" : 107,"comment" : "Random: for sparse hash tables","filters" : [["IsHash","IsSparseHashRep"]]},{"rank" : 107,"comment" : "Random: for dense hash tables","filters" : [["IsHash","IsDenseHashRep"]]},{"rank" : 72,"comment" : "Random: alternating group: floyd's algorithm","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 72,"comment" : "Random: symmetric group: floyd's algorithm","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 69,"comment" : "Random: for Rationals","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 68,"comment" : "Random: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "Random: for a finite prime field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 57,"comment" : "Random: for a finite field with known primitive root","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","Tester(PrimitiveRoot)"]]},{"rank" : 53,"comment" : "Random: Alg","filters" : [["IsAlgebraicExtension"]]},{"rank" : 49,"comment" : "Random: for full ring Z\/nZ","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 48,"comment" : "Random: for full matrix module","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "Random: for full row module","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 46,"comment" : "Random: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 44,"comment" : "Random: fp group","filters" : [["IsFinite","Tester(IsFinite)","IsSubgroupFpGroup"]]},{"rank" : 44,"comment" : "Random: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 43,"comment" : "Random: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 43,"comment" : "Random: pcgs computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 39,"comment" : "Random: for `Integers'","filters" : [["IsIntegers"]]},{"rank" : 36,"comment" : "Random: for full hom space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 35,"comment" : "Random: LAGUNA: for full ot normalized unit group of group ring","filters" : [["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]]},{"rank" : 24,"comment" : "Random: for a free monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 23,"comment" : "Random: for a free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 18,"comment" : "Random: for a free semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 18,"comment" : "Random: zmodnze : for full collection Z\/nZ(m)","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZepsObj)"]]},{"rank" : 16,"comment" : "Random: RightCoset","filters" : [["IsRightCoset"]]},{"rank" : 13,"comment" : "Random: for a free magma","filters" : [["IsMagma","CategoryCollections(IsNonassocWord)"]]},{"rank" : 12,"comment" : "Random: for an additive coset","filters" : [["IsAdditiveCoset"]]},{"rank" : 10,"comment" : "Random: for external orbit: via acting domain","filters" : [["IsExternalOrbit"]]},{"rank" : 9,"comment" : "Random: for a dense small list","filters" : [["IsList","IsDenseList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 8,"comment" : "Random: double coset","filters" : [["IsDoubleCoset"]]},{"rank" : 5,"comment" : "Random","filters" : [["CategoryFamily(IsPadicExtensionNumber)"]]},{"rank" : 5,"comment" : "Random","filters" : [["CategoryFamily(IsPurePadicNumber)"]]},{"rank" : 4,"comment" : "Random: for an infinite list of generators","filters" : [["IsList","IsInfiniteListOfGeneratorsRep"]]},{"rank" : 4,"comment" : "Random: for a (finite) collection","filters" : [["IsCollection","IsFinite","Tester(IsFinite)"]]},{"rank" : 3,"comment" : "Random: for a dense (small) list","filters" : [["IsList","IsDenseList"]]},{"rank" : 0,"comment" : "Random:  fallback method to test conditions","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 36,"comment" : "Random: for two integers","filters" : [["IsInt"],["IsInt"]]},{"rank" : 5,"comment" : "Random: for a real random source and a list","filters" : [["IsRealRandomSource"],["IsList"]]},{"rank" : 5,"comment" : "Random","filters" : [["IsMersenneTwister"],["IsList"]]},{"rank" : 5,"comment" : "Random","filters" : [["IsGAPRandomSource"],["IsList"]]},{"rank" : 5,"comment" : "Random","filters" : [["IsGlobalRandomSource"],["IsList"]]},{"rank" : 4,"comment" : "Random","filters" : [["IsRandomSource"],["IsList"]]}],"3args" : [{"rank" : 39,"comment" : "Random: for a real random source and two integers","filters" : [["IsRealRandomSource"],["IsInt"],["IsInt"]]},{"rank" : 39,"comment" : "Random","filters" : [["IsMersenneTwister"],["IsInt"],["IsInt"]]},{"rank" : 38,"comment" : "Random","filters" : [["IsRandomSource"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PseudoRandom","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 111,"comment" : "PseudoRandom: for an internal list","filters" : [["IsList","IsInternalRep"]]},{"rank" : 35,"comment" : "PseudoRandom: subgroups fp group: force generators","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 34,"comment" : "PseudoRandom: product replacement","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 27,"comment" : "PseudoRandom: polynomial ring","filters" : [["IsPolynomialRing"]]},{"rank" : 16,"comment" : "PseudoRandom: RightCoset","filters" : [["IsRightCoset"]]},{"rank" : 8,"comment" : "PseudoRandom: double coset","filters" : [["IsDoubleCoset"]]},{"rank" : 1,"comment" : "PseudoRandom: for a list or collection (delegate to `Random')","filters" : [["IsListOrCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PseudoRandomSeed","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "PseudoRandomSeed: system getter","filters" : [["IsAttributeStoringRep","Tester(PseudoRandomSeed)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PseudoRandomSeed)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PseudoRandomSeed): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PseudoRandomSeed): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PseudoRandomSeed)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Enumerator","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "Enumerator: system getter","filters" : [["IsAttributeStoringRep","Tester(Enumerator)"]]},{"rank" : 10023,"comment" : "Enumerator: for full ring Z\/nZ","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 10003,"comment" : "Enumerator: for a collection with known `AsSSortedList' value","filters" : [["IsCollection","Tester(AsSSortedList)"]]},{"rank" : 10003,"comment" : "Enumerator: for a collection with known `AsList' value","filters" : [["IsCollection","Tester(AsList)"]]},{"rank" : 432,"comment" : "Enumerator","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 377,"comment" : "Enumerator: use nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 69,"comment" : "Enumerator: for `Rationals'","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 69,"comment" : "Enumerator: for trivial magma-with-one","filters" : [["IsTrivial","Tester(IsTrivial)","IsMagmaWithOne"]]},{"rank" : 58,"comment" : "Enumerator: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "Enumerator: for a finite prime field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 48,"comment" : "Enumerator: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 47,"comment" : "Enumerator: for enumerator of a free group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 44,"comment" : "Enumerator: fp gp.","filters" : [["IsFinite","Tester(IsFinite)","IsSubgroupFpGroup"]]},{"rank" : 43,"comment" : "Enumerator: finite pc computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 39,"comment" : "Enumerator: for integers","filters" : [["IsIntegers"]]},{"rank" : 35,"comment" : "Enumerator: generic method for a group","filters" : [["IsAttributeStoringRep","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 30,"comment" : "Enumerator: generic method for a ring-with-one with known generators","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRingWithOne)"]]},{"rank" : 27,"comment" : "Enumerator: generic method for a two-sided ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)"]]},{"rank" : 27,"comment" : "Enumerator: generic method for a right ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)"]]},{"rank" : 27,"comment" : "Enumerator: generic method for a left ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)"]]},{"rank" : 27,"comment" : "Enumerator: generic method for a two-sided ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)"]]},{"rank" : 27,"comment" : "Enumerator: generic method for a right ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)"]]},{"rank" : 27,"comment" : "Enumerator: generic method for a left ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)"]]},{"rank" : 27,"comment" : "Enumerator: generic method for a ring with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 26,"comment" : "Enumerator: for a free monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 23,"comment" : "Enumerator: for free left module (delegate to 'EnumeratorByBasis')","filters" : [["IsFreeLeftModule"]]},{"rank" : 20,"comment" : "Enumerator: for a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)","Tester(UnderlyingSemigroup)"]]},{"rank" : 20,"comment" : "Enumerator: for a full transformation semigroup","filters" : [["IsFullTransformationSemigroup","Tester(IsFullTransformationSemigroup)"]]},{"rank" : 20,"comment" : "Enumerator: for a free semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 20,"comment" : "Enumerator: for an underlying relation of a general mapping","filters" : [["IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"]]},{"rank" : 19,"comment" : "Enumerator: for trivial add. magma-with-zero","filters" : [["IsTrivial","Tester(IsTrivial)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 18,"comment" : "Enumerator: zmodnze : for full collection Z\/nZ(m)","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZepsObj)"]]},{"rank" : 18,"comment" : "Enumerator: for a semigroup ideal","filters" : [["Tester(GeneratorsOfMagmaIdeal)","IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]]},{"rank" : 17,"comment" : "Enumerator: generic method for a magma ideal","filters" : [["IsAttributeStoringRep","IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]},{"rank" : 16,"comment" : "Enumerator: for a right coset","filters" : [["IsRightCoset"]]},{"rank" : 16,"comment" : "Enumerator: for a left semigroup ideal","filters" : [["Tester(GeneratorsOfExtLSet)","IsLeftSemigroupIdeal","Tester(IsLeftSemigroupIdeal)"]]},{"rank" : 16,"comment" : "Enumerator: for a right semigroup ideal","filters" : [["Tester(GeneratorsOfExtRSet)","IsRightSemigroupIdeal","Tester(IsRightSemigroupIdeal)"]]},{"rank" : 15,"comment" : "Enumerator: for a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 14,"comment" : "Enumerator: for a free magma","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","CategoryCollections(IsWord)"]]},{"rank" : 14,"comment" : "Enumerator: generic method for an add. magma","filters" : [["IsAttributeStoringRep","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 14,"comment" : "Enumerator: for a generic semigroup","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "Enumerator","filters" : [["IsConjugacyClassPermGroupRep"]]},{"rank" : 13,"comment" : "Enumerator: generic method for a magma","filters" : [["IsAttributeStoringRep","IsMagma"]]},{"rank" : 12,"comment" : "Enumerator","filters" : [["IsRationalClassPermGroupRep"]]},{"rank" : 12,"comment" : "Enumerator: for an additive coset","filters" : [["IsAdditiveCoset"]]},{"rank" : 11,"comment" : "Enumerator","filters" : [["IsRationalClassGroupRep"]]},{"rank" : 11,"comment" : "Enumerator: xorb by stabilizer","filters" : [["IsExternalOrbitByStabilizerRep"]]},{"rank" : 11,"comment" : "Enumerator: <xorb by pcgs>","filters" : [["IsExternalOrbit","IsExternalSetByPcgs"]]},{"rank" : 10,"comment" : "Enumerator: for external orbit: compute orbit","filters" : [["IsExternalOrbit"]]},{"rank" : 10,"comment" : "Enumerator: for external subset with home enumerator","filters" : [["IsExternalSubset","Tester(HomeEnumerator)"]]},{"rank" : 10,"comment" : "Enumerator: method for a subspaces domain","filters" : [["IsSubspacesVectorSpace","IsSubspacesVectorSpaceDefaultRep"]]},{"rank" : 10,"comment" : "Enumerator: for a magma congruence class","filters" : [["IsCongruenceClass"]]},{"rank" : 9,"comment" : "Enumerator: for degenerated residue class unions of Z^2 (ResClasses)","filters" : [["IsFinite","Tester(IsFinite)","IsResidueClassUnionOfZxZ"]]},{"rank" : 8,"comment" : "Enumerator: for a double coset","filters" : [["IsDoubleCoset"]]},{"rank" : 8,"comment" : "Enumerator","filters" : [["IsAttributeStoringRep","IsCollection","Tester(EnumeratorSorted)","IsGeneralizedDomain"]]},{"rank" : 7,"comment" : "Enumerator: for sparse hash tables","filters" : [["IsHash","IsSparseHashRep"]]},{"rank" : 7,"comment" : "Enumerator: for dense hash tables","filters" : [["IsDenseHashRep"]]},{"rank" : 6,"comment" : "Enumerator: external set -> HomeEnumerator","filters" : [["IsExternalSet"]]},{"rank" : 6,"comment" : "Enumerator: for list dictionaries","filters" : [["IsListDictionary"]]},{"rank" : 6,"comment" : "Enumerator: for equivalence classes","filters" : [["IsEquivalenceClass"]]},{"rank" : 6,"comment" : "Enumerator: for a domain with stored domain generators","filters" : [["IsCollection","IsGeneralizedDomain","Tester(GeneratorsOfDomain)"]]},{"rank" : 5,"comment" : "Enumerator: for a collection that is a list","filters" : [["IsList","IsCollection"]]},{"rank" : 5,"comment" : "Enumerator","filters" : [["IsAttributeStoringRep","IsCollection","Tester(AsList)"]]},{"rank" : 2,"comment" : "Enumerator: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Enumerator)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Enumerator): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Enumerator): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Enumerator)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EnumeratorSorted","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "EnumeratorSorted: system getter","filters" : [["IsAttributeStoringRep","Tester(EnumeratorSorted)"]]},{"rank" : 10003,"comment" : "EnumeratorSorted: for a collection with known `AsSSortedList' value","filters" : [["IsCollection","Tester(AsSSortedList)"]]},{"rank" : 58,"comment" : "EnumeratorSorted: for a finite prime field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 48,"comment" : "EnumeratorSorted: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 21,"comment" : "EnumeratorSorted: for a plist","filters" : [["IsList","IsPlistRep"]]},{"rank" : 5,"comment" : "EnumeratorSorted: for a domain","filters" : [["IsCollection","IsGeneralizedDomain"]]},{"rank" : 5,"comment" : "EnumeratorSorted","filters" : [["IsAttributeStoringRep","IsCollection","Tester(AsSSortedList)"]]},{"rank" : 2,"comment" : "EnumeratorSorted: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EnumeratorSorted)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EnumeratorSorted): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EnumeratorSorted): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EnumeratorSorted)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingCollection","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "UnderlyingCollection: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingCollection)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingCollection)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingCollection): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingCollection): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingCollection)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ListOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]],[["IsListOrCollection"],["IsFunction"]],[["IsRowVectorObj"]],[["IsRowVectorObj"],["IsFunction"]],[["IsRowListMatrix"]],[["IsRowListMatrix"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "ListOp: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 11,"comment" : "ListOp: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 5,"comment" : "ListOp: for a collection that is a list","filters" : [["IsList","IsCollection"]]},{"rank" : 2,"comment" : "ListOp: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "ListOp: for a collection","filters" : [["IsCollection"]]},{"rank" : 1,"comment" : "ListOp","filters" : [["IsIterator"]]}],"2args" : [{"rank" : 16,"comment" : "ListOp: for a plist matrix and a function","filters" : [["IsPlistMatrixRep"],["IsFunction"]]},{"rank" : 12,"comment" : "ListOp: for a plist vector and a function","filters" : [["IsPlistVectorRep"],["IsFunction"]]},{"rank" : 10,"comment" : "ListOp: for degenerated residue class unions of Z^2 (ResClasses)","filters" : [["IsFinite","Tester(IsFinite)","IsResidueClassUnionOfZxZ"],["IsFunction"]]},{"rank" : 4,"comment" : "ListOp: for a dense list, and a function","filters" : [["IsDenseList"],["IsFunction"]]},{"rank" : 3,"comment" : "ListOp: for a list, and a function","filters" : [["IsList"],["IsFunction"]]},{"rank" : 2,"comment" : "ListOp: for a list\/collection, and a function","filters" : [["IsListOrCollection"],["IsFunction"]]},{"rank" : 1,"comment" : "ListOp","filters" : [["IsPcp"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SortedList","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 1,"comment" : "SortedList: for a list or collection","filters" : [["IsListOrCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SSortedList","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "SSortedList: for a plist","filters" : [["IsList","IsPlistRep"]]},{"rank" : 9,"comment" : "SSortedList: for a collection that is a small list","filters" : [["IsList","IsCollection","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 5,"comment" : "SSortedList: for a collection that is a list","filters" : [["IsList","IsCollection"]]},{"rank" : 2,"comment" : "SSortedList: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "SSortedList: for a collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 3,"comment" : "SSortedList: for a list, and a function","filters" : [["IsList"],["IsFunction"]]},{"rank" : 3,"comment" : "SSortedList: for a collection, and a function","filters" : [["IsCollection"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsList","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AsList: system getter","filters" : [["IsAttributeStoringRep","Tester(AsList)"]]},{"rank" : 432,"comment" : "AsList","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 58,"comment" : "AsList: permgp: AsSSortedList","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "AsList: for a finite prime field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 49,"comment" : "AsList: for full ring Z\/nZ","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 48,"comment" : "AsList: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 46,"comment" : "AsList: pc group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 24,"comment" : "AsList: pcgs","filters" : [["IsPcgs","IsPcgsDefaultRep"]]},{"rank" : 23,"comment" : "AsList: for a free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 11,"comment" : "AsList: for classes of subgroups","filters" : [["IsConjugacyClassSubgroupsRep"]]},{"rank" : 11,"comment" : "AsList","filters" : [["IsRationalClassGroupRep"]]},{"rank" : 11,"comment" : "AsList: xorb by stabilizer","filters" : [["IsExternalOrbitByStabilizerRep"]]},{"rank" : 10,"comment" : "AsList: for Pc transversals","filters" : [["IsList","IsRightTransversalPcGroupRep"]]},{"rank" : 10,"comment" : "AsList: external orbit","filters" : [["IsExternalOrbit"]]},{"rank" : 8,"comment" : "AsList: double coset","filters" : [["IsDoubleCoset"]]},{"rank" : 8,"comment" : "AsList","filters" : [["IsAttributeStoringRep","IsCollection","Tester(AsSSortedList)","IsGeneralizedDomain"]]},{"rank" : 7,"comment" : "AsList: for an enumerator that perhaps has its own `AsList' function","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"]]},{"rank" : 6,"comment" : "AsList: for a domain with stored domain generators","filters" : [["IsCollection","IsGeneralizedDomain","Tester(GeneratorsOfDomain)"]]},{"rank" : 6,"comment" : "AsList: for collections that are constant time access lists","filters" : [["IsCollection","IsConstantTimeAccessList"]]},{"rank" : 3,"comment" : "AsList: for a constant time access list","filters" : [["IsList","IsConstantTimeAccessList"]]},{"rank" : 2,"comment" : "AsList: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "AsList: for a collection","filters" : [["IsCollection"]]},{"rank" : 1,"comment" : "AsList","filters" : [["IsPcp"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsList)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "Setter(AsList): for an underlying relation and a list of direct product elements","filters" : [["IsAttributeStoringRep","IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"],["CategoryCollections(IsDirectProductElement)"]]},{"rank" : 2,"comment" : "Setter(AsList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsList)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSortedList","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AsSortedList: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSortedList)"]]},{"rank" : 1,"comment" : "AsSortedList: for a list or collection","filters" : [["IsListOrCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSortedList)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSortedList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSortedList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSortedList)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSSortedList","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AsSSortedList: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSSortedList)"]]},{"rank" : 58,"comment" : "AsSSortedList: via stabchain","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "AsSSortedList: pcgs computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 49,"comment" : "AsSSortedList: for full ring Z\/nZ","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 43,"comment" : "AsSSortedList: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 23,"comment" : "AsSSortedList: for a free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 21,"comment" : "AsSSortedList: for a plist","filters" : [["IsList","IsPlistRep"]]},{"rank" : 14,"comment" : "AsSSortedList: for a left magma ideal","filters" : [["IsLeftActedOnBySuperset","Tester(GeneratorsOfExtLSet)","IsMagma"]]},{"rank" : 14,"comment" : "AsSSortedList: for a right magma ideal","filters" : [["IsRightActedOnBySuperset","Tester(GeneratorsOfExtRSet)","IsMagma"]]},{"rank" : 10,"comment" : "AsSSortedList: external orbit","filters" : [["IsExternalOrbit"]]},{"rank" : 7,"comment" : "AsSSortedList: for a Green's class","filters" : [["IsGreensClass"]]},{"rank" : 6,"comment" : "AsSSortedList: for a collection that is a constant time access list","filters" : [["IsCollection","IsConstantTimeAccessList"]]},{"rank" : 2,"comment" : "AsSSortedList: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "AsSSortedList: for a list","filters" : [["IsList"]]},{"rank" : 2,"comment" : "AsSSortedList: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSSortedList)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSSortedList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSSortedList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSSortedList)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSSortedListNonstored","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10002,"comment" : "AsSSortedListNonstored: if `AsSSortedList' is known","filters" : [["IsListOrCollection","Tester(AsSSortedList)"]]},{"rank" : 2502,"comment" : "AsSSortedListNonstored: if `AsList' is known:sort","filters" : [["IsListOrCollection","Tester(AsList)"]]},{"rank" : 58,"comment" : "AsSSortedListNonstored: via stabchain","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "AsSSortedListNonstored: pcgs computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 33,"comment" : "AsSSortedListNonstored: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SumOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "SumOp: for a dense list","filters" : [["IsDenseList"]]},{"rank" : 1,"comment" : "SumOp: for a list\/collection","filters" : [["IsListOrCollection"]]}],"2args" : [{"rank" : 6,"comment" : "SumOp: for a list, and initial value","filters" : [["IsList"],["IsAdditiveElement"]]},{"rank" : 5,"comment" : "SumOp: for a dense list, and a function","filters" : [["IsDenseList"],["IsFunction"]]},{"rank" : 4,"comment" : "SumOp: for a list\/collection, and init. value","filters" : [["IsListOrCollection"],["IsAdditiveElement"]]},{"rank" : 2,"comment" : "SumOp: for a list\/collection, and a function","filters" : [["IsListOrCollection"],["IsFunction"]]}],"3args" : [{"rank" : 7,"comment" : "SumOp: for a list, a function, and initial value","filters" : [["IsList"],["IsFunction"],["IsAdditiveElement"]]},{"rank" : 5,"comment" : "SumOp: for a list\/collection, and a function, and an initial value","filters" : [["IsListOrCollection"],["IsFunction"],["IsAdditiveElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProductOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "ProductOp: for a dense list","filters" : [["IsDenseList"]]},{"rank" : 1,"comment" : "ProductOp: for a list\/collection","filters" : [["IsListOrCollection"]]}],"2args" : [{"rank" : 6,"comment" : "ProductOp: for a list, and initial value","filters" : [["IsList"],["IsMultiplicativeElement"]]},{"rank" : 5,"comment" : "ProductOp: for a dense list and a function","filters" : [["IsDenseList"],["IsFunction"]]},{"rank" : 4,"comment" : "ProductOp: for a list\/collection, and initial value","filters" : [["IsListOrCollection"],["IsMultiplicativeElement"]]},{"rank" : 2,"comment" : "ProductOp: for a list\/collection, and a function","filters" : [["IsListOrCollection"],["IsFunction"]]}],"3args" : [{"rank" : 7,"comment" : "ProductOp: for a list, a function, and initial value","filters" : [["IsList"],["IsFunction"],["IsMultiplicativeElement"]]},{"rank" : 5,"comment" : "ProductOp: for a list\/collection, a function, and an initial value","filters" : [["IsListOrCollection"],["IsFunction"],["IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FilteredOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10004,"comment" : "FilteredOp: for an empty list\/collection, and a function","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsFunction"]]},{"rank" : 10,"comment" : "FilteredOp: for degenerated residue class unions of Z^2 (ResClasses)","filters" : [["IsFinite","Tester(IsFinite)","IsResidueClassUnionOfZxZ"],["IsFunction"]]},{"rank" : 4,"comment" : "FilteredOp: for a dense list, and a function","filters" : [["IsDenseList"],["IsFunction"]]},{"rank" : 3,"comment" : "FilteredOp: for a list, and a function","filters" : [["IsList"],["IsFunction"]]},{"rank" : 2,"comment" : "FilteredOp: for a list\/collection, and a function","filters" : [["IsListOrCollection"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumberOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "NumberOp: for a dense list","filters" : [["IsDenseList"]]},{"rank" : 2,"comment" : "NumberOp: for a list","filters" : [["IsList"]]},{"rank" : 1,"comment" : "NumberOp: for a list\/collection","filters" : [["IsListOrCollection"]]}],"2args" : [{"rank" : 4,"comment" : "NumberOp: for a dense list, and a function","filters" : [["IsDenseList"],["IsFunction"]]},{"rank" : 3,"comment" : "NumberOp: for a list, and a function","filters" : [["IsList"],["IsFunction"]]},{"rank" : 2,"comment" : "NumberOp: for a list\/collection, and a function","filters" : [["IsListOrCollection"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ForAllOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10004,"comment" : "ForAllOp: for an empty list\/collection, and a function","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsFunction"]]},{"rank" : 10,"comment" : "ForAllOp: for degenerated residue class unions of Z^2 (ResClasses)","filters" : [["IsFinite","Tester(IsFinite)","IsResidueClassUnionOfZxZ"],["IsFunction"]]},{"rank" : 8,"comment" : "ForAllOp: for a dense list, and a function","filters" : [["IsDenseList","IsFinite","Tester(IsFinite)"],["IsFunction"]]},{"rank" : 8,"comment" : "ForAllOp: for a list, and a function","filters" : [["IsList","IsFinite","Tester(IsFinite)"],["IsFunction"]]},{"rank" : 2,"comment" : "ForAllOp: for a list\/collection, and a function","filters" : [["IsListOrCollection"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ForAnyOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10004,"comment" : "ForAnyOp: for an empty list\/collection, and a function","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsFunction"]]},{"rank" : 10,"comment" : "ForAnyOp: for degenerated residue class unions of Z^2 (ResClasses)","filters" : [["IsFinite","Tester(IsFinite)","IsResidueClassUnionOfZxZ"],["IsFunction"]]},{"rank" : 8,"comment" : "ForAnyOp: for a dense list, and a function","filters" : [["IsDenseList","IsFinite","Tester(IsFinite)"],["IsFunction"]]},{"rank" : 8,"comment" : "ForAnyOp: for a list, and a function","filters" : [["IsList","IsFinite","Tester(IsFinite)"],["IsFunction"]]},{"rank" : 2,"comment" : "ForAnyOp: for a list\/collection, and a function","filters" : [["IsListOrCollection"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubset","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10120,"comment" : "IsSubset: permgrp of natsymmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 10092,"comment" : "IsSubset: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 10011,"comment" : "IsSubset: test whether domain is parent of the other","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection","IsGeneralizedDomain","Tester(ParentAttr)"]]},{"rank" : 10008,"comment" : "IsSubset: for two collections with known sizes, check sizes","filters" : [["IsCollection","Tester(Size)"],["IsCollection","Tester(Size)"]]},{"rank" : 10008,"comment" : "IsSubset: for two collections, the first containing the whole family","filters" : [["IsCollection","IsWholeFamily","Tester(IsWholeFamily)"],["IsCollection"]]},{"rank" : 10005,"comment" : "IsSubset: for two collections, check for identity","filters" : [["IsCollection"],["IsCollection"]]},{"rank" : 736,"comment" : "IsSubset: handled by nice monomorphism: attribute CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 475,"comment" : "IsSubset: field, 8bit-vector","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)","Is8BitVectorRep"]]},{"rank" : 472,"comment" : "IsSubset: field, 8bit-vector","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)","IsGF2VectorRep"]]},{"rank" : 129,"comment" : "IsSubset: polynomial rings","filters" : [["IsPolynomialRing"],["IsCollection"]]},{"rank" : 112,"comment" : "IsSubset: for two finite fields in the same family","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 109,"comment" : "IsSubset: for Integers and Rationals (ResClasses)","filters" : [["IsIntegers"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 102,"comment" : "IsSubset: for Z_pi and Rationals (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 102,"comment" : "IsSubset: for Rationals and Z_(pi) (ResClasses)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 100,"comment" : "IsSubset","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 100,"comment" : "IsSubset","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 100,"comment" : "IsSubset: for subgroups of free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 100,"comment" : "IsSubset: for two division rings","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 82,"comment" : "IsSubset: for certain cyclotomic semirings","filters" : [["CategoryCollections(IsCyclotomic)","IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsCyclotomic)","IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 80,"comment" : "IsSubset: 2-sided ideal in ring, naive","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 74,"comment" : "IsSubset: for two FLMLORs-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 73,"comment" : "IsSubset: for Z_(pi) and Integers (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsIntegers"]]},{"rank" : 72,"comment" : "IsSubset: subgroups of fp group by quot. rep","filters" : [["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 71,"comment" : "IsSubset: subgroups of fp group: test generators","filters" : [["IsSubgroupFpGroup"],["Tester(GeneratorsOfMagmaWithInverses)","IsSubgroupFpGroup"]]},{"rank" : 70,"comment" : "IsSubset: subgp fp group: via quotient rep","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 68,"comment" : "IsSubset: pcgs computable groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FamilyPcgs)","CanEasilyComputePcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 68,"comment" : "IsSubset: for two FLMLORs","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 66,"comment" : "IsSubset: for Z_(pi)'s (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 66,"comment" : "IsSubset: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 56,"comment" : "IsSubset: for two rings-with-one","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRingWithOne)"]]},{"rank" : 53,"comment" : "IsSubset: for two rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 46,"comment" : "IsSubset: for two free left modules","filters" : [["IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 34,"comment" : "IsSubset: for two magmas with inverses","filters" : [["IsMagmaWithInverses"],["IsMagmaWithInverses"]]},{"rank" : 32,"comment" : "IsSubset: for two additive magmas with inverses","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 28,"comment" : "IsSubset: for two additive magmas with zero","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 28,"comment" : "IsSubset: for two magmas with one","filters" : [["IsMagmaWithOne"],["IsMagmaWithOne"]]},{"rank" : 24,"comment" : "IsSubset: for two additive magmas","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 22,"comment" : "IsSubset: for two magmas","filters" : [["IsMagma"],["IsMagma"]]},{"rank" : 22,"comment" : "IsSubset: for two collections that are internal lists","filters" : [["IsList","IsInternalRep","IsCollection"],["IsList","IsInternalRep","IsCollection"]]},{"rank" : 22,"comment" : "IsSubset: for two internal lists","filters" : [["IsList","IsInternalRep"],["IsList","IsInternalRep"]]},{"rank" : 19,"comment" : "IsSubset: for collection and empty list","filters" : [["IsCollection"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 19,"comment" : "IsSubset: for empty list and collection","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsCollection"]]},{"rank" : 18,"comment" : "IsSubset: for two residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 12,"comment" : "IsSubset: for two unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 11,"comment" : "IsSubset: for a residue class union and the base ring (ResClasses)","filters" : [["IsResidueClassUnion"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 11,"comment" : "IsSubset: for the base ring and a residue class union (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsResidueClassUnion"]]},{"rank" : 8,"comment" : "IsSubset: for residue class union and element list (ResClasses)","filters" : [["IsResidueClassUnion"],["IsList"]]},{"rank" : 6,"comment" : "IsSubset: for two collections with known `AsSSortedList'","filters" : [["IsCollection","Tester(AsSSortedList)"],["IsCollection","Tester(AsSSortedList)"]]},{"rank" : 4,"comment" : "IsSubset: for two collections (loop over the elements of the second)","filters" : [["IsCollection"],["IsCollection"]]},{"rank" : 4,"comment" : "IsSubset: for two collections in different families","filters" : [["IsCollection"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Intersection2","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10009,"comment" : "Intersection2: domain and whole family","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection","IsWholeFamily","Tester(IsWholeFamily)"]]},{"rank" : 10009,"comment" : "Intersection2: whole family and domain","filters" : [["IsCollection","IsWholeFamily","Tester(IsWholeFamily)"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 10002,"comment" : "Intersection2: for two times the same ring (ResClasses)","filters" : [["IsListOrCollection"],["IsListOrCollection"]]},{"rank" : 838,"comment" : "Intersection2: for two fields of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 736,"comment" : "Intersection2: handled by nice monomorphism:group CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 134,"comment" : "Intersection2: for two cyclotomic fields of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"],["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 132,"comment" : "Intersection2: for abelian number field and cyclotomic field","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 132,"comment" : "Intersection2: for cyclotomic field and abelian number field","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 130,"comment" : "Intersection2: for two abelian number fields","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 124,"comment" : "Intersection2","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 124,"comment" : "Intersection2","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 124,"comment" : "Intersection2","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 124,"comment" : "Intersection2","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 120,"comment" : "Intersection2","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 120,"comment" : "Intersection2","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 120,"comment" : "Intersection2","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 120,"comment" : "Intersection2","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 116,"comment" : "Intersection2: perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 106,"comment" : "Intersection2: two AffineCrystGroupsOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "Intersection2: two AffineCrystGroupsOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 102,"comment" : "Intersection2: for Z_(pi) and Rationals (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 102,"comment" : "Intersection2: for Rationals and Z_(pi) (ResClasses)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 100,"comment" : "Intersection2: for subgroups of free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 96,"comment" : "Intersection2: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 82,"comment" : "Intersection2: for certain cyclotomic semirings","filters" : [["CategoryCollections(IsCyclotomic)","IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsCyclotomic)","IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 74,"comment" : "Intersection2: generic method for two FLMLORs-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 72,"comment" : "Intersection2: subgroups of fp group by quotient","filters" : [["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 70,"comment" : "Intersection2: subgroups of fp group","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 70,"comment" : "Intersection2: for two spaces in a common s.c. algebra","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","CategoryCollections(IsSCAlgebraObj)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","CategoryCollections(IsSCAlgebraObj)"]]},{"rank" : 68,"comment" : "Intersection2: groups with pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 68,"comment" : "Intersection2: generic method for two FLMLORs","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 66,"comment" : "Intersection2: for Z_(pi)'s (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsZ_pi","Tester(IsZ_pi)"]]},{"rank" : 66,"comment" : "Intersection2: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 60,"comment" : "Intersection2: for two Gaussian row spaces","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]},{"rank" : 50,"comment" : "Intersection2: method for two vector spaces","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 28,"comment" : "Intersection2: for Fitting sets","filters" : [["IsFittingSetRep"],["IsFittingSetRep"]]},{"rank" : 26,"comment" : "Intersection2: for Fitting class and Fitting set","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"],["IsFittingSetRep"]]},{"rank" : 26,"comment" : "Intersection2: for Fitting set and Fitting class","filters" : [["IsFittingSetRep"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 24,"comment" : "Intersection2: for two additive cosets","filters" : [["IsAdditiveCoset"],["IsAdditiveCoset"]]},{"rank" : 18,"comment" : "Intersection2: for the empty set and a set (ResClasses)","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsListOrCollection"]]},{"rank" : 18,"comment" : "Intersection2: for a set and the empty set (ResClasses)","filters" : [["IsListOrCollection"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 18,"comment" : "Intersection2: for two residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 12,"comment" : "Intersection2: for two unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 11,"comment" : "Intersection2: for the base ring and a residue class union (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsResidueClassUnion"]]},{"rank" : 11,"comment" : "Intersection2: for a residue class union and the base ring (ResClasses)","filters" : [["IsResidueClassUnion"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 11,"comment" : "Intersection2: for a residue class union and a finite set (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsList"]]},{"rank" : 10,"comment" : "Intersection2: for two group classes by list","filters" : [["IsGroupClassByListRep"],["IsGroupClassByListRep"]]},{"rank" : 10,"comment" : "Intersection2: of two class intersections","filters" : [["IsClassByIntersectionRep"],["IsClassByIntersectionRep"]]},{"rank" : 10,"comment" : "Intersection2: for two collections in the same family, both lists","filters" : [["IsList","IsCollection"],["IsList","IsCollection"]]},{"rank" : 9,"comment" : "Intersection2: for grp class and group class by list","filters" : [["IsGroupClass","Tester(IsGroupClass)"],["IsGroupClassByListRep"]]},{"rank" : 9,"comment" : "Intersection2: for group class by list and group class","filters" : [["IsGroupClassByListRep"],["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 9,"comment" : "Intersection2: of class and small list","filters" : [["IsClass"],["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 8,"comment" : "Intersection2: for a finite set and a residue class union (ResClasses)","filters" : [["IsList"],["IsResidueClassUnion"]]},{"rank" : 8,"comment" : "Intersection2: of class and small list\/coll","filters" : [["IsClass"],["IsListOrCollection","IsFinite","Tester(IsFinite)","Tester(Size)"]]},{"rank" : 8,"comment" : "Intersection2: of small list and class\/list\/coll","filters" : [["IsList","IsFinite","Tester(IsFinite)"],["IsListOrCollection"]]},{"rank" : 8,"comment" : "Intersection2: of small list\/coll and class","filters" : [["IsListOrCollection","IsFinite","Tester(IsFinite)","Tester(Size)"],["IsClass"]]},{"rank" : 7,"comment" : "Intersection2: for two collections in the same family, the first being a list","filters" : [["IsList","IsCollection"],["IsCollection"]]},{"rank" : 7,"comment" : "Intersection2: for two collections in the same family, the second being a list","filters" : [["IsCollection"],["IsList","IsCollection"]]},{"rank" : 6,"comment" : "Intersection2: of class intersection and class\/list\/coll","filters" : [["IsClassByIntersectionRep"],["IsListOrCollection"]]},{"rank" : 6,"comment" : "Intersection2: of class\/list\/coll and class intersection","filters" : [["IsListOrCollection"],["IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "Intersection2: of two classes","filters" : [["IsClass"],["IsClass"]]},{"rank" : 4,"comment" : "Intersection2: for two collections in the same family","filters" : [["IsCollection"],["IsCollection"]]},{"rank" : 4,"comment" : "Intersection2: for two collections in different families","filters" : [["IsCollection"],["IsCollection"]]},{"rank" : 4,"comment" : "Intersection2: for two lists (not necessarily in the same family)","filters" : [["IsList"],["IsList"]]},{"rank" : 3,"comment" : "Intersection2: of list\/collection and class","filters" : [["IsListOrCollection"],["IsClass"]]},{"rank" : 2,"comment" : "Intersection2: of list\/collection and list\/collection","filters" : [["IsListOrCollection"],["IsListOrCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Union2","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 54,"comment" : "Union2: for two times the same row module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 52,"comment" : "Union2: for two times the same ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 18,"comment" : "Union2: for two residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 12,"comment" : "Union2: for two unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 11,"comment" : "Union2: for the base ring and a residue class union (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsResidueClassUnion"]]},{"rank" : 11,"comment" : "Union2: for a residue class union and the base ring (ResClasses)","filters" : [["IsResidueClassUnion"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 11,"comment" : "Union2: for a residue class union and a finite set (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsList"]]},{"rank" : 10,"comment" : "Union2: for two class unions","filters" : [["IsClassByUnionRep"],["IsClassByUnionRep"]]},{"rank" : 10,"comment" : "Union2: for two collections that are lists","filters" : [["IsList","IsCollection"],["IsList","IsCollection"]]},{"rank" : 8,"comment" : "Union2: for a finite set and a residue class union (ResClasses)","filters" : [["IsList"],["IsResidueClassUnion"]]},{"rank" : 7,"comment" : "Union2: for the base ring and a finite set (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsList"]]},{"rank" : 7,"comment" : "Union2: for a finite set and the base ring (ResClasses)","filters" : [["IsList"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 7,"comment" : "Union2: for two collections, the first being a list","filters" : [["IsList","IsCollection"],["IsCollection"]]},{"rank" : 7,"comment" : "Union2: for two collections, the second being a list","filters" : [["IsCollection"],["IsList","IsCollection"]]},{"rank" : 6,"comment" : "Union2: for class union and class\/list\/collection","filters" : [["IsClassByUnionRep"],["IsListOrCollection"]]},{"rank" : 6,"comment" : "Union2: for class\/list\/collection and class union","filters" : [["IsListOrCollection"],["IsClassByUnionRep"]]},{"rank" : 4,"comment" : "Union2: for two collections","filters" : [["IsCollection"],["IsCollection"]]},{"rank" : 4,"comment" : "Union2: for two lists","filters" : [["IsList"],["IsList"]]},{"rank" : 2,"comment" : "Union2: for two classes\/lists\/collections","filters" : [["IsListOrCollection"],["IsListOrCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Difference","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10022,"comment" : "Difference: for a domain and the empty set (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 10010,"comment" : "Difference: for two times the same ring (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 111,"comment" : "Difference: for a residue class union and a finite set (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsList"]]},{"rank" : 29,"comment" : "Difference: for Z^2 and a finite set (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsList"]]},{"rank" : 28,"comment" : "Difference: for a ring and a finite set (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]},{"rank" : 19,"comment" : "Difference: for collection, and empty list","filters" : [["IsCollection"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 18,"comment" : "Difference: for two residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"],["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 18,"comment" : "Difference: for empty list, and collection","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsListOrCollection"]]},{"rank" : 12,"comment" : "Difference: for two unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 11,"comment" : "Difference: for a residue class union and the base ring (ResClasses)","filters" : [["IsResidueClassUnion"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 11,"comment" : "Difference: for the base ring and a residue class union (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],["IsResidueClassUnion"]]},{"rank" : 10,"comment" : "Difference: for two collections that are lists","filters" : [["IsList","IsCollection"],["IsList","IsCollection"]]},{"rank" : 9,"comment" : "Difference: for group class by list and group class","filters" : [["IsGroupClassByListRep"],["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 8,"comment" : "Difference: for a finite set and a residue class union (ResClasses)","filters" : [["IsList"],["IsResidueClassUnion"]]},{"rank" : 7,"comment" : "Difference: for two collections, the second being a list","filters" : [["IsCollection"],["IsList","IsCollection"]]},{"rank" : 7,"comment" : "Difference: for two collections, the first being a list","filters" : [["IsList","IsCollection"],["IsCollection"]]},{"rank" : 4,"comment" : "Difference: for two collections","filters" : [["IsCollection"],["IsCollection"]]},{"rank" : 4,"comment" : "Difference: for two lists (assume one can produce a sorted result)","filters" : [["IsList"],["IsList"]]},{"rank" : 2,"comment" : "Difference: for two classes\/lists\/collections","filters" : [["IsListOrCollection"],["IsListOrCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanEasilyCompareElements","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "CanEasilyCompareElements: system getter","filters" : [["IsAttributeStoringRep","Tester(CanEasilyCompareElements)"]]},{"rank" : 17,"comment" : "CanEasilyCompareElements: empty homogeneous list","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "CanEasilyCompareElements: for direct product element","filters" : [["IsDirectProductElement"]]},{"rank" : 4,"comment" : "CanEasilyCompareElements: homogeneous list","filters" : [["IsHomogeneousList"]]},{"rank" : 1,"comment" : "CanEasilyCompareElements: family: default false","filters" : [["IsFamily"]]},{"rank" : 0,"comment" : "CanEasilyCompareElements: generic: inherit `true' from family","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanEasilyCompareElements)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanEasilyCompareElements): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 1,"comment" : "Setter(CanEasilyCompareElements): family setter","filters" : [["IsFamily"],[]]},{"rank" : 0,"comment" : "Setter(CanEasilyCompareElements): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanEasilyCompareElements)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanEasilySortElements","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "CanEasilySortElements: system getter","filters" : [["IsAttributeStoringRep","Tester(CanEasilySortElements)"]]},{"rank" : 17,"comment" : "CanEasilySortElements: empty homogeneous list","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 4,"comment" : "CanEasilySortElements: homogeneous list","filters" : [["IsHomogeneousList"]]},{"rank" : 1,"comment" : "CanEasilySortElements: family: default false","filters" : [["IsFamily"]]},{"rank" : 0,"comment" : "CanEasilySortElements: generic: inherit `true' from family","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanEasilySortElements)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanEasilySortElements): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 1,"comment" : "Setter(CanEasilySortElements): family setter","filters" : [["IsFamily"],[]]},{"rank" : 0,"comment" : "Setter(CanEasilySortElements): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanEasilySortElements)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanComputeIsSubset","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 106,"comment" : "CanComputeIsSubset","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "CanComputeIsSubset","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 73,"comment" : "CanComputeIsSubset: whole fp family group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 40,"comment" : "CanComputeIsSubset: if membership test works","filters" : [["IsCollection","IsGeneralizedDomain","CanEasilyTestMembership"],["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 10,"comment" : "CanComputeIsSubset: default for domains: no unless identical","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 0,"comment" : "CanComputeIsSubset: default: no, unless identical","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Randomizer","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CheapRandomizer","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RandomizerAttr","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "RandomizerAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(RandomizerAttr)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RandomizerAttr)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RandomizerAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RandomizerAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RandomizerAttr)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CheapRandomizerAttr","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "CheapRandomizerAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(CheapRandomizerAttr)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CheapRandomizerAttr)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CheapRandomizerAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CheapRandomizerAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CheapRandomizerAttr)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSmallList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsSmallList: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSmallList)"]]},{"rank" : 10,"comment" : "IsSmallList","filters" : [["IsAttributeStoringRep","IsBasis","Tester(UnderlyingLeftModule)"]]},{"rank" : 10,"comment" : "IsSmallList","filters" : [["IsAttributeStoringRep","IsBasis","Tester(BasisVectors)"]]},{"rank" : 2,"comment" : "IsSmallList: for a list","filters" : [["IsList"]]},{"rank" : 0,"comment" : "IsSmallList: for a non-list","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSmallList)","type" : "GAP_Operation","filters" : [[["IsList"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSmallList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSmallList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSmallList)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Length","type" : "GAP_Operation","filters" : [[["IsList"]],[["IsAssociativeElement","IsWord"]],[["IsRowVectorObj"]],[["IsMatrixObj"]],[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "Length: system getter","filters" : [["Tester(LENGTH)","IsAttributeStoringRep"]]},{"rank" : 134,"comment" : "Length: for a matrix with memory","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsObjWithMemory"]]},{"rank" : 109,"comment" : "Length: for a straight line program word","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"]]},{"rank" : 108,"comment" : "Length: for a word with memory","filters" : [["IsWord","IsObjWithMemory"]]},{"rank" : 44,"comment" : "Length: for GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"]]},{"rank" : 34,"comment" : "Length: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 33,"comment" : "Length: for Lie matrix in default representation","filters" : [["IsPackedElementDefaultRep","IsLieMatrix"]]},{"rank" : 31,"comment" : "Length: for class function","filters" : [["IsClassFunction"]]},{"rank" : 31,"comment" : "Length: for null map matrix","filters" : [["IsNullMapMatrix"]]},{"rank" : 28,"comment" : "Length: For a compressed MatFFE","filters" : [["IsList","Is8BitMatrixRep"]]},{"rank" : 28,"comment" : "Length: for an empty row vector","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 24,"comment" : "Length: pcgs","filters" : [["IsPcgs","IsPcgsDefaultRep"]]},{"rank" : 24,"comment" : "Length: For a compressed VecFFE","filters" : [["IsList","Is8BitVectorRep"]]},{"rank" : 21,"comment" : "Length: for GF2 vector","filters" : [["IsList","IsGF2VectorRep"]]},{"rank" : 20,"comment" : "Length: modulo pcgs","filters" : [["IsModuloPcgs"]]},{"rank" : 17,"comment" : "Length: for a direct product element in default representation","filters" : [["IsDefaultDirectProductElementRep"]]},{"rank" : 15,"comment" : "Length: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 13,"comment" : "Length: LAGUNA: for an element of a magma ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]},{"rank" : 11,"comment" : "Length: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 10,"comment" : "Length: for a right transversal in cosets representation","filters" : [["IsList","IsRightTransversalViaCosetsRep"]]},{"rank" : 10,"comment" : "Length: for a right transversal in cosets representation","filters" : [["IsList","IsRightTransversalViaCosetsRep"]]},{"rank" : 10,"comment" : "Length: method for a weak pointer object","filters" : [["IsWeakPointerObject"]]},{"rank" : 9,"comment" : "Length: for degenerated residue class unions of Z^2 (ResClasses)","filters" : [["IsFinite","Tester(IsFinite)","IsResidueClassUnionOfZxZ"]]},{"rank" : 9,"comment" : "Length: for an element of an f.p. group (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpGroup"]]},{"rank" : 9,"comment" : "Length: for right transversal","filters" : [["IsList","IsRightTransversalRep"]]},{"rank" : 8,"comment" : "Length: for a 32 bits assoc. word","filters" : [["Is32BitsAssocWord"]]},{"rank" : 8,"comment" : "Length: for a 16 bits assoc. word","filters" : [["Is16BitsAssocWord"]]},{"rank" : 8,"comment" : "Length: for an 8 bits assoc. word","filters" : [["Is8BitsAssocWord"]]},{"rank" : 7,"comment" : "Length","filters" : [["IsUnicodeString"]]},{"rank" : 7,"comment" : "Length: for a basis","filters" : [["IsBasis"]]},{"rank" : 7,"comment" : "Length: for an enumerator that perhaps has its own `Length' function","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"]]},{"rank" : 6,"comment" : "Length: assoc word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]},{"rank" : 6,"comment" : "Length: for an assoc. word in syllable rep","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]]},{"rank" : 5,"comment" : "Length: enum-by-niceomorphism","filters" : [["IsList","IsEnumeratorByNiceomorphismRep"]]},{"rank" : 5,"comment" : "Length: enum-by-pcgs","filters" : [["IsList","IsEnumeratorByPcgsRep"]]},{"rank" : 5,"comment" : "Length: for a nonassoc. word","filters" : [["IsNonassocWord"]]},{"rank" : 4,"comment" : "Length: for an infinite list of generators","filters" : [["IsList","IsInfiniteListOfGeneratorsRep"]]},{"rank" : 4,"comment" : "Length: for an infinite list of names","filters" : [["IsList","IsInfiniteListOfNamesRep"]]},{"rank" : 1,"comment" : "Length","filters" : [["IsPcp"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LENGTH)","type" : "GAP_Operation","filters" : [[["IsList"],[]],[["IsAssociativeElement","IsWord"],[]],[["IsRowVectorObj"],[]],[["IsMatrixObj"],[]],[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LENGTH): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LENGTH): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LENGTH)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBound[]","type" : "GAP_Operation","filters" : [[["IsList"],[]],[["IsRowListMatrix"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "IsBound[]: for Lie matrix in default representation, and integer","filters" : [["IsPackedElementDefaultRep","IsLieMatrix"],["IsInt","IsPosRat"]]},{"rank" : 50,"comment" : "IsBound[]: for class function and positive integer","filters" : [["IsClassFunction"],["IsInt","IsPosRat"]]},{"rank" : 47,"comment" : "IsBound[]: for an empty row vector, and a positive integer","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "IsBound[]: pcgs","filters" : [["IsPcgs"],["IsInt","IsPosRat"]]},{"rank" : 39,"comment" : "IsBound[]","filters" : [["IsModuloPcgs"],["IsInt","IsPosRat"]]},{"rank" : 34,"comment" : "IsBound[]: for a plist matrix, and a position","filters" : [["IsPlistMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "IsBound[]: method for a weak pointer object","filters" : [["IsWeakPointerObject"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "IsBound[]: for an enumerator that perhaps has its own `IsBound' function","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"],["IsInt","IsPosRat"]]},{"rank" : 22,"comment" : "IsBound[]: for a dense list and positive integer","filters" : [["IsDenseList"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "[]","type" : "GAP_Operation","filters" : [[["IsList"],[]],[["IsRowVectorObj"],["IsInt","IsPosRat"]],[["IsMatrixObj"],["IsInt","IsPosRat"]],[["IsReesMatrixSemigroupElement"],["IsInt","IsPosRat"]],[["IsReesZeroMatrixSemigroupElement"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 153,"comment" : "[]: for a matrix with memory","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsObjWithMemory"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "[]: for GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "[]: for an ordinary block matrix and a positive integer","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 52,"comment" : "[]: for Lie matrix in default representation, and positive integer","filters" : [["IsPackedElementDefaultRep","IsLieMatrix"],["IsInt","IsPosRat"]]},{"rank" : 50,"comment" : "[]: for class function and positive integer","filters" : [["IsClassFunction"],["IsInt","IsPosRat"]]},{"rank" : 47,"comment" : "[]: For a compressed MatFFE","filters" : [["IsList","Is8BitMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 43,"comment" : "[]: pcgs, pos int","filters" : [["IsPcgs","IsPcgsDefaultRep"],["IsInt","IsPosRat"]]},{"rank" : 43,"comment" : "[]: For a compressed VecFFE","filters" : [["IsList","Is8BitVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "[]: for GF2 vector","filters" : [["IsList","IsGF2VectorRep"],["IsInt","IsPosRat"]]},{"rank" : 39,"comment" : "[]: modulo pcgs","filters" : [["IsModuloPcgs"],["IsInt","IsPosRat"]]},{"rank" : 36,"comment" : "[]: for a direct product element in default repres., and a pos. integer","filters" : [["IsDefaultDirectProductElementRep"],["IsInt","IsPosRat"]]},{"rank" : 34,"comment" : "[]: for a plist matrix and a positive integer","filters" : [["IsPlistMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 30,"comment" : "[]: for classes of subgroups","filters" : [["IsConjugacyClassSubgroupsRep"],["IsInt","IsPosRat"]]},{"rank" : 30,"comment" : "[]: for a plist vector and a positive integer","filters" : [["IsPlistVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "[]: right transversal fp group","filters" : [["IsList","IsRightTransversalFpGroupRep"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "[]: for Pc transversals","filters" : [["IsList","IsRightTransversalPcGroupRep"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "[]: for right transversal of perm. group, and pos. integer","filters" : [["IsList","IsRightTransversalPermGroupRep"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "[]: factored transversal","filters" : [["IsList","IsFactoredTransversalRep"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "[]: rt via coset","filters" : [["IsList","IsRightTransversalViaCosetsRep"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "[]: method for a weak pointer object","filters" : [["IsWeakPointerObject"],["IsInt","IsPosRat"]]},{"rank" : 28,"comment" : "[]: for degenerated residue class unions of Z^2 (ResClasses)","filters" : [["IsFinite","Tester(IsFinite)","IsResidueClassUnionOfZxZ"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "[]","filters" : [["IsUnicodeString"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "[]: for a basis and a positive integer","filters" : [["IsBasis"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "[]: for enumerator by functions","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"],["IsInt","IsPosRat"]]},{"rank" : 24,"comment" : "[]: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"],["IsInt","IsPosRat"]]},{"rank" : 24,"comment" : "[]: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"],["IsInt","IsPosRat"]]},{"rank" : 24,"comment" : "[]: enum-by-niceo","filters" : [["IsList","IsEnumeratorByNiceomorphismRep"],["IsInt","IsPosRat"]]},{"rank" : 24,"comment" : "[]: enum-by-pcgs","filters" : [["IsList","IsEnumeratorByPcgsRep"],["IsInt","IsPosRat"]]},{"rank" : 23,"comment" : "[]: for an infinite list of generators","filters" : [["IsList","IsInfiniteListOfGeneratorsRep"],["IsInt","IsPosRat"]]},{"rank" : 23,"comment" : "[]: for an infinite list of names","filters" : [["IsList","IsInfiniteListOfNamesRep"],["IsInt","IsPosRat"]]},{"rank" : 20,"comment" : "[]","filters" : [["IsPcp"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "{}","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]],[["IsRowVectorObj"],["IsList"]],[["IsRowListMatrix"],["IsList"]],[["IsFlatMatrix"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "{}: For an 8 bit vector and a range","filters" : [["IsList","Is8BitVectorRep"],["IsRange","IsInternalRep"]]},{"rank" : 45,"comment" : "{}: For an 8 bit vector and a plain list","filters" : [["IsList","Is8BitVectorRep"],["IsDenseList","IsPlistRep"]]},{"rank" : 40,"comment" : "{}: for GF2 vector","filters" : [["IsList","IsGF2VectorRep"],["IsList","IsDenseList","IsInternalRep"]]},{"rank" : 24,"comment" : "{}: pcgs, range","filters" : [["IsPcgs"],["IsDenseList"]]},{"rank" : 18,"comment" : "{}: for a small list and a small dense list","filters" : [["IsList","IsSmallList","Tester(IsSmallList)"],["IsDenseList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 17,"comment" : "{}: for a plist matrix and a list","filters" : [["IsPlistMatrixRep"],["IsList"]]},{"rank" : 13,"comment" : "{}: for a plist vector and a list","filters" : [["IsPlistVectorRep"],["IsList"]]},{"rank" : 9,"comment" : "{}","filters" : [["IsUnicodeString"],["IsList"]]},{"rank" : 5,"comment" : "{}: for a list and a dense list","filters" : [["IsList"],["IsDenseList"]]},{"rank" : 4,"comment" : "{}","filters" : [["IsPcp"],["IsDenseList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Elm0List","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 47,"comment" : "Elm0List: For an 8 bit matrix","filters" : [["IsList","Is8BitMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 43,"comment" : "Elm0List: For an 8 bit vector","filters" : [["IsList","Is8BitVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "Elm0List: for GF2 vector","filters" : [["IsList","IsGF2VectorRep"],["IsInt","IsPosRat"]]},{"rank" : 20,"comment" : "Elm0List","filters" : [["IsList"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Unbind[]","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],[]],[["IsRowListMatrix"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 48,"comment" : "Unbind[]: For a compressed MatFFE","filters" : [["IsMutable","IsList","Is8BitMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 45,"comment" : "Unbind[]: for GF2 matrix","filters" : [["IsMutable","IsList","IsGF2MatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 44,"comment" : "Unbind[]: For a compressed VecFFE","filters" : [["IsMutable","IsList","Is8BitVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 44,"comment" : "Unbind[]: for GF2 matrix","filters" : [["IsList","IsGF2MatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "Unbind[]: for GF2 vector","filters" : [["IsList","IsGF2VectorRep"],["IsInt","IsPosRat"]]},{"rank" : 35,"comment" : "Unbind[]: for a plist matrix, and a position","filters" : [["IsMutable","IsPlistMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 31,"comment" : "Unbind[]: method for a weak pointer object","filters" : [["IsMutable","IsWeakPointerObject"],["IsInt","IsPosRat"]]},{"rank" : 28,"comment" : "Unbind[]","filters" : [["IsMutable","IsUnicodeString"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "[]:=","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],[],[]],[["IsRowVectorObj"],["IsInt","IsPosRat"],[]],[["IsRowListMatrix"],["IsInt","IsPosRat"],[]],[["IsFlatMatrix"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 48,"comment" : "[]:=","filters" : [["IsMutable","IsUnicodeString"],["IsInt","IsPosRat"],["IsUnicodeCharacter"]]},{"rank" : 48,"comment" : "[]:=: For a compressed MatFE","filters" : [["IsMutable","IsList","Is8BitMatrixRep"],["IsInt","IsPosRat"],[]]},{"rank" : 47,"comment" : "[]:=: for a checking plist matrix, a positive integer, and a plist vector","filters" : [["IsMutable","IsPlistMatrixRep","IsCheckingMatrix"],["IsInt","IsPosRat"],["IsPlistVectorRep"]]},{"rank" : 46,"comment" : "[]:=: for a plist matrix, a positive integer, and a plist vector","filters" : [["IsMutable","IsPlistMatrixRep"],["IsInt","IsPosRat"],["IsPlistVectorRep"]]},{"rank" : 45,"comment" : "[]:=: for GF2 matrix","filters" : [["IsMutable","IsList","IsGF2MatrixRep"],["IsInt","IsPosRat"],[]]},{"rank" : 44,"comment" : "[]:=: For a compressed VecFFE","filters" : [["IsMutable","IsList","Is8BitVectorRep"],["IsInt","IsPosRat"],[]]},{"rank" : 44,"comment" : "[]:=: for GF2 matrix","filters" : [["IsList","IsGF2MatrixRep"],["IsInt","IsPosRat"],[]]},{"rank" : 42,"comment" : "[]:=: for plain list and external objects","filters" : [["IsMutable","IsList","IsPlistRep"],["IsInt","IsPosRat"],[]]},{"rank" : 40,"comment" : "[]:=: for GF2 vector","filters" : [["IsList","IsGF2VectorRep"],["IsInt","IsPosRat"],[]]},{"rank" : 31,"comment" : "[]:=: for a checking plist vector, a positive integer, and an obj","filters" : [["IsPlistVectorRep","IsCheckingVector"],["IsInt","IsPosRat"],[]]},{"rank" : 31,"comment" : "[]:=: method for a weak pointer object","filters" : [["IsMutable","IsWeakPointerObject"],["IsInt","IsPosRat"],[]]},{"rank" : 30,"comment" : "[]:=: for a plist vector, a positive integer, and an obj","filters" : [["IsPlistVectorRep"],["IsInt","IsPosRat"],[]]},{"rank" : -79,"comment" : "[]:=: error message for immutable list","filters" : [["IsList"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "{}:=","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"],["IsList"]],[["IsRowListMatrix"],["IsList"],["IsRowListMatrix"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 34,"comment" : "{}:=: for a checking plist matrix, a list, and a plist matrix","filters" : [["IsMutable","IsPlistMatrixRep","IsCheckingMatrix"],["IsList"],["IsPlistMatrixRep"]]},{"rank" : 33,"comment" : "{}:=: for a plist matrix, a list, and a plist matrix","filters" : [["IsMutable","IsPlistMatrixRep"],["IsList"],["IsPlistMatrixRep"]]},{"rank" : 29,"comment" : "{}:=: for a small mutable list, a small dense list, and a small list","filters" : [["IsMutable","IsList","IsSmallList","Tester(IsSmallList)"],["IsDenseList","IsSmallList","Tester(IsSmallList)"],["IsList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 9,"comment" : "{}:=: for a mutable list, a dense list, and a list","filters" : [["IsMutable","IsList"],["IsDenseList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConstantTimeAccessList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "ConstantTimeAccessList: system getter","filters" : [["IsAttributeStoringRep","Tester(ConstantTimeAccessList)"]]},{"rank" : 10003,"comment" : "ConstantTimeAccessList: for a constant time access list","filters" : [["IsList","IsConstantTimeAccessList"]]},{"rank" : 9,"comment" : "ConstantTimeAccessList: for a strictly sorted dense list","filters" : [["IsList","IsDenseList","IsSSortedList","Tester(IS_SSORT_LIST)"]]},{"rank" : 8,"comment" : "ConstantTimeAccessList: for a strictly sorted list","filters" : [["IsList","IsSSortedList","Tester(IS_SSORT_LIST)"]]},{"rank" : 3,"comment" : "ConstantTimeAccessList: for a dense list","filters" : [["IsList","IsDenseList"]]},{"rank" : 2,"comment" : "ConstantTimeAccessList: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConstantTimeAccessList)","type" : "GAP_Operation","filters" : [[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConstantTimeAccessList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConstantTimeAccessList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConstantTimeAccessList)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsPlist","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "AsPlist: for a plist","filters" : [["IsList","IsPlistRep"]]},{"rank" : 2,"comment" : "AsPlist: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSortedList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsSortedList: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSortedList)"]]},{"rank" : 7,"comment" : "IsSortedList: for a finite list","filters" : [["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 2,"comment" : "IsSortedList: for a list (not nec. finite)","filters" : [["IsList"]]},{"rank" : 0,"comment" : "IsSortedList: for non-lists","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSortedList)","type" : "GAP_Operation","filters" : [[["IsList"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSortedList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSortedList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSortedList)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSSortedList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsSSortedList: system getter","filters" : [["Tester(IS_SSORT_LIST)","IsAttributeStoringRep"]]},{"rank" : 9,"comment" : "IsSSortedList: for a small homogeneous list","filters" : [["IsHomogeneousList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 4,"comment" : "IsSSortedList: for a homogeneous list (not nec. finite)","filters" : [["IsHomogeneousList"]]},{"rank" : 0,"comment" : "IsSSortedList: for non-lists","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IS_SSORT_LIST)","type" : "GAP_Operation","filters" : [[["IsList"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "Setter(IS_SSORT_LIST): method for an internal list and a Boolean","filters" : [["IsList","IsInternalRep"],["IsBool"]]},{"rank" : 2,"comment" : "Setter(IS_SSORT_LIST): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IS_SSORT_LIST): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IS_SSORT_LIST)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNSortedList","type" : "GAP_Operation","filters" : [[["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "IsNSortedList: system getter","filters" : [["Tester(IS_NSORT_LIST)","IsAttributeStoringRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IS_NSORT_LIST)","type" : "GAP_Operation","filters" : [[["IsDenseList"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IS_NSORT_LIST): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IS_NSORT_LIST): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IS_NSORT_LIST)","type" : "GAP_Operation","filters" : [[["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsDuplicateFree","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsDuplicateFree: system getter","filters" : [["IsAttributeStoringRep","Tester(IsDuplicateFree)"]]},{"rank" : 2,"comment" : "IsDuplicateFree: for a finite list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsDuplicateFree)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsDuplicateFree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsDuplicateFree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsDuplicateFree)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPositionsList","type" : "GAP_Operation","filters" : [[["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "IsPositionsList: system getter","filters" : [["Tester(IS_POSS_LIST)","IsAttributeStoringRep"]]},{"rank" : 9,"comment" : "IsPositionsList: for a small homogeneous list","filters" : [["IsHomogeneousList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 4,"comment" : "IsPositionsList: for a homogeneous list","filters" : [["IsHomogeneousList"]]},{"rank" : 0,"comment" : "IsPositionsList: for non-lists","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IS_POSS_LIST)","type" : "GAP_Operation","filters" : [[["IsDenseList"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IS_POSS_LIST): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IS_POSS_LIST): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IS_POSS_LIST)","type" : "GAP_Operation","filters" : [[["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Position","type" : "GAP_Operation","filters" : [[["IsList"],[]],[["IsList"],[],["IsInt"]],[["IsMatrixObj"],["IsRowVectorObj"]],[["IsMatrixObj"],["IsRowVectorObj"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 27,"comment" : "Position","filters" : [["IsUnicodeString"],["IsUnicodeCharacter"]]},{"rank" : 26,"comment" : "Position: for a plist matrix, and a plist vector","filters" : [["IsPlistMatrixRep"],["IsPlistVectorRep"]]}],"3args" : [{"rank" : 65,"comment" : "Position: for class function, cyclotomic, and nonnegative integer","filters" : [["IsClassFunction"],["IsCyc"],["IsInt"]]},{"rank" : 63,"comment" : "Position: for Lie matrix in default representation, row vector, and integer","filters" : [["IsPackedElementDefaultRep","IsLieMatrix"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsInt"]]},{"rank" : 45,"comment" : "Position","filters" : [["IsUnicodeString"],["IsUnicodeCharacter"],["IsInt"]]},{"rank" : 44,"comment" : "Position: for a plist matrix, and a plist vector","filters" : [["IsPlistMatrixRep"],["IsPlistVectorRep"],["IsInt"]]},{"rank" : 42,"comment" : "Position: pcgs, object, int","filters" : [["IsPcgs","IsPcgsDefaultRep"],[],["IsInt"]]},{"rank" : 38,"comment" : "Position: modulo pcgs","filters" : [["IsModuloPcgs"],[],["IsInt"]]},{"rank" : 37,"comment" : "Position: for enumerator by functions","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"],[],["IsZeroCyc"]]},{"rank" : 36,"comment" : "Position: right transversal fp gp.","filters" : [["IsList","IsRightTransversalFpGroupRep"],["IsMultiplicativeElementWithInverse"],["IsZeroCyc"]]},{"rank" : 33,"comment" : "Position: for a small sorted list, an object, and an integer","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)","IsSmallList","Tester(IsSmallList)"],[],["IsInt"]]},{"rank" : 32,"comment" : "Position: right transversal: Use PositionCanonical","filters" : [["IsList","IsRightTransversalRep"],["IsMultiplicativeElementWithInverse"],["IsInt"]]},{"rank" : 31,"comment" : "Position: enum-by-niceo","filters" : [["IsList","IsEnumeratorByNiceomorphismRep"],["IsMultiplicativeElementWithInverse"],["IsZeroCyc"]]},{"rank" : 31,"comment" : "Position: enum-by-pcgs","filters" : [["IsList","IsEnumeratorByPcgsRep"],["IsMultiplicativeElementWithInverse"],["IsZeroCyc"]]},{"rank" : 27,"comment" : "Position: for a small list, an object, and an integer","filters" : [["IsList","IsSmallList","Tester(IsSmallList)"],[],["IsInt"]]},{"rank" : 26,"comment" : "Position: for a sorted list, an object, and an integer","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)"],[],["IsInt"]]},{"rank" : 25,"comment" : "Position","filters" : [["IsPcp"],["IsPcpElement"],["IsInt"]]},{"rank" : 25,"comment" : "Position: for an infinite list of generators, an object, and zero","filters" : [["IsList","IsInfiniteListOfGeneratorsRep"],[],["IsZeroCyc"]]},{"rank" : 25,"comment" : "Position: for an infinite list of names, an object, and zero","filters" : [["IsList","IsInfiniteListOfNamesRep"],[],["IsZeroCyc"]]},{"rank" : 25,"comment" : "Position: for a basis, an object, and a nonnegative integer","filters" : [["IsBasis"],[],["IsInt"]]},{"rank" : 23,"comment" : "Position: for duplicate free list, object, and positive integer","filters" : [["IsList","IsDuplicateFree","Tester(IsDuplicateFree)"],[],["IsInt","IsPosRat"]]},{"rank" : 22,"comment" : "Position: for a homog. list, an object not in the elements family, and an int.","filters" : [["IsHomogeneousList"],[],["IsInt"]]},{"rank" : 20,"comment" : "Position: for a (small) list, an object, and an integer","filters" : [["IsList"],[],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionsOp","type" : "GAP_Operation","filters" : [[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "PositionsOp","filters" : [["IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionCanonical","type" : "GAP_Operation","filters" : [[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "PositionCanonical: for 8bit matrices lists, fall back on `Position'","filters" : [["IsList","Is8BitMatrixRep"],[]]},{"rank" : 25,"comment" : "PositionCanonical: for internally represented lists, fall back on `Position'","filters" : [["IsList","IsGF2MatrixRep"],[]]},{"rank" : 25,"comment" : "PositionCanonical: internal small sorted lists, use `POSITION_SORTED_LIST'","filters" : [["IsList","IsSSortedList","Tester(IS_SSORT_LIST)","IsInternalRep","IsSmallList","Tester(IsSmallList)"],[]]},{"rank" : 19,"comment" : "PositionCanonical: for internally represented lists, fall back on `Position'","filters" : [["IsList","IsInternalRep"],[]]},{"rank" : 18,"comment" : "PositionCanonical: for right transversal of perm. group, and permutation","filters" : [["IsList","IsRightTransversalPermGroupRep"],["IsPerm"]]},{"rank" : 15,"comment" : "PositionCanonical: right transversal fp gp.","filters" : [["IsList","IsRightTransversalFpGroupRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 15,"comment" : "PositionCanonical: RT","filters" : [["IsList","IsRightTransversalPcGroupRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 15,"comment" : "PositionCanonical: factored transversal","filters" : [["IsList","IsFactoredTransversalRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 15,"comment" : "PositionCanonical: rt via coset","filters" : [["IsList","IsRightTransversalViaCosetsRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 10,"comment" : "PositionCanonical: enum-by-niceo","filters" : [["IsList","IsEnumeratorByNiceomorphismRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 10,"comment" : "PositionCanonical: enum-by-pcgs","filters" : [["IsList","IsEnumeratorByPcgsRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 7,"comment" : "PositionCanonical: for enumerator by functions","filters" : [["IsList","IsDenseList","IsDuplicateFree","Tester(IsDuplicateFree)","IsEnumeratorByFunctionsRep"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionNthOccurrence","type" : "GAP_Operation","filters" : [[["IsList"],[],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 24,"comment" : "PositionNthOccurrence: for boolean list, boolean, integer","filters" : [["IsBlist"],["IsBool"],["IsInt"]]},{"rank" : 20,"comment" : "PositionNthOccurrence: for list, object, integer","filters" : [["IsList"],[],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionSortedOp","type" : "GAP_Operation","filters" : [[["IsList"],[]],[["IsList"],[],["IsFunction"]],[["IsMatrixObj"],["IsRowVectorObj"]],[["IsMatrixObj"],["IsRowVectorObj"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "PositionSortedOp: for a plist matrix, and a plist vector","filters" : [["IsPlistMatrixRep"],["IsPlistVectorRep"]]},{"rank" : 9,"comment" : "PositionSortedOp: for small list, and object","filters" : [["IsList","IsSmallList","Tester(IsSmallList)"],[]]},{"rank" : 2,"comment" : "PositionSortedOp","filters" : [["IsList"],[]]}],"3args" : [{"rank" : 27,"comment" : "PositionSortedOp: for a plist matrix, and a plist vector","filters" : [["IsPlistMatrixRep"],["IsPlistVectorRep"],["IsFunction"]]},{"rank" : 10,"comment" : "PositionSortedOp: for small list, object, and function","filters" : [["IsList","IsSmallList","Tester(IsSmallList)"],[],["IsFunction"]]},{"rank" : 3,"comment" : "PositionSortedOp: for list, object, and function","filters" : [["IsList"],[],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionProperty","type" : "GAP_Operation","filters" : [[["IsList"],["IsFunction"]],[["IsList"],["IsFunction"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 4,"comment" : "PositionProperty: for dense list and function","filters" : [["IsDenseList"],["IsFunction"]]},{"rank" : 3,"comment" : "PositionProperty: for list and function","filters" : [["IsList"],["IsFunction"]]}],"3args" : [{"rank" : 22,"comment" : "PositionProperty: for dense list, function, and integer","filters" : [["IsDenseList"],["IsFunction"],["IsInt"]]},{"rank" : 21,"comment" : "PositionProperty: for list, function, and integer","filters" : [["IsList"],["IsFunction"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionsProperty","type" : "GAP_Operation","filters" : [[["IsDenseList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 4,"comment" : "PositionsProperty: for dense list and function","filters" : [["IsDenseList"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionBound","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "PositionBound: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionSublist","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 14,"comment" : "PositionSublist","filters" : [["IsUnicodeString"],["IsUnicodeString"]]},{"rank" : 4,"comment" : "PositionSublist: for two args in IsStringRep","filters" : [["IsStringRep"],["IsStringRep"]]},{"rank" : 0,"comment" : "PositionSublist: list, sub","filters" : [[],[]]}],"3args" : [{"rank" : 32,"comment" : "PositionSublist","filters" : [["IsUnicodeString"],["IsUnicodeString"],["IsInt"]]},{"rank" : 23,"comment" : "PositionSublist: list,empty,pos","filters" : [["IsList"],["IsEmpty","Tester(IsEmpty)"],["IsInt"]]},{"rank" : 23,"comment" : "PositionSublist: empty list,sub,pos","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsList"],["IsInt"]]},{"rank" : 22,"comment" : "PositionSublist: for two args in IsStringRep and offset","filters" : [["IsStringRep"],["IsStringRep"],["IsInt"]]},{"rank" : 22,"comment" : "PositionSublist: list,sub,pos","filters" : [["IsList"],["IsList"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMatchingSublist","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 0,"comment" : "IsMatchingSublist: list, sub","filters" : [[],[]]}],"3args" : [{"rank" : 23,"comment" : "IsMatchingSublist: list,empty,pos","filters" : [["IsList"],["IsEmpty","Tester(IsEmpty)"],["IsInt"]]},{"rank" : 23,"comment" : "IsMatchingSublist: empty list,sub,pos","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsList"],["IsInt"]]},{"rank" : 22,"comment" : "IsMatchingSublist: list,sub,pos","filters" : [["IsList"],["IsList"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Add","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],[]],[["IsMutable","IsList"],[],["IsInt"]],[["IsRowListMatrix"],["IsRowVectorObj"]],[["IsRowListMatrix"],["IsRowVectorObj"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "Add: for a checking plist matrix and a plist vector","filters" : [["IsMutable","IsPlistMatrixRep","IsCheckingMatrix"],["IsPlistVectorRep"]]},{"rank" : 27,"comment" : "Add: for a plist matrix and a plist vector","filters" : [["IsMutable","IsPlistMatrixRep"],["IsPlistVectorRep"]]},{"rank" : 4,"comment" : "Add: for mutable list and list","filters" : [["IsMutable","IsList"],[]]}],"3args" : [{"rank" : 48,"comment" : "Add: three arguments fast version sorted","filters" : [["IsMutable","IsSSortedList","Tester(IS_SSORT_LIST)","IsPlistRep"],[],["IsInt","IsPosRat"]]},{"rank" : 47,"comment" : "Add: for a checking plist matrix, a plist vector, and a pos","filters" : [["IsMutable","IsPlistMatrixRep","IsCheckingMatrix"],["IsPlistVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 46,"comment" : "Add: for a plist matrix, a plist vector, and a pos. int","filters" : [["IsMutable","IsPlistMatrixRep"],["IsPlistVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 42,"comment" : "Add: three arguments fast version","filters" : [["IsMutable","IsList","IsPlistRep"],[],["IsInt","IsPosRat"]]},{"rank" : 23,"comment" : "Add: three arguments general version","filters" : [["IsMutable","IsList"],[],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Remove","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"]],[["IsMutable","IsList"],["IsInt"]],[["IsRowListMatrix"]],[["IsRowListMatrix"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 16,"comment" : "Remove: for a plist matrix","filters" : [["IsMutable","IsPlistMatrixRep"]]},{"rank" : 4,"comment" : "Remove: one argument","filters" : [["IsMutable","IsList"]]}],"2args" : [{"rank" : 42,"comment" : "Remove: two arguments, fast","filters" : [["IsMutable","IsList","IsPlistRep"],["IsInt","IsPosRat"]]},{"rank" : 35,"comment" : "Remove: for a plist matrix, and a position","filters" : [["IsMutable","IsPlistMatrixRep"],["IsInt","IsPosRat"]]},{"rank" : 23,"comment" : "Remove: two arguments, general","filters" : [["IsMutable","IsList"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Append","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"]],[["IsRowListMatrix"],["IsRowListMatrix"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 49,"comment" : "Append: for 8bitm vectors","filters" : [["IsMutable","IsList","Is8BitVectorRep"],["IsList","Is8BitVectorRep"]]},{"rank" : 43,"comment" : "Append: for GF2 vectors","filters" : [["IsMutable","IsList","IsGF2VectorRep"],["IsList","IsGF2VectorRep"]]},{"rank" : 32,"comment" : "Append: for a checking plist matrix, and a plist matrix","filters" : [["IsMutable","IsPlistMatrixRep","IsCheckingMatrix"],["IsPlistMatrixRep"]]},{"rank" : 32,"comment" : "Append: for mutable list in plist representation, and small list","filters" : [["IsMutable","IsList","IsPlistRep"],["IsList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 31,"comment" : "Append: for two plist matrices","filters" : [["IsMutable","IsPlistMatrixRep"],["IsPlistMatrixRep"]]},{"rank" : 16,"comment" : "Append","filters" : [["IsMutable","IsUnicodeString"],["IsUnicodeString"]]},{"rank" : 6,"comment" : "Append: for mutable list and list","filters" : [["IsMutable","IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Compacted","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Compacted: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Collected","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Collected: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DuplicateFreeList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "DuplicateFreeList: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsDuplicateFreeList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "AsDuplicateFreeList: system getter","filters" : [["IsAttributeStoringRep","Tester(AsDuplicateFreeList)"]]},{"rank" : 2,"comment" : "AsDuplicateFreeList: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsDuplicateFreeList)","type" : "GAP_Operation","filters" : [[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsDuplicateFreeList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsDuplicateFreeList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsDuplicateFreeList)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DifferenceLists","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "DifferenceLists: homogeneous lists","filters" : [["IsHomogeneousList"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Flat","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Flat: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReversedOp","type" : "GAP_Operation","filters" : [[["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "ReversedOp: for a range","filters" : [["IsRange"]]},{"rank" : 6,"comment" : "ReversedOp: for an assoc. word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]},{"rank" : 6,"comment" : "ReversedOp: for an assoc. word in syllable rep","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]]},{"rank" : 3,"comment" : "ReversedOp: for a dense list","filters" : [["IsDenseList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Shuffle","type" : "GAP_Operation","filters" : [[["IsMutable","IsDenseList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "Shuffle","filters" : [["IsMutable","IsDenseList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sort","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"]],[["IsMutable","IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10006,"comment" : "Sort: for a mutable set","filters" : [["IsMutable","IsList","IsSortedList","Tester(IsSortedList)"]]},{"rank" : 11,"comment" : "Sort: for a mutable small list","filters" : [["IsMutable","IsList","IsSmallList","Tester(IsSmallList)"]]},{"rank" : 4,"comment" : "Sort: for a mutable list","filters" : [["IsMutable","IsList"]]},{"rank" : 2,"comment" : "Sort: for an immutable list","filters" : [["IsList"]]}],"2args" : [{"rank" : 12,"comment" : "Sort: for a mutable small list and a function","filters" : [["IsMutable","IsList","IsSmallList","Tester(IsSmallList)"],["IsFunction"]]},{"rank" : 5,"comment" : "Sort: for a mutable list and a function","filters" : [["IsMutable","IsList"],["IsFunction"]]},{"rank" : 3,"comment" : "Sort: for an immutable list and a function","filters" : [["IsList"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SortBy","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 5,"comment" : "SortBy: for a mutable list and a function","filters" : [["IsMutable","IsList"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sortex","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"]],[["IsMutable","IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10007,"comment" : "Sortex: for a mutable sorted list","filters" : [["IsMutable","IsDenseList","IsSortedList","Tester(IsSortedList)"]]},{"rank" : 4,"comment" : "Sortex: for a mutable list","filters" : [["IsMutable","IsList"]]},{"rank" : 2,"comment" : "Sortex: for an immutable list","filters" : [["IsList"]]}],"2args" : [{"rank" : 5,"comment" : "Sortex: for a mutable list and a function","filters" : [["IsMutable","IsList"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SortingPerm","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "SortingPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(SortingPerm)"]]},{"rank" : 10005,"comment" : "SortingPerm: for a dense and sorted list","filters" : [["IsDenseList","IsSortedList","Tester(IsSortedList)"]]},{"rank" : 3,"comment" : "SortingPerm","filters" : [["IsDenseList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SortingPerm)","type" : "GAP_Operation","filters" : [[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SortingPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SortingPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SortingPerm)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SortParallel","type" : "GAP_Operation","filters" : [[["IsMutable","IsDenseList"],["IsMutable","IsDenseList"]],[["IsMutable","IsDenseList"],["IsMutable","IsDenseList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10012,"comment" : "SortParallel: for a mutable set and a dense mutable list","filters" : [["IsMutable","IsDenseList","IsSortedList","Tester(IsSortedList)"],["IsMutable","IsDenseList"]]},{"rank" : 10,"comment" : "SortParallel: for two dense and mutable lists","filters" : [["IsMutable","IsDenseList"],["IsMutable","IsDenseList"]]},{"rank" : 4,"comment" : "SortParallel: for two immutable lists","filters" : [["IsList"],["IsList"]]}],"3args" : [{"rank" : 11,"comment" : "SortParallel: for two dense and mutable lists, and function","filters" : [["IsMutable","IsDenseList"],["IsMutable","IsDenseList"],["IsFunction"]]},{"rank" : 5,"comment" : "SortParallel: for two immutable lists and function","filters" : [["IsList"],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximumList","type" : "GAP_Operation","filters" : [[["IsList"]],[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "MaximumList: for a range","filters" : [["IsRange"]]},{"rank" : 8,"comment" : "MaximumList: for a sorted list","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)"]]},{"rank" : 2,"comment" : "MaximumList: for a list","filters" : [["IsList"]]}],"2args" : [{"rank" : 30,"comment" : "MaximumList: for a range and a seed","filters" : [["IsRange"],[]]},{"rank" : 8,"comment" : "MaximumList: for a sorted list and a seed","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)"],[]]},{"rank" : 2,"comment" : "MaximumList: for a list and a seed","filters" : [["IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimumList","type" : "GAP_Operation","filters" : [[["IsList"]],[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "MinimumList: for a range","filters" : [["IsRange"]]},{"rank" : 8,"comment" : "MinimumList: for a sorted list","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)"]]},{"rank" : 2,"comment" : "MinimumList: for a list","filters" : [["IsList"]]}],"2args" : [{"rank" : 30,"comment" : "MinimumList: for a range and a seed","filters" : [["IsRange"],[]]},{"rank" : 8,"comment" : "MinimumList: for a sorted list and a seed","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)"],[]]},{"rank" : 2,"comment" : "MinimumList: for a list","filters" : [["IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Permuted","type" : "GAP_Operation","filters" : [[["IsList"],["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 39,"comment" : "Permuted: for a class function, and a permutation","filters" : [["IsClassFunction"],["IsPerm"]]},{"rank" : 10,"comment" : "Permuted: for a list and a permutation","filters" : [["IsList"],["IsPerm"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FirstOp","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "FirstOp: for a list or collection and a function","filters" : [["IsListOrCollection"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Iterated","type" : "GAP_Operation","filters" : [[["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 3,"comment" : "Iterated: for a list and a function","filters" : [["IsList"],["IsFunction"]]}],"3args" : [{"rank" : 3,"comment" : "Iterated","filters" : [["IsList"],["IsFunction"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PlainListCopyOp","type" : "GAP_Operation","filters" : [[["IsSmallList","Tester(IsSmallList)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 28,"comment" : "PlainListCopyOp: For an 8 bit vector","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitMatrixRep"]]},{"rank" : 25,"comment" : "PlainListCopyOp: for a GF2 matrix","filters" : [["IsSmallList","Tester(IsSmallList)","IsGF2MatrixRep"]]},{"rank" : 24,"comment" : "PlainListCopyOp: For an 8 bit vector","filters" : [["IsSmallList","Tester(IsSmallList)","Is8BitVectorRep"]]},{"rank" : 21,"comment" : "PlainListCopyOp: for a GF2 vector","filters" : [["IsSmallList","Tester(IsSmallList)","IsGF2VectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionNot","type" : "GAP_Operation","filters" : [[["IsList"],[]],[["IsList"],[],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "PositionNot: for 8-bit vector and 0*Z(p)","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE","IsZero","Tester(IsZero)"]]},{"rank" : 39,"comment" : "PositionNot: for GF(2) vector and 0*Z(2)","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE","IsZero","Tester(IsZero)"]]},{"rank" : 2,"comment" : "PositionNot: default value of third argument ","filters" : [["IsList"],[]]}],"3args" : [{"rank" : 60,"comment" : "PositionNot: for 8-bit vector and 0*Z(p) and starting ix","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE","IsZero","Tester(IsZero)"],["IsInt"]]},{"rank" : 57,"comment" : "PositionNot: for GF(2) vector and 0*Z(2) and offset","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE","IsZero","Tester(IsZero)"],["IsInt"]]},{"rank" : 20,"comment" : "PositionNot: default method ","filters" : [["IsList"],[],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionNonZero","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"]],[["IsHomogeneousList"],["IsInt"]],[["IsRowVectorObj"]],[["IsMatrixObj"]],[["IsMatrixObj"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 25,"comment" : "PositionNonZero: for 8-bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 22,"comment" : "PositionNonZero: for GF(2) vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 15,"comment" : "PositionNonZero: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 12,"comment" : "PositionNonZero: General method for a row vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 11,"comment" : "PositionNonZero: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 4,"comment" : "PositionNonZero: default method","filters" : [["IsHomogeneousList"]]}],"2args" : [{"rank" : 43,"comment" : "PositionNonZero: for 8-bit vector and starting point","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"]]},{"rank" : 40,"comment" : "PositionNonZero: for GF(2) vector and offset","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"]]},{"rank" : 33,"comment" : "PositionNonZero: for a plist matrix, and a position","filters" : [["IsPlistMatrixRep"],["IsInt"]]},{"rank" : 22,"comment" : "PositionNonZero: default method with start","filters" : [["IsHomogeneousList"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NestingDepthA","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "NestingDepthA: system getter","filters" : [["IsAttributeStoringRep","Tester(NestingDepthA)"]]},{"rank" : 33,"comment" : "NestingDepthA","filters" : [["IsGeneralizedRowVector","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 33,"comment" : "NestingDepthA","filters" : [["IsGeneralizedRowVector","CategoryCollections(CategoryCollections(IsCyclotomic))"]]},{"rank" : 30,"comment" : "NestingDepthA","filters" : [["IsGeneralizedRowVector","CategoryCollections(IsFFE)"]]},{"rank" : 30,"comment" : "NestingDepthA","filters" : [["IsGeneralizedRowVector","CategoryCollections(IsCyclotomic)"]]},{"rank" : 15,"comment" : "NestingDepthA","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "NestingDepthA","filters" : [["IsGF2MatrixRep"]]},{"rank" : 11,"comment" : "NestingDepthA","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "NestingDepthA","filters" : [["IsGF2VectorRep"]]},{"rank" : 0,"comment" : "NestingDepthA","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NestingDepthA)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NestingDepthA): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NestingDepthA): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NestingDepthA)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NestingDepthM","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "NestingDepthM: system getter","filters" : [["IsAttributeStoringRep","Tester(NestingDepthM)"]]},{"rank" : 45,"comment" : "NestingDepthM","filters" : [["IsMultiplicativeGeneralizedRowVector","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 45,"comment" : "NestingDepthM","filters" : [["IsMultiplicativeGeneralizedRowVector","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCyclotomic))"]]},{"rank" : 31,"comment" : "NestingDepthM","filters" : [["IsMultiplicativeGeneralizedRowVector","CategoryCollections(IsFFE)"]]},{"rank" : 31,"comment" : "NestingDepthM","filters" : [["IsMultiplicativeGeneralizedRowVector","CategoryCollections(IsCyclotomic)"]]},{"rank" : 15,"comment" : "NestingDepthM","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "NestingDepthM","filters" : [["IsGF2MatrixRep"]]},{"rank" : 11,"comment" : "NestingDepthM","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "NestingDepthM","filters" : [["IsGF2VectorRep"]]},{"rank" : 0,"comment" : "NestingDepthM","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NestingDepthM)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NestingDepthM): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NestingDepthM): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NestingDepthM)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZero","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsZero: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZero)"]]},{"rank" : 31,"comment" : "IsZero: for null map matrix","filters" : [["IsNullMapMatrix"]]},{"rank" : 30,"comment" : "IsZero: method for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 17,"comment" : "IsZero","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 15,"comment" : "IsZero: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 14,"comment" : "IsZero","filters" : [["IsPadicExtensionNumber"]]},{"rank" : 14,"comment" : "IsZero","filters" : [["IsPurePadicNumber"]]},{"rank" : 12,"comment" : "IsZero: for a row vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 11,"comment" : "IsZero: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 7,"comment" : "IsZero: for general mapping","filters" : [["IsGeneralMapping"]]},{"rank" : 4,"comment" : "IsZero: for an additive-element-with-zero","filters" : [["IsNearAdditiveElementWithZero","IsAdditiveElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZero)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZero)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsOne","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]],[["IsReesMatrixSemigroupElement"]],[["IsReesZeroMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsOne: system getter","filters" : [["IsAttributeStoringRep","Tester(IsOne)"]]},{"rank" : 110,"comment" : "IsOne: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"]]},{"rank" : 107,"comment" : "IsOne: object with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 23,"comment" : "IsOne: method for s.v. gen. mapping that is a field homomorphism","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]]},{"rank" : 21,"comment" : "IsOne: method for s.v. gen. mapping that respect add.,add.inv.,mult.,one,scal. mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 19,"comment" : "IsOne: method for s.v. gen. mapping that respect add.,add.inv.,mult.,scal. mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 19,"comment" : "IsOne: method for s.v. gen. mapping that respect mult.,one,add.,add.inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 18,"comment" : "IsOne: using `MappingGeneratorsImages'","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","Tester(MappingGeneratorsImages)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 17,"comment" : "IsOne","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "IsOne: method for s.v. gen. mapping that respect add.,add.inv.,scal. mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 17,"comment" : "IsOne: method for s.v. gen. mapping that respect mult.,add.,add.inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 15,"comment" : "IsOne: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "IsOne: method for s.v. gen. mapping that respect add. and add. inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 15,"comment" : "IsOne: method for s.v. gen. mapping that respect mult. and inv.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 13,"comment" : "IsOne: method for s.v. gen. mapping that respect add. and zero","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 13,"comment" : "IsOne: method for s.v. gen. mapping that respect mult. and one","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)"]]},{"rank" : 11,"comment" : "IsOne: method for s.v. gen. mapping that respect add.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)"]]},{"rank" : 11,"comment" : "IsOne: method for s.v. gen. mapping that respect mult.","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)"]]},{"rank" : 9,"comment" : "IsOne: method for s.v. gen. mapping","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 7,"comment" : "IsOne: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "IsOne: for a transformation","filters" : [["IsTransformation"]]},{"rank" : 5,"comment" : "IsOne: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 5,"comment" : "IsOne: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"]]},{"rank" : 4,"comment" : "IsOne: for a multiplicative-element-with-one","filters" : [["IsMultiplicativeElementWithOne"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsOne)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsOne)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroImmutable","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"]],[["IsFamily"]],[["IsCollection","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "ZeroImmutable: system getter","filters" : [["IsAttributeStoringRep","Tester(ZeroImmutable)"]]},{"rank" : 10014,"comment" : "ZeroImmutable: for additive magma with zero (look at family)","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 45,"comment" : "ZeroImmutable: for GF2 Matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 44,"comment" : "ZeroImmutable: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithZero","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 30,"comment" : "ZeroImmutable","filters" : [["IsInternalRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsRectangularTable","Tester(IsRectangularTable)"]]},{"rank" : 29,"comment" : "ZeroImmutable: for a matrix space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)"]]},{"rank" : 29,"comment" : "ZeroImmutable: for a row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)"]]},{"rank" : 27,"comment" : "ZeroImmutable: for a right ideal","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 27,"comment" : "ZeroImmutable: for a left ideal","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)"]]},{"rank" : 17,"comment" : "ZeroImmutable","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 15,"comment" : "ZeroImmutable: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 15,"comment" : "ZeroImmutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "ZeroImmutable: univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "ZeroImmutable: for an add. magma-with-zero with parent (ask the parent)","filters" : [["Tester(ParentAttr)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 14,"comment" : "ZeroImmutable: for additive magma with zero","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 12,"comment" : "ZeroImmutable: for floats","filters" : [["IsFloat"]]},{"rank" : 12,"comment" : "ZeroImmutable: for additive magma","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 11,"comment" : "ZeroImmutable: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 6,"comment" : "ZeroImmutable: for a zero element","filters" : [["IsNearAdditiveElementWithZero","IsAdditiveElement","IsZero","Tester(IsZero)"]]},{"rank" : 5,"comment" : "ZeroImmutable","filters" : [["CategoryFamily(IsPadicExtensionNumber)"]]},{"rank" : 5,"comment" : "ZeroImmutable","filters" : [["CategoryFamily(IsPurePadicNumber)"]]},{"rank" : 5,"comment" : "ZeroImmutable: for a family of FFEs","filters" : [["CategoryFamily(IsFFE)"]]},{"rank" : 4,"comment" : "ZeroImmutable: for an additive-element-with-zero (look at the family)","filters" : [["IsNearAdditiveElementWithZero","IsAdditiveElement"]]},{"rank" : 0,"comment" : "ZeroImmutable: for any object (call `ZERO')","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ZeroImmutable)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"],[]],[["IsFamily"],[]],[["IsCollection","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ZeroImmutable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ZeroImmutable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ZeroImmutable)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroMutable","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"]],[["IsReesMatrixSemigroupElement"]],[["IsReesZeroMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10013,"comment" : "ZeroMutable: for Lie object in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 45,"comment" : "ZeroMutable: for GF2 Matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 44,"comment" : "ZeroMutable: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithZero","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 31,"comment" : "ZeroMutable: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 28,"comment" : "ZeroMutable: for empty row vector","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 25,"comment" : "ZeroMutable: For an 8 bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 25,"comment" : "ZeroMutable: for GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 23,"comment" : "ZeroMutable: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "ZeroMutable","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "ZeroMutable","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 15,"comment" : "ZeroMutable: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 15,"comment" : "ZeroMutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "ZeroMutable: univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "ZeroMutable: for a direct product element","filters" : [["IsDirectProductElement"]]},{"rank" : 14,"comment" : "ZeroMutable: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj"]]},{"rank" : 13,"comment" : "ZeroMutable: for a p-adic number","filters" : [["IsPadicNumber"]]},{"rank" : 12,"comment" : "ZeroMutable: defer to family","filters" : [["IsPolynomialFunction"]]},{"rank" : 12,"comment" : "ZeroMutable: for UEALattice element","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 11,"comment" : "ZeroMutable: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "ZeroMutable: zmodnze : for element in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj"]]},{"rank" : 11,"comment" : "ZeroMutable: for s. c. ring element","filters" : [["IsSCRingObj"]]},{"rank" : 11,"comment" : "ZeroMutable: for a 0-cochain","filters" : [["IsCochain","IsZeroCochainRep"]]},{"rank" : 11,"comment" : "ZeroMutable: for s. c. algebra element","filters" : [["IsSCAlgebraObj"]]},{"rank" : 11,"comment" : "ZeroMutable: for an f.p. algebra element","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 11,"comment" : "ZeroMutable: for magma ring element","filters" : [["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 10,"comment" : "ZeroMutable: for weight rep element","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 10,"comment" : "ZeroMutable: for a cochain","filters" : [["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 10,"comment" : "ZeroMutable: for direct sum elements","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 10,"comment" : "ZeroMutable: for sparse rowspace elements","filters" : [["IsPackedElementDefaultRep","IsSparseRowSpaceElement"]]},{"rank" : 10,"comment" : "ZeroMutable: for monomial elements","filters" : [["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 10,"comment" : "ZeroMutable: for an algebra module element in packed representation","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 7,"comment" : "ZeroMutable: for a general mapping","filters" : [["IsGeneralMapping"]]},{"rank" : 6,"comment" : "ZeroMutable: for a (non-copyable) zero element","filters" : [["IsNearAdditiveElementWithZero","IsAdditiveElement","IsZero","Tester(IsZero)"]]},{"rank" : 5,"comment" : "ZeroMutable: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 5,"comment" : "ZeroMutable: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"]]},{"rank" : 4,"comment" : "ZeroMutable: for an additive-element-with-zero (look at the family)","filters" : [["IsNearAdditiveElementWithZero","IsAdditiveElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroSameMutability","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithZero","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 45,"comment" : "ZeroSameMutability: for GF2 Matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 44,"comment" : "ZeroSameMutability: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithZero","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 31,"comment" : "ZeroSameMutability: for null map matrix","filters" : [["IsNullMapMatrix"]]},{"rank" : 26,"comment" : "ZeroSameMutability: for GF2 vector, mutable","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 25,"comment" : "ZeroSameMutability: For an 8 bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 25,"comment" : "ZeroSameMutability: for GF2 vector, immutable","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 17,"comment" : "ZeroSameMutability","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 15,"comment" : "ZeroSameMutability: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 11,"comment" : "ZeroSameMutability: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 0,"comment" : "ZeroSameMutability: for an (immutable) object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "+","type" : "GAP_Operation","filters" : [[["IsExtAElement"],["IsExtAElement"]],[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10027,"comment" : "+: for a scalar and the base module (ResClasses)","filters" : [[],["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 10026,"comment" : "+: for a ring element and the base ring (ResClasses)","filters" : [[],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 10005,"comment" : "+: for the base ring and a ring element (ResClasses)","filters" : [["IsCollection","IsGeneralizedDomain"],[]]},{"rank" : 90,"comment" : "+: for GF2 matrix and GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 88,"comment" : "+: For two 8 bit matrices in same characteristic","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 84,"comment" : "+: for two empty matrices","filters" : [["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 70,"comment" : "+: for two characters","filters" : [["IsClassFunction","IsCharacter","Tester(IsCharacter)"],["IsClassFunction","IsCharacter","Tester(IsCharacter)"]]},{"rank" : 68,"comment" : "+: for two ordinary block matrices","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 66,"comment" : "+: for two virtual characters","filters" : [["IsClassFunction","IsVirtualCharacter","Tester(IsVirtualCharacter)"],["IsClassFunction","IsVirtualCharacter","Tester(IsVirtualCharacter)"]]},{"rank" : 62,"comment" : "+: for two null map matrices","filters" : [["IsNullMapMatrix"],["IsNullMapMatrix"]]},{"rank" : 60,"comment" : "+: for two Gaussian row spaces","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]},{"rank" : 56,"comment" : "+: method for two two-sided ideals","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 56,"comment" : "+: for two empty row vectors in the same family","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"],["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 54,"comment" : "+: for linear m.b.i. and linear m.b.m.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearGeneralMappingByImagesDefaultRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 54,"comment" : "+: for linear m.b.m. and linear m.b.i.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearMappingByMatrixDefaultRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 54,"comment" : "+: method for two right ideals","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(RightActingRingOfIdeal)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 54,"comment" : "+: method for two left ideals","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)"]]},{"rank" : 52,"comment" : "+: for two rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 50,"comment" : "+: For two 8 bit vectors in same characteristic","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 50,"comment" : "+: for GF2 vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 47,"comment" : "+: For an 8 bit vector of char 2 and a GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 47,"comment" : "+: For a GF2 vector and an 8 bit vector of char 2","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 44,"comment" : "+: for two left modules","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 42,"comment" : "+: for a grv, and an ordinary block matrix","filters" : [["IsGeneralizedRowVector"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 42,"comment" : "+: for an ordinary block matrix, and a grv","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsGeneralizedRowVector"]]},{"rank" : 38,"comment" : "+: for ring ring general mapping and ring g.m.b.i.","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 38,"comment" : "+: for ring g.m.b.i. and ring general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 38,"comment" : "+: for mapping and linear m.b.m.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 38,"comment" : "+: for linear m.b.m. and mapping","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearMappingByMatrixDefaultRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 38,"comment" : "+: for mapping and linear m.b.i.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 38,"comment" : "+: for linear m.b.i. and mapping","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearGeneralMappingByImagesDefaultRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 36,"comment" : "+: for internal FFE and element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 36,"comment" : "+: for element in Z\/pZ (ModulusRep) and internal FFE","filters" : [["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsInternalRep"]]},{"rank" : 34,"comment" : "+","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 34,"comment" : "+: for integer and element in Z\/nZ (ModulusRep)","filters" : [["IsInt"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 34,"comment" : "+: for element in Z\/nZ (ModulusRep) and integer","filters" : [["IsZmodnZObj","IsModulusRep"],["IsInt"]]},{"rank" : 34,"comment" : "+: BFElm+BFElm","filters" : [["IsAlgBFRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "+: BFElm+AlgElm","filters" : [["IsAlgBFRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "+: AlgElm+BFElm","filters" : [["IsKroneckerConstRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "+: AlgElm+AlgElm","filters" : [["IsKroneckerConstRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "+: laurent + laurent","filters" : [["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 34,"comment" : "+","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 33,"comment" : "+: for rational and element in Z\/nZ (ModulusRep)","filters" : [["IsRat"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 33,"comment" : "+: for element in Z\/nZ (ModulusRep) and rational","filters" : [["IsZmodnZObj","IsModulusRep"],["IsRat"]]},{"rank" : 32,"comment" : "+: for two checking plist matrices","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"],["IsPlistMatrixRep","IsCheckingMatrix"]]},{"rank" : 32,"comment" : "+","filters" : [["IsFFE"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 32,"comment" : "+","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE"]]},{"rank" : 32,"comment" : "+: for a rational and a FFE","filters" : [["IsRat"],["IsFFE"]]},{"rank" : 32,"comment" : "+: for a FFE and a rational","filters" : [["IsFFE"],["IsRat"]]},{"rank" : 32,"comment" : "+: for two elements in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 32,"comment" : "+: for two unknowns","filters" : [["IsUnknown"],["IsUnknown"]]},{"rank" : 32,"comment" : "+: for cyclotomic and unknown","filters" : [["IsCyc"],["IsUnknown"]]},{"rank" : 32,"comment" : "+: for unknown and cyclotomic","filters" : [["IsUnknown"],["IsCyc"]]},{"rank" : 32,"comment" : "+: for general mapping and algebra g.m.b.i.","filters" : [["IsGeneralMapping"],["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 32,"comment" : "+: for an algebra g.m.b.i. and general mapping","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"],["IsGeneralMapping"]]},{"rank" : 32,"comment" : "+: for `-infinity' and `-infinity'","filters" : [["IsNegInfinity"],["IsNegInfinity"]]},{"rank" : 32,"comment" : "+: for cyclotomic and `-infinity'","filters" : [["IsCyc"],["IsNegInfinity"]]},{"rank" : 32,"comment" : "+: for `-infinity' and cyclotomic","filters" : [["IsNegInfinity"],["IsCyc"]]},{"rank" : 32,"comment" : "+: for `infinity' and `infinity'","filters" : [["IsInfinity"],["IsInfinity"]]},{"rank" : 32,"comment" : "+: for cyclotomic and `infinity'","filters" : [["IsCyc"],["IsInfinity"]]},{"rank" : 32,"comment" : "+: for `infinity' and cyclotomic","filters" : [["IsInfinity"],["IsCyc"]]},{"rank" : 31,"comment" : "+: for object, and class function","filters" : [[],["IsClassFunction"]]},{"rank" : 31,"comment" : "+: for class function, and object","filters" : [["IsClassFunction"],[]]},{"rank" : 30,"comment" : "+: for two plist matrices","filters" : [["IsPlistMatrixRep"],["IsPlistMatrixRep"]]},{"rank" : 30,"comment" : "+","filters" : [["IsFFE"],["IsFFE"]]},{"rank" : 30,"comment" : "+: univariate + univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 30,"comment" : "+: for general mapping and linear g.m.b.i.","filters" : [["IsGeneralMapping"],["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 30,"comment" : "+: for linear g.m.b.i. and general mapping","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"],["IsGeneralMapping"]]},{"rank" : 30,"comment" : "+: for two direct product elements","filters" : [["IsDirectProductElement"],["IsDirectProductElement"]]},{"rank" : 29,"comment" : "+: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "+: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 28,"comment" : "+","filters" : [["IsPadicExtensionNumber"],["IsPadicExtensionNumber"]]},{"rank" : 28,"comment" : "+","filters" : [["IsPurePadicNumber"],["IsPurePadicNumber"]]},{"rank" : 28,"comment" : "+: zmodnze : for cyclotomic and element in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsCyclotomic"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 28,"comment" : "+: zmodnze : for element in Z\/nZ(m) (ZmodnZepsRep) and cyclotomic","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"],["IsCyclotomic"]]},{"rank" : 28,"comment" : "+: polynomial + polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 26,"comment" : "+: zmodnze : for two elements in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 26,"comment" : "+: rat-fun + rat-fun","filters" : [["IsRationalFunction"],["IsRationalFunction"]]},{"rank" : 26,"comment" : "+: for s. c. ring elements in dense vector rep.","filters" : [["IsSCRingObj","IsDenseCoeffVectorRep"],["IsSCRingObj","IsDenseCoeffVectorRep"]]},{"rank" : 26,"comment" : "+: for two Lie objects in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 26,"comment" : "+: for s. c. algebra elements in dense vector rep.","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 25,"comment" : "+: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 25,"comment" : "+: FElm+BFElm","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsAlgBFRep"]]},{"rank" : 25,"comment" : "+: BFElm+FElm","filters" : [["IsAlgBFRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "+: FElm+AlgElm","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsKroneckerConstRep"]]},{"rank" : 25,"comment" : "+: AlgElm+FElm","filters" : [["IsKroneckerConstRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "+: laurent + coeff(embed)","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "+: coeff(embed) + laurent","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 25,"comment" : "+: laurent + coeff","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "+: coeff + laurent","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 25,"comment" : "+: for a default list, and a direct product element","filters" : [["IsListDefault"],["IsDirectProductElement"]]},{"rank" : 25,"comment" : "+: for a direct product element, and a default list","filters" : [["IsDirectProductElement"],["IsListDefault"]]},{"rank" : 24,"comment" : "+: for two checking plist vectors","filters" : [["IsPlistVectorRep","IsCheckingVector"],["IsPlistVectorRep","IsCheckingVector"]]},{"rank" : 24,"comment" : "+: for two UEALattice elements","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"],["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 24,"comment" : "+: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 24,"comment" : "+: for zero mapping and general mapping","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],["IsGeneralMapping"]]},{"rank" : 24,"comment" : "+: for general mapping and zero mapping","filters" : [["IsGeneralMapping"],["IsZero","Tester(IsZero)","IsGeneralMapping"]]},{"rank" : 24,"comment" : "+: for two info selectors","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)","CategoryCollections(IsInfoClass)"],["IsSSortedList","Tester(IS_SSORT_LIST)","CategoryCollections(IsInfoClass)"]]},{"rank" : 23,"comment" : "+: univariate + coeff","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 23,"comment" : "+: coeff + univariate","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 22,"comment" : "+: for two plist vectors","filters" : [["IsPlistVectorRep"],["IsPlistVectorRep"]]},{"rank" : 22,"comment" : "+: coeff + polynomial ","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 22,"comment" : "+: polynomial + coeff","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 22,"comment" : "+: for two 0-cochains","filters" : [["IsCochain","IsZeroCochainRep"],["IsCochain","IsZeroCochainRep"]]},{"rank" : 22,"comment" : "+: for s. c. algebra elements","filters" : [["IsSCAlgebraObj"],["IsSCAlgebraObj"]]},{"rank" : 22,"comment" : "+: fp algebra elements","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"],["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 22,"comment" : "+: for two magma ring elements","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 21,"comment" : "+: for ring element, and Lie object in default representation","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 21,"comment" : "+: for Lie object in default representation, and ring element","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 20,"comment" : "+: coeff + ratfun ","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPolynomialFunction"]]},{"rank" : 20,"comment" : "+: ratfun + coeff","filters" : [["IsPolynomialFunction"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 20,"comment" : "+: for weight rep elements","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"],["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 20,"comment" : "+: for two cochains","filters" : [["IsPackedElementDefaultRep","IsCochain"],["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 20,"comment" : "+: for direct sum elements","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"],["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 20,"comment" : "+: for sparse rowspace elements","filters" : [["IsPackedElementDefaultRep","IsSparseRowSpaceElement"],["IsPackedElementDefaultRep","IsSparseRowSpaceElement"]]},{"rank" : 20,"comment" : "+: for monomial elements","filters" : [["IsMonomialElement","IsMonomialElementRep"],["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 20,"comment" : "+: for two algebra module elements in packed representation","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"],["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 19,"comment" : "+: for additive element and additive group","filters" : [["IsAdditiveElement"],["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 19,"comment" : "+: for additive group and additive element","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsAdditiveElement"]]},{"rank" : 17,"comment" : "+: for a vector and an algebra module element in packed representation","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 17,"comment" : "+: for an algebra module element in packed representation and a vector","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 17,"comment" : "+","filters" : [[],["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 17,"comment" : "+","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],[]]},{"rank" : 15,"comment" : "+: univariate + rat","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRat"]]},{"rank" : 15,"comment" : "+: rat + univariate","filters" : [["IsRat"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "+: for additive element and additive coset","filters" : [["IsAdditiveElement"],["IsAdditiveCoset"]]},{"rank" : 15,"comment" : "+: for additive coset and additive element","filters" : [["IsAdditiveCoset"],["IsAdditiveElement"]]},{"rank" : 15,"comment" : "+: for a non-list, and a direct product element","filters" : [[],["IsDirectProductElement"]]},{"rank" : 15,"comment" : "+: for a direct product element, and a non-list","filters" : [["IsDirectProductElement"],[]]},{"rank" : 14,"comment" : "+: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 14,"comment" : "+: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "+: for magma ring element and magma element","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "+: for magma element and magma ring element","filters" : [["IsMultiplicativeElement"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 13,"comment" : "+: for info selector and info class","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)","CategoryCollections(IsInfoClass)"],["IsInfoClass"]]},{"rank" : 13,"comment" : "+: for info class and info selector","filters" : [["IsInfoClass"],["IsSSortedList","Tester(IS_SSORT_LIST)","CategoryCollections(IsInfoClass)"]]},{"rank" : 12,"comment" : "+: rat + ratfun ","filters" : [["IsRat"],["IsPolynomialFunction"]]},{"rank" : 12,"comment" : "+: ratfun + rat","filters" : [["IsPolynomialFunction"],["IsRat"]]},{"rank" : 6,"comment" : "+: for ring element and residue class union (ResClasses)","filters" : [[],["IsResidueClassUnion"]]},{"rank" : 6,"comment" : "+: for residue class union and ring element (ResClasses)","filters" : [["IsResidueClassUnion"],[]]},{"rank" : 2,"comment" : "+: for two info classes","filters" : [["IsInfoClass"],["IsInfoClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditiveInverseImmutable","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "AdditiveInverseImmutable: system getter","filters" : [["IsAttributeStoringRep","Tester(AdditiveInverseImmutable)"]]},{"rank" : 45,"comment" : "AdditiveInverseImmutable: for GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 44,"comment" : "AdditiveInverseImmutable: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithZero","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 25,"comment" : "AdditiveInverseImmutable: For an 8 bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 25,"comment" : "AdditiveInverseImmutable: for GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 15,"comment" : "AdditiveInverseImmutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 11,"comment" : "AdditiveInverseImmutable: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 7,"comment" : "AdditiveInverseImmutable: for a zero element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsZero","Tester(IsZero)"]]},{"rank" : 0,"comment" : "AdditiveInverseImmutable: for any object (call `AINV')","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdditiveInverseImmutable)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdditiveInverseImmutable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdditiveInverseImmutable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdditiveInverseImmutable)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditiveInverseMutable","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 45,"comment" : "AdditiveInverseMutable: for GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 44,"comment" : "AdditiveInverseMutable: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithZero","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 34,"comment" : "AdditiveInverseMutable: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 33,"comment" : "AdditiveInverseMutable: for a virtual character","filters" : [["IsClassFunction","IsVirtualCharacter","Tester(IsVirtualCharacter)"]]},{"rank" : 31,"comment" : "AdditiveInverseMutable: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 31,"comment" : "AdditiveInverseMutable: for a null map matrix","filters" : [["IsNullMapMatrix"]]},{"rank" : 28,"comment" : "AdditiveInverseMutable: for empty row vector","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 27,"comment" : "AdditiveInverseMutable: for base module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "AdditiveInverseMutable: for base ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 25,"comment" : "AdditiveInverseMutable: For an 8 bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 25,"comment" : "AdditiveInverseMutable: for GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 25,"comment" : "AdditiveInverseMutable: for algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "AdditiveInverseMutable: for ring g.m.b.i.","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "AdditiveInverseMutable: for linear m.b.m.","filters" : [["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 23,"comment" : "AdditiveInverseMutable: for linear g.m.b.i.","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 17,"comment" : "AdditiveInverseMutable","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "AdditiveInverseMutable: BFElm","filters" : [["IsAlgBFRep"]]},{"rank" : 17,"comment" : "AdditiveInverseMutable: AlgElm","filters" : [["IsKroneckerConstRep"]]},{"rank" : 17,"comment" : "AdditiveInverseMutable: laurent polynomial","filters" : [["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 17,"comment" : "AdditiveInverseMutable","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 16,"comment" : "AdditiveInverseMutable: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"]]},{"rank" : 16,"comment" : "AdditiveInverseMutable: for an unknown","filters" : [["IsUnknown"]]},{"rank" : 16,"comment" : "AdditiveInverseMutable: for `-infinity'","filters" : [["IsNegInfinity"]]},{"rank" : 16,"comment" : "AdditiveInverseMutable: for `infinity'","filters" : [["IsInfinity"]]},{"rank" : 15,"comment" : "AdditiveInverseMutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "AdditiveInverseMutable: univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "AdditiveInverseMutable: for a direct product element","filters" : [["IsDirectProductElement"]]},{"rank" : 14,"comment" : "AdditiveInverseMutable","filters" : [["IsPadicExtensionNumber"]]},{"rank" : 14,"comment" : "AdditiveInverseMutable","filters" : [["IsPurePadicNumber"]]},{"rank" : 14,"comment" : "AdditiveInverseMutable: polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 13,"comment" : "AdditiveInverseMutable: zmodnze : for element in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 13,"comment" : "AdditiveInverseMutable: rational function","filters" : [["IsRationalFunction"]]},{"rank" : 13,"comment" : "AdditiveInverseMutable: for Lie object in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 12,"comment" : "AdditiveInverseMutable: for UEALattice element","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 11,"comment" : "AdditiveInverseMutable: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "AdditiveInverseMutable: for s. c. ring element","filters" : [["IsSCRingObj"]]},{"rank" : 11,"comment" : "AdditiveInverseMutable: for a 0-cochain","filters" : [["IsCochain","IsZeroCochainRep"]]},{"rank" : 11,"comment" : "AdditiveInverseMutable: for s. c. algebra element","filters" : [["IsSCAlgebraObj"]]},{"rank" : 11,"comment" : "AdditiveInverseMutable: fp algebra element","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 11,"comment" : "AdditiveInverseMutable: for magma ring element","filters" : [["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 10,"comment" : "AdditiveInverseMutable: for a weight rep element","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 10,"comment" : "AdditiveInverseMutable: for a cochain","filters" : [["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 10,"comment" : "AdditiveInverseMutable: for a direct sum element","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 10,"comment" : "AdditiveInverseMutable: for a sparse rowspace element","filters" : [["IsPackedElementDefaultRep","IsSparseRowSpaceElement"]]},{"rank" : 10,"comment" : "AdditiveInverseMutable: for a monomial element","filters" : [["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 10,"comment" : "AdditiveInverseMutable: for an algebra module element in packed representation","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 7,"comment" : "AdditiveInverseMutable: for a (non-copyable) zero element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsZero","Tester(IsZero)"]]},{"rank" : 6,"comment" : "AdditiveInverseMutable: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 6,"comment" : "AdditiveInverseMutable: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditiveInverseSameMutability","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 45,"comment" : "AdditiveInverseSameMutability: for GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 44,"comment" : "AdditiveInverseSameMutability: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithZero","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 31,"comment" : "AdditiveInverseSameMutability: for a null map matrix","filters" : [["IsNullMapMatrix"]]},{"rank" : 26,"comment" : "AdditiveInverseSameMutability: for GF2 vector, mutable","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 25,"comment" : "AdditiveInverseSameMutability: For an 8 bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 25,"comment" : "AdditiveInverseSameMutability: for GF2 vector, immutable","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 17,"comment" : "AdditiveInverseSameMutability","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 15,"comment" : "AdditiveInverseSameMutability: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 11,"comment" : "AdditiveInverseSameMutability: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 0,"comment" : "AdditiveInverseSameMutability: for an (immutable) object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "-","type" : "GAP_Operation","filters" : [[["IsExtAElement"],["IsNearAdditiveElementWithInverse"]],[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 90,"comment" : "-: for GF2 matrix and GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 88,"comment" : "-: For two 8 bit matrices in same characteristic","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 50,"comment" : "-: For two 8bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 50,"comment" : "-: for GF2 vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 47,"comment" : "-: For an 8 bit vector of char 2 and a GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 47,"comment" : "-: For a GF2 vector and an 8 bit vector of char 2","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 36,"comment" : "-: for internal FFE and element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 36,"comment" : "-: for element in Z\/pZ (ModulusRep) and internal FFE","filters" : [["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsInternalRep"]]},{"rank" : 36,"comment" : "-: for two unknowns in default representation","filters" : [["IsUnknown","IsUnknownDefaultRep"],["IsUnknown","IsUnknownDefaultRep"]]},{"rank" : 34,"comment" : "-","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 34,"comment" : "-: for integer and element in Z\/nZ (ModulusRep)","filters" : [["IsInt"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 34,"comment" : "-: for element in Z\/nZ (ModulusRep) and integer","filters" : [["IsZmodnZObj","IsModulusRep"],["IsInt"]]},{"rank" : 34,"comment" : "-: laurent - laurent","filters" : [["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 34,"comment" : "-","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 33,"comment" : "-: for rational and element in Z\/nZ (ModulusRep)","filters" : [["IsRat"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 33,"comment" : "-: for element in Z\/nZ (ModulusRep) and rational","filters" : [["IsZmodnZObj","IsModulusRep"],["IsRat"]]},{"rank" : 32,"comment" : "-: for two checking plist matrices","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"],["IsPlistMatrixRep","IsCheckingMatrix"]]},{"rank" : 32,"comment" : "-","filters" : [["IsFFE"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 32,"comment" : "-","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE"]]},{"rank" : 32,"comment" : "-: for two elements in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 32,"comment" : "-: for cyclotomic and unknown","filters" : [["IsCyc"],["IsUnknown"]]},{"rank" : 32,"comment" : "-: for unknown and cyclotomic","filters" : [["IsUnknown"],["IsCyc"]]},{"rank" : 30,"comment" : "-: for two plist matrices","filters" : [["IsPlistMatrixRep"],["IsPlistMatrixRep"]]},{"rank" : 30,"comment" : "-","filters" : [["IsFFE"],["IsFFE"]]},{"rank" : 30,"comment" : "-: univariate - univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 29,"comment" : "-: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "-: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 28,"comment" : "-","filters" : [["IsPadicExtensionNumber"],["IsPadicExtensionNumber"]]},{"rank" : 26,"comment" : "-: for s. c. ring elements in dense vector rep.","filters" : [["IsSCRingObj","IsDenseCoeffVectorRep"],["IsSCRingObj","IsDenseCoeffVectorRep"]]},{"rank" : 26,"comment" : "-: for two Lie objects in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 26,"comment" : "-: for s. c. algebra elements in dense vector rep.","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 25,"comment" : "-: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 24,"comment" : "-: for two checking plist vectors","filters" : [["IsPlistVectorRep","IsCheckingVector"],["IsPlistVectorRep","IsCheckingVector"]]},{"rank" : 24,"comment" : "-: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 22,"comment" : "-: for two plist vectors","filters" : [["IsPlistVectorRep"],["IsPlistVectorRep"]]},{"rank" : 22,"comment" : "-: for s. c. algebra elements","filters" : [["IsSCAlgebraObj"],["IsSCAlgebraObj"]]},{"rank" : 22,"comment" : "-: fp algebra elements","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"],["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 21,"comment" : "-: for ring element, and Lie object in default representation","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 21,"comment" : "-: for Lie object in default representation, and ring element","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 16,"comment" : "-","filters" : [["IsGeneralizedRowVector"],["IsGeneralizedRowVector"]]},{"rank" : 14,"comment" : "-: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 14,"comment" : "-: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "-: for magma ring element and magma element","filters" : [["IsMultiplicativeElement"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 14,"comment" : "-: for magma ring element and magma element","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsMultiplicativeElement"]]},{"rank" : 8,"comment" : "-","filters" : [[],["IsGeneralizedRowVector"]]},{"rank" : 8,"comment" : "-","filters" : [["IsGeneralizedRowVector"],[]]},{"rank" : 5,"comment" : "-: for external add. element, and additive-element-with-zero","filters" : [["IsExtAElement"],["IsNearAdditiveElementWithInverse"]]},{"rank" : 1,"comment" : "-: for ring element and residue class union (ResClasses)","filters" : [[],["IsListOrCollection"]]},{"rank" : 1,"comment" : "-: for residue class union and ring element (ResClasses)","filters" : [["IsListOrCollection"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "*","type" : "GAP_Operation","filters" : [[["IsExtRElement"],["IsExtLElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10024,"comment" : "*: additive element with zero * zero integer","filters" : [["IsNearAdditiveElementWithZero"],["IsInt","IsZeroCyc"]]},{"rank" : 10024,"comment" : "*: zero integer * additive element with zero","filters" : [["IsInt","IsZeroCyc"],["IsNearAdditiveElementWithZero"]]},{"rank" : 214,"comment" : "*: objects with memory","filters" : [["IsObjWithMemory"],["IsObjWithMemory"]]},{"rank" : 214,"comment" : "*: straight line program elements","filters" : [["IsStraightLineProgElm"],["IsStraightLineProgElm"]]},{"rank" : 151,"comment" : "*: for a row vector and a matrix with memory","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsObjWithMemory"]]},{"rank" : 144,"comment" : "*: for a matrix with memory and a scalar","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsObjWithMemory"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 144,"comment" : "*: for a scalar and a matrix with memory","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsObjWithMemory"]]},{"rank" : 110,"comment" : "*: x with straight line program element","filters" : [["IsMultiplicativeElement"],["IsStraightLineProgElm"]]},{"rank" : 110,"comment" : "*: straight line program element with x","filters" : [["IsStraightLineProgElm"],["IsMultiplicativeElement"]]},{"rank" : 96,"comment" : "*: More efficient non-recursive kernel method for vector*matrix of cyclotomics","filters" : [["IsPlistRep","IsSmallList","Tester(IsSmallList)","CategoryCollections(IsCyclotomic)","IsListDefault"],["IsPlistRep","IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsCyclotomic))","IsListDefault","IsRectangularTable","Tester(IsRectangularTable)"]]},{"rank" : 95,"comment" : "*: More efficient non-recursive method for matrix*matrix of cyclotomics","filters" : [["IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsCyclotomic))","IsListDefault"],["IsPlistRep","IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsCyclotomic))","IsListDefault","IsRectangularTable","Tester(IsRectangularTable)"]]},{"rank" : 90,"comment" : "*: for GF2 matrix and GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 88,"comment" : "*: 8 bit matrix * 8 bit matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 84,"comment" : "*: for two empty matrices","filters" : [["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 78,"comment" : "*: for GF2 vector and GF2 matrix","filters" : [["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 77,"comment" : "*: 8 bit matrix * 8 bit vector","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"],["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 77,"comment" : "*: 8 bit vector * 8 bit matrix","filters" : [["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 74,"comment" : "*: For an 8 bit vector and a compatible matrix","filters" : [["IsList","IsHomogeneousList","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 74,"comment" : "*: for two ordinary block matrices","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 71,"comment" : "*: For a GF2 vector and a compatible matrix","filters" : [["IsList","IsHomogeneousList","IsSmallList","Tester(IsSmallList)","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 70,"comment" : "*: for two characters","filters" : [["IsCharacter","Tester(IsCharacter)"],["IsCharacter","Tester(IsCharacter)"]]},{"rank" : 70,"comment" : "*: for GF2 matrix and GF2 vector","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 66,"comment" : "*: for two virtual characters","filters" : [["IsVirtualCharacter","Tester(IsVirtualCharacter)"],["IsVirtualCharacter","Tester(IsVirtualCharacter)"]]},{"rank" : 66,"comment" : "*: for GF2 vectors","filters" : [["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"],["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsListDefault","IsGF2VectorRep"]]},{"rank" : 64,"comment" : "*: For 2 8 bit vectors","filters" : [["IsList","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)","Is8BitVectorRep"],["IsList","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)","Is8BitVectorRep"]]},{"rank" : 62,"comment" : "*: for two class functions","filters" : [["IsClassFunction"],["IsClassFunction"]]},{"rank" : 62,"comment" : "*: for ffe and ordinary block matrix of integers","filters" : [["IsFFE"],["IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCyclotomic))","IsBlockMatrixRep"]]},{"rank" : 62,"comment" : "*: for ordinary block matrix of integers and ffe","filters" : [["IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCyclotomic))","IsBlockMatrixRep"],["IsFFE"]]},{"rank" : 62,"comment" : "*: for two null map matrices","filters" : [["IsNullMapMatrix"],["IsNullMapMatrix"]]},{"rank" : 61,"comment" : "*: for matrix and null map matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNullMapMatrix"]]},{"rank" : 60,"comment" : "*: for GF2 matrix and GF2 element","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"],["IsFFE"]]},{"rank" : 60,"comment" : "*: for GF2 element and GF2 matrix","filters" : [["IsFFE"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsListDefault","IsGF2MatrixRep"]]},{"rank" : 59,"comment" : "*: scalar * 8 bit matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"],["IsFFE"]]},{"rank" : 59,"comment" : "*: scalar * 8 bit matrix","filters" : [["IsFFE"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 59,"comment" : "*: for empty list, and empty matrix","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 59,"comment" : "*: for empty matrix, and empty list","filters" : [["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 59,"comment" : "*","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 56,"comment" : "*: for two empty row vectors in the same family","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"],["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 55,"comment" : "*: for GF2 vector and FFE","filters" : [["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE"]]},{"rank" : 55,"comment" : "*: for FFE and GF2 vector","filters" : [["IsFFE"],["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 54,"comment" : "*: for character, and positive integer","filters" : [["IsCharacter","Tester(IsCharacter)"],["IsInt","IsPosRat"]]},{"rank" : 54,"comment" : "*: for positive integer, and character","filters" : [["IsInt","IsPosRat"],["IsCharacter","Tester(IsCharacter)"]]},{"rank" : 53,"comment" : "*: for ring and right ideal (construct a two-sided ideal)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 53,"comment" : "*: for left ideal and ring (construct a two-sided ideal)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 52,"comment" : "*: for integer and ordinary block matrix","filters" : [["IsInt"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 52,"comment" : "*: for ordinary block matrix and integer","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsInt"]]},{"rank" : 51,"comment" : "*: for virtual character, and integer","filters" : [["IsVirtualCharacter","Tester(IsVirtualCharacter)"],["IsInt"]]},{"rank" : 51,"comment" : "*: for integer, and virtual character","filters" : [["IsInt"],["IsVirtualCharacter","Tester(IsVirtualCharacter)"]]},{"rank" : 50,"comment" : "*: for ring element, and empty matrix","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 50,"comment" : "*: for empty matrix, and ring element","filters" : [["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 48,"comment" : "*: for empty list and null map matrix","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsNullMapMatrix"]]},{"rank" : 47,"comment" : "*: for empty list and matrix (ResClasses)","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 47,"comment" : "*: for class function, and cyclotomic","filters" : [["IsClassFunction"],["IsCyc"]]},{"rank" : 47,"comment" : "*: for cyclotomic, and class function","filters" : [["IsCyc"],["IsClassFunction"]]},{"rank" : 47,"comment" : "*: For an 8 bit vector of char 2 and a GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 47,"comment" : "*: For a GF2 vector and an 8 bit vector of char 2","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 46,"comment" : "*: for vector and ordinary block matrix","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 46,"comment" : "*: for ordinary block matrix and vector","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 46,"comment" : "*: for empty row vector, and integer","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"],["IsInt"]]},{"rank" : 46,"comment" : "*: for integer, and empty row vector","filters" : [["IsInt"],["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 45,"comment" : "*: for a scalar and Z^2 (ResClasses)","filters" : [["IsInt"],["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 45,"comment" : "*: for FFE and GF2 vector","filters" : [["IsFFE"],["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 45,"comment" : "*: for FFE and GF2 vector","filters" : [["IsFFE"],["IsList","IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElement)","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 44,"comment" : "*","filters" : [["IsRat"],["IsList","CategoryCollections(IsPadicNumber)"]]},{"rank" : 44,"comment" : "*","filters" : [["IsList","CategoryCollections(IsPadicNumber)"],["IsRat"]]},{"rank" : 43,"comment" : "*: for a mgrv, and an ordinary block matrix","filters" : [["IsMultiplicativeGeneralizedRowVector"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 43,"comment" : "*: for an ordinary block matrix, and a mgrv","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsMultiplicativeGeneralizedRowVector"]]},{"rank" : 42,"comment" : "*: For an FFE and an 8 bit vector ","filters" : [["IsFFE","IsInternalRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 42,"comment" : "*: For an 8 bit vector and an FFE","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE","IsInternalRep"]]},{"rank" : 42,"comment" : "*: for ring element and ordinary block matrix","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 42,"comment" : "*: for ordinary block matrix and ring element","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 41,"comment" : "*: for list in `IsListDefault', and class function","filters" : [["IsListDefault"],["IsClassFunction"]]},{"rank" : 41,"comment" : "*: for class function, and list in `IsListDefault'","filters" : [["IsClassFunction"],["IsListDefault"]]},{"rank" : 41,"comment" : "*: for a null map matrix and a scalar","filters" : [["IsNullMapMatrix"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 41,"comment" : "*: for a scalar and a null map matrix","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsNullMapMatrix"]]},{"rank" : 40,"comment" : "*: for two nearly character tables (call `CharacterTableDirectProduct')","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]},{"rank" : 38,"comment" : "*: group times element","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 38,"comment" : "*: for vector and null map matrix","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsNullMapMatrix"]]},{"rank" : 37,"comment" : "*: for residue class union of Z^2 and matrix (ResClasses)","filters" : [["IsResidueClassUnionOfZxZ"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 36,"comment" : "*: for a ring element and the base ring (ResClasses)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsMagma","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 36,"comment" : "*: for internal FFE and element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 36,"comment" : "*: for element in Z\/pZ (ModulusRep) and internal FFE","filters" : [["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsInternalRep"]]},{"rank" : 35,"comment" : "*: for the base module and a scalar \/ matrix (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 35,"comment" : "*: internal ffe * (large) integer","filters" : [["IsFFE","IsInternalRep"],["IsInt"]]},{"rank" : 34,"comment" : "*: for the base ring and a ring element (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 34,"comment" : "*","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 34,"comment" : "*: for integer and element in Z\/nZ (ModulusRep)","filters" : [["IsInt"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 34,"comment" : "*: for element in Z\/nZ (ModulusRep) and integer","filters" : [["IsZmodnZObj","IsModulusRep"],["IsInt"]]},{"rank" : 34,"comment" : "*: BFElm*BFElm","filters" : [["IsAlgBFRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "*: BFElm*AlgElm","filters" : [["IsAlgBFRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "*: AlgElm*BFElm","filters" : [["IsKroneckerConstRep"],["IsAlgBFRep"]]},{"rank" : 34,"comment" : "*: AlgElm*AlgElm","filters" : [["IsKroneckerConstRep"],["IsKroneckerConstRep"]]},{"rank" : 34,"comment" : "*: laurent * laurent","filters" : [["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 34,"comment" : "*: for ring and ring element (construct a left ideal)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 34,"comment" : "*: for ring element and ring (construct a right ideal)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 34,"comment" : "*","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 33,"comment" : "*: for rational and element in Z\/nZ (ModulusRep)","filters" : [["IsRat"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 33,"comment" : "*: for element in Z\/nZ (ModulusRep) and rational","filters" : [["IsZmodnZObj","IsModulusRep"],["IsRat"]]},{"rank" : 33,"comment" : "*: for list and null map matrix","filters" : [["IsList"],["IsNullMapMatrix"]]},{"rank" : 32,"comment" : "*: for pcp elements","filters" : [["IsPcpElement"],["IsPcpElement"]]},{"rank" : 32,"comment" : "*: RightCosets","filters" : [["IsRightCoset"],["IsRightCoset"]]},{"rank" : 32,"comment" : "*","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE"]]},{"rank" : 32,"comment" : "*","filters" : [["IsFFE"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 32,"comment" : "*: for a rational and a FFE","filters" : [["IsRat"],["IsFFE"]]},{"rank" : 32,"comment" : "*: for a FFE and a rational","filters" : [["IsFFE"],["IsRat"]]},{"rank" : 32,"comment" : "*: for two elements in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 32,"comment" : "*: for two unknowns","filters" : [["IsUnknown"],["IsUnknown"]]},{"rank" : 32,"comment" : "*: for cyclotomic and unknown","filters" : [["IsCyc"],["IsUnknown"]]},{"rank" : 32,"comment" : "*: for unknown and cyclotomic","filters" : [["IsUnknown"],["IsCyc"]]},{"rank" : 31,"comment" : "*: for s. c. ring element in dense vector rep. and integer","filters" : [["IsSCRingObj","IsDenseCoeffVectorRep"],["IsInt"]]},{"rank" : 31,"comment" : "*: for integer and s. c. ring element in dense vector rep.","filters" : [["IsInt"],["IsSCRingObj","IsDenseCoeffVectorRep"]]},{"rank" : 31,"comment" : "*: for s. c. algebra element in dense vector rep. and integer","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsInt"]]},{"rank" : 31,"comment" : "*: for integer and s. c. algebra element in dense vector rep.","filters" : [["IsInt"],["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 31,"comment" : "*: for empty row vector, and multiplicative element","filters" : [["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"],["IsMultiplicativeElement"]]},{"rank" : 31,"comment" : "*: for multiplicative element, and empty row vector","filters" : [["IsMultiplicativeElement"],["IsHomogeneousList","IsEmpty","Tester(IsEmpty)","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsEmptyRowVectorRep"]]},{"rank" : 30,"comment" : "*: for two plist matrices","filters" : [["IsPlistMatrixRep"],["IsPlistMatrixRep"]]},{"rank" : 30,"comment" : "*","filters" : [["IsRat"],["IsPadicNumber"]]},{"rank" : 30,"comment" : "*","filters" : [["IsPadicNumber"],["IsRat"]]},{"rank" : 30,"comment" : "*","filters" : [["IsFFE"],["IsFFE"]]},{"rank" : 30,"comment" : "*: univariate * univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 30,"comment" : "*: for two direct product elements","filters" : [["IsDirectProductElement"],["IsDirectProductElement"]]},{"rank" : 29,"comment" : "*: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "*: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 29,"comment" : "*: zmodnze : for element x in Z\/nZ and y in Z\/nZ(m)","filters" : [["IsZmodnZObj","IsModulusRep"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 29,"comment" : "*: zmodnze : for element x in Z\/nZ(m) and y in Z\/nZ","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 29,"comment" : "*: for s. c. algebra element and integer","filters" : [["IsSCAlgebraObj"],["IsInt"]]},{"rank" : 29,"comment" : "*: for integer and s. c. algebra element","filters" : [["IsInt"],["IsSCAlgebraObj"]]},{"rank" : 28,"comment" : "*","filters" : [["IsPadicExtensionNumber"],["IsPadicExtensionNumber"]]},{"rank" : 28,"comment" : "*","filters" : [["IsPadicExtensionNumber"],["IsPurePadicNumber"]]},{"rank" : 28,"comment" : "*","filters" : [["IsPurePadicNumber"],["IsPadicExtensionNumber"]]},{"rank" : 28,"comment" : "*","filters" : [["IsPurePadicNumber"],["IsPurePadicNumber"]]},{"rank" : 28,"comment" : "*: zmodnze : for element x in Z\/nZ(m) (ZmodnZepsRep) and cyclotomic y","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"],["IsCyclotomic"]]},{"rank" : 28,"comment" : "*: zmodnze : for cyclotomic x and element y in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsCyclotomic"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 28,"comment" : "*: polynomial * polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 28,"comment" : "*: for scalar and algebra g.m.b.i.","filters" : [["IsMultiplicativeElement"],["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 28,"comment" : "*: for rational, and magma ring element","filters" : [["IsRat"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 28,"comment" : "*: for magma ring element, and rational","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsRat"]]},{"rank" : 26,"comment" : "*: for a plist vector and a plist matrix","filters" : [["IsPlistVectorRep"],["IsPlistMatrixRep"]]},{"rank" : 26,"comment" : "*: zmodnze : for two elements in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 26,"comment" : "*: univariate * coeff","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 26,"comment" : "*: coeff * univariate","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 26,"comment" : "*: rat-fun * rat-fun","filters" : [["IsRationalFunction"],["IsRationalFunction"]]},{"rank" : 26,"comment" : "*: for s. c. ring elements in dense vector rep.","filters" : [["IsSCRingObj","IsDenseCoeffVectorRep"],["IsSCRingObj","IsDenseCoeffVectorRep"]]},{"rank" : 26,"comment" : "*: for two Lie objects in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 26,"comment" : "*: for s. c. algebra elements in dense vector rep.","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 26,"comment" : "*: for scalar and linear m.b.m.","filters" : [["IsMultiplicativeElement"],["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 26,"comment" : "*: for scalar and linear g.m.b.i.","filters" : [["IsMultiplicativeElement"],["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 25,"comment" : "*: for an integer and a residue class union of Z^2 (ResClasses)","filters" : [["IsInt"],["IsResidueClassUnionOfZxZ"]]},{"rank" : 25,"comment" : "*: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 25,"comment" : "*: laurent * coeff","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "*: coeff * laurent","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 25,"comment" : "*: for row vector and Lie object","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 25,"comment" : "*: for Lie object and row vector","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 25,"comment" : "*: for a default list, and a direct product element","filters" : [["IsListDefault"],["IsDirectProductElement"]]},{"rank" : 25,"comment" : "*: for a direct product element, and a default list","filters" : [["IsDirectProductElement"],["IsListDefault"]]},{"rank" : 24,"comment" : "*: for two UEALattice elements","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"],["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 24,"comment" : "*: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 23,"comment" : "*: FElm*Alg","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsAlgebraicElement"]]},{"rank" : 23,"comment" : "*: Alg*FElm","filters" : [["IsAlgebraicElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 23,"comment" : "*: rat-fun * coeff","filters" : [["IsPolynomialFunction"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 23,"comment" : "*: coeff * rat-fun","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPolynomialFunction"]]},{"rank" : 23,"comment" : "*: additive element with inverse * negative integer","filters" : [["IsNearAdditiveElementWithInverse"],["IsInt","IsNegRat"]]},{"rank" : 23,"comment" : "*: negative integer * additive element with inverse","filters" : [["IsInt","IsNegRat"],["IsNearAdditiveElementWithInverse"]]},{"rank" : 22,"comment" : "*: for UEALattice element and scalar","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 22,"comment" : "*: for scalar and UEALattice element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 22,"comment" : "*: for cochain and scalar","filters" : [["IsPackedElementDefaultRep","IsCochain"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse","IsZero","Tester(IsZero)"]]},{"rank" : 22,"comment" : "*: for scalar and cochain","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse","IsZero","Tester(IsZero)"],["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 22,"comment" : "*: for s. c. algebra elements","filters" : [["IsSCAlgebraObj"],["IsSCAlgebraObj"]]},{"rank" : 22,"comment" : "*: fp algebra elements","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"],["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 22,"comment" : "*: for two magma ring elements","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 21,"comment" : "*: RightCoset with element","filters" : [["IsRightCoset"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "*: for a scalar and a checking plist vector","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsPlistVectorRep"]]},{"rank" : 21,"comment" : "*: for a scalar and a plist vector","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsPlistVectorRep"]]},{"rank" : 21,"comment" : "*: for a checking plist vector and a scalar","filters" : [["IsPlistVectorRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "*: for a plist vector and a scalar","filters" : [["IsPlistVectorRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "*: for 0-cochain and scalar","filters" : [["IsCochain","IsZeroCochainRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "*: for scalar and 0-cochain","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsCochain","IsZeroCochainRep"]]},{"rank" : 21,"comment" : "*: for ring element, and Lie object in default representation","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 21,"comment" : "*: for Lie object in default representation, and ring element","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 21,"comment" : "*: for s. c. algebra element in dense vector rep. and ring element","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 21,"comment" : "*: for ring element and s. c. algebra element in dense vector rep.","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsSCAlgebraObj","IsDenseCoeffVectorRep"]]},{"rank" : 21,"comment" : "*: additive element * positive integer","filters" : [["IsNearAdditiveElement"],["IsInt","IsPosRat"]]},{"rank" : 21,"comment" : "*: positive integer * additive element","filters" : [["IsInt","IsPosRat"],["IsNearAdditiveElement"]]},{"rank" : 20,"comment" : "*: generic method for n bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 20,"comment" : "*: for cochain and scalar","filters" : [["IsPackedElementDefaultRep","IsCochain"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 20,"comment" : "*: for scalar and cochain","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsPackedElementDefaultRep","IsCochain"]]},{"rank" : 20,"comment" : "*: for a scalar and an algebra module element in packed representation","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 20,"comment" : "*: for an algebra module element in packed representation and a scalar","filters" : [["IsPackedElementDefaultRep","IsAlgebraModuleElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 20,"comment" : "*: for two magma congruence classes","filters" : [["IsCongruenceClass"],["IsCongruenceClass"]]},{"rank" : 20,"comment" : "*: for permutation and binary relation on points","filters" : [["IsPerm"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 20,"comment" : "*: for binary relation on points and permutation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsPerm"]]},{"rank" : 19,"comment" : "*: for s. c. algebra element and ring element","filters" : [["IsSCAlgebraObj"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 19,"comment" : "*: for ring element and s. c. algebra element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsSCAlgebraObj"]]},{"rank" : 19,"comment" : "*: fp algebra el*ring el","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 19,"comment" : "*: ring el *fp algebra el","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 19,"comment" : "*: for ring element, and magma ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 19,"comment" : "*: for magma ring element, and ring element","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 19,"comment" : "*: for binary relation on points and transformation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsTransformation"]]},{"rank" : 19,"comment" : "*: for transformation and binary relation on points","filters" : [["IsTransformation"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 19,"comment" : "*: for zero and total general mapping","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement","IsZero","Tester(IsZero)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)"]]},{"rank" : 18,"comment" : "*: for weight rep element and a scalar","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 18,"comment" : "*: for weight rep element and a scalar","filters" : [["IsPackedElementDefaultRep","IsWeightRepElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 18,"comment" : "*: for a direct sum element and a scalar","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsDirectSumElement"]]},{"rank" : 18,"comment" : "*: for a direct sum element and a scalar","filters" : [["IsPackedElementDefaultRep","IsDirectSumElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 18,"comment" : "*: for a scalar and a sparse rowspace element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsSparseRowSpaceElement"]]},{"rank" : 18,"comment" : "*: for a sparse rowspace element and a scalar","filters" : [["IsPackedElementDefaultRep","IsSparseRowSpaceElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 18,"comment" : "*: for a scalar and a monomial element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 18,"comment" : "*: for a monomial element and a scalar","filters" : [["IsMonomialElement","IsMonomialElementRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 17,"comment" : "*: List*Alg","filters" : [["IsList"],["IsAlgebraicElement"]]},{"rank" : 17,"comment" : "*: Alg*List","filters" : [["IsAlgebraicElement"],["IsList"]]},{"rank" : 17,"comment" : "*","filters" : [[],["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 17,"comment" : "*","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],[]]},{"rank" : 16,"comment" : "*: for two 32 bits assoc. words","filters" : [["Is32BitsAssocWord"],["Is32BitsAssocWord"]]},{"rank" : 16,"comment" : "*: for two 16 bits assoc. words","filters" : [["Is16BitsAssocWord"],["Is16BitsAssocWord"]]},{"rank" : 16,"comment" : "*: for two 8 bits assoc. words","filters" : [["Is8BitsAssocWord"],["Is8BitsAssocWord"]]},{"rank" : 15,"comment" : "*: univariate * rat","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRat"]]},{"rank" : 15,"comment" : "*: rat * univariate","filters" : [["IsRat"],["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "*: for a non-list, and a direct product element","filters" : [[],["IsDirectProductElement"]]},{"rank" : 15,"comment" : "*: for a direct product element, and a non-list","filters" : [["IsDirectProductElement"],[]]},{"rank" : 14,"comment" : "*: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 14,"comment" : "*: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "*: for ring element and residue class union (ResClasses)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsResidueClassUnion"]]},{"rank" : 14,"comment" : "*: for residue class union and ring element (ResClasses)","filters" : [["IsResidueClassUnion"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "*: for a transformation and a general mapping","filters" : [["IsTransformation"],["IsGeneralMapping"]]},{"rank" : 14,"comment" : "*: for a general mapping and a transformation","filters" : [["IsGeneralMapping"],["IsTransformation"]]},{"rank" : 14,"comment" : "*: for two f.p. group elements","filters" : [["IsElementOfFpGroup"],["IsElementOfFpGroup"]]},{"rank" : 14,"comment" : "*: wreath elements","filters" : [["IsWreathProductElement"],["IsWreathProductElement"]]},{"rank" : 14,"comment" : "*: for two elements of magma by mult. table","filters" : [["IsMagmaByMultiplicationTableObj"],["IsMagmaByMultiplicationTableObj"]]},{"rank" : 14,"comment" : "*: assoc words in B letter rep","filters" : [["IsAssociativeElement","IsWord","IsBLetterAssocWordRep"],["IsAssociativeElement","IsWord","IsBLetterAssocWordRep"]]},{"rank" : 14,"comment" : "*: assoc words in W letter rep","filters" : [["IsAssociativeElement","IsWord","IsWLetterAssocWordRep"],["IsAssociativeElement","IsWord","IsWLetterAssocWordRep"]]},{"rank" : 14,"comment" : "*: for magma ring element and magma element","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "*: for magma element and magma ring element","filters" : [["IsMultiplicativeElement"],["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 14,"comment" : "*: for two elements of a magma with zero adjoined","filters" : [["IsMagmaWithZeroAdjoinedElementRep"],["IsMagmaWithZeroAdjoinedElementRep"]]},{"rank" : 14,"comment" : "*: for two general mappings","filters" : [["IsGeneralMapping"],["IsGeneralMapping"]]},{"rank" : 13,"comment" : "*: for list and binary relation on points","filters" : [["IsListOrCollection"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 13,"comment" : "*: for binary relation on points and list","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsListOrCollection"]]},{"rank" : 12,"comment" : "*","filters" : [["IsMonoidByAdjoiningIdentityElt"],["IsMonoidByAdjoiningIdentityElt"]]},{"rank" : 12,"comment" : "*: for two elements of a fp monoid","filters" : [["IsElementOfFpMonoid"],["IsElementOfFpMonoid"]]},{"rank" : 12,"comment" : "*: rws-element * rws-element","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 12,"comment" : "*: for two assoc. words in syllable rep","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]]},{"rank" : 10,"comment" : "*: for elements of a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroupElement"],["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 10,"comment" : "*: for elements of a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroupElement"],["IsReesMatrixSemigroupElement"]]},{"rank" : 10,"comment" : "*: for two elements of a f.p. semigroup","filters" : [["IsElementOfFpSemigroup"],["IsElementOfFpSemigroup"]]},{"rank" : 10,"comment" : "*: for two assoc. words: force syllable rep","filters" : [["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]},{"rank" : 10,"comment" : "*: for two nonassoc. words","filters" : [["IsNonassocWord"],["IsNonassocWord"]]},{"rank" : 10,"comment" : "*: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"],["IsAdditiveElementAsMultiplicativeElementRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OneImmutable","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]],[["IsFamily"]],[["IsCollection","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "OneImmutable: system getter","filters" : [["IsAttributeStoringRep","Tester(OneImmutable)"]]},{"rank" : 10015,"comment" : "OneImmutable: for a magma-with-one that has a parent","filters" : [["Tester(ParentAttr)","IsMagmaWithOne"]]},{"rank" : 134,"comment" : "OneImmutable: partial method for a group (beats to ask family)","filters" : [["IsMagmaWithOne","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 114,"comment" : "OneImmutable: partial method for a magma-with-one (ask family)","filters" : [["IsMagmaWithOne"]]},{"rank" : 107,"comment" : "OneImmutable: objects with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 56,"comment" : "OneImmutable: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsMultiplicativeElementWithInverse","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 44,"comment" : "OneImmutable: for GF2 Matrix","filters" : [["IsMultiplicativeElementWithOne","IsOrdinaryMatrix","IsGF2MatrixRep"]]},{"rank" : 43,"comment" : "OneImmutable: for matrix group, call `IdentityMat'","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 26,"comment" : "OneImmutable: for a partial perm monoid with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagmaWithOne","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 26,"comment" : "OneImmutable: for SC Rings -- try generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 26,"comment" : "OneImmutable: for finite SC Rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 22,"comment" : "OneImmutable: for a partial perm semigroup with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "OneImmutable","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 15,"comment" : "OneImmutable: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 15,"comment" : "OneImmutable: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 15,"comment" : "OneImmutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "OneImmutable: univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 14,"comment" : "OneImmutable: for a magma-with-one","filters" : [["IsMagmaWithOne"]]},{"rank" : 12,"comment" : "OneImmutable: for floats","filters" : [["IsFloat"]]},{"rank" : 12,"comment" : "OneImmutable: for binary relation on points and a set of integers","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 11,"comment" : "OneImmutable: One(<congruence class>)","filters" : [["IsMultiplicativeElementWithOne","IsCongruenceClass"]]},{"rank" : 11,"comment" : "OneImmutable: for a magma","filters" : [["IsMagma"]]},{"rank" : 8,"comment" : "OneImmutable: for a multiplicative element with one collection","filters" : [["CategoryCollections(IsMultiplicativeElementWithOne)"]]},{"rank" : 7,"comment" : "OneImmutable: for an f.p. group element","filters" : [["IsElementOfFpGroup"]]},{"rank" : 6,"comment" : "OneImmutable: for pcp elements","filters" : [["IsPcpElement"]]},{"rank" : 6,"comment" : "OneImmutable","filters" : [["IsMonoidByAdjoiningIdentityElt"]]},{"rank" : 6,"comment" : "OneImmutable: for an fp monoid element","filters" : [["IsElementOfFpMonoid"]]},{"rank" : 6,"comment" : "OneImmutable: for an identity element","filters" : [["IsMultiplicativeElementWithOne","IsOne","Tester(IsOne)"]]},{"rank" : 5,"comment" : "OneImmutable","filters" : [["CategoryFamily(IsPadicExtensionNumber)"]]},{"rank" : 5,"comment" : "OneImmutable","filters" : [["CategoryFamily(IsPurePadicNumber)"]]},{"rank" : 5,"comment" : "OneImmutable: for a family of FFEs","filters" : [["CategoryFamily(IsFFE)"]]},{"rank" : 4,"comment" : "OneImmutable: for family of s. c. algebra elements","filters" : [["CategoryFamily(IsSCAlgebraObj)"]]},{"rank" : 4,"comment" : "OneImmutable: for a multiplicative-element-with-one (look at the family)","filters" : [["IsMultiplicativeElementWithOne"]]},{"rank" : 3,"comment" : "OneImmutable: for a family of free monoid elements","filters" : [["CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 2,"comment" : "OneImmutable: for a family of fp monoid elements","filters" : [["CategoryFamily(IsElementOfFpMonoid)"]]},{"rank" : 2,"comment" : "OneImmutable: for a family of f.p. group elements","filters" : [["CategoryFamily(IsElementOfFpGroup)"]]},{"rank" : 0,"comment" : "OneImmutable: for any object (call `OneOp' and make immutable)","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OneImmutable)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"],[]],[["IsFamily"],[]],[["IsCollection","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OneImmutable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OneImmutable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OneImmutable)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OneMutable","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 107,"comment" : "OneMutable: objects with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 107,"comment" : "OneMutable: straight line program elements","filters" : [["IsStraightLineProgElm"]]},{"rank" : 56,"comment" : "OneMutable: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsMultiplicativeElementWithInverse","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 44,"comment" : "OneMutable: for GF2 Matrix","filters" : [["IsMultiplicativeElementWithOne","IsOrdinaryMatrix","IsGF2MatrixRep"]]},{"rank" : 37,"comment" : "OneMutable: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 31,"comment" : "OneMutable: for class function","filters" : [["IsClassFunction"]]},{"rank" : 23,"comment" : "OneMutable: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "OneMutable: for a quaternion","filters" : [["IsQuaternion","IsSCAlgebraObj"]]},{"rank" : 17,"comment" : "OneMutable","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 16,"comment" : "OneMutable: Right cosets","filters" : [["IsRightCoset"]]},{"rank" : 15,"comment" : "OneMutable: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 15,"comment" : "OneMutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "OneMutable: univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "OneMutable: for a direct product element","filters" : [["IsDirectProductElement"]]},{"rank" : 14,"comment" : "OneMutable: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj"]]},{"rank" : 13,"comment" : "OneMutable: for a transformation coll","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 13,"comment" : "OneMutable: for a p-adic number","filters" : [["IsPadicNumber"]]},{"rank" : 12,"comment" : "OneMutable: defer to family","filters" : [["IsPolynomialFunction"]]},{"rank" : 12,"comment" : "OneMutable: for UEALattice element","filters" : [["IsPackedElementDefaultRep","IsUEALatticeElement"]]},{"rank" : 11,"comment" : "OneMutable: zmodnze : for element in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj"]]},{"rank" : 11,"comment" : "OneMutable: for s. c. ring element","filters" : [["IsSCRingObj"]]},{"rank" : 11,"comment" : "OneMutable: for Lie object","filters" : [["IsLieObject"]]},{"rank" : 11,"comment" : "OneMutable: for s. c. algebra element","filters" : [["IsSCAlgebraObj"]]},{"rank" : 11,"comment" : "OneMutable: for an f.p. algebra element","filters" : [["IsPackedElementDefaultRep","IsElementOfFpAlgebra"]]},{"rank" : 11,"comment" : "OneMutable: for magma ring element","filters" : [["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 10,"comment" : "OneMutable","filters" : [["IsListDefault"]]},{"rank" : 9,"comment" : "OneMutable: for an inf. bits assoc. word-with-one","filters" : [["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord","IsInfBitsAssocWord"]]},{"rank" : 9,"comment" : "OneMutable: for a 32 bits assoc. word-with-one","filters" : [["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord","Is32BitsAssocWord"]]},{"rank" : 9,"comment" : "OneMutable: for a 16 bits assoc. word-with-one","filters" : [["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord","Is16BitsAssocWord"]]},{"rank" : 9,"comment" : "OneMutable: for an 8 bits assoc. word-with-one","filters" : [["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord","Is8BitsAssocWord"]]},{"rank" : 8,"comment" : "OneMutable: assoc word in B letter rep","filters" : [["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord","IsBLetterAssocWordRep"]]},{"rank" : 8,"comment" : "OneMutable: assoc word in W letter rep","filters" : [["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord","IsWLetterAssocWordRep"]]},{"rank" : 8,"comment" : "OneMutable: for an element of a magma with zero adjoined","filters" : [["IsMultiplicativeElementWithOne","IsMagmaWithZeroAdjoinedElementRep"]]},{"rank" : 7,"comment" : "OneMutable: for an f.p. group element","filters" : [["IsElementOfFpGroup"]]},{"rank" : 7,"comment" : "OneMutable: wreath elements","filters" : [["IsWreathProductElement"]]},{"rank" : 7,"comment" : "OneMutable: for an element in a magma by mult. table","filters" : [["IsMagmaByMultiplicationTableObj"]]},{"rank" : 7,"comment" : "OneMutable: for a general mapping","filters" : [["IsGeneralMapping"]]},{"rank" : 6,"comment" : "OneMutable: for an fp monoid element","filters" : [["IsElementOfFpMonoid"]]},{"rank" : 6,"comment" : "OneMutable: rws-element","filters" : [["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 6,"comment" : "OneMutable: for a nonassoc. word-with-one","filters" : [["IsMultiplicativeElementWithOne","IsWord","IsNonassocWord"]]},{"rank" : 6,"comment" : "OneMutable: wrapped additive elements","filters" : [["IsMultiplicativeElementWithOne","IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 6,"comment" : "OneMutable: for a (non-copyable) identity element","filters" : [["IsMultiplicativeElementWithOne","IsOne","Tester(IsOne)"]]},{"rank" : 4,"comment" : "OneMutable: for finite SC Rings family","filters" : [["CategoryFamily(IsSCRingObj)"]]},{"rank" : 4,"comment" : "OneMutable: for a multiplicative-element-with-one (look at the family)","filters" : [["IsMultiplicativeElementWithOne"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OneSameMutability","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 56,"comment" : "OneSameMutability: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsMultiplicativeElementWithInverse","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 44,"comment" : "OneSameMutability: for GF2 Matrix","filters" : [["IsMultiplicativeElementWithOne","IsOrdinaryMatrix","IsGF2MatrixRep"]]},{"rank" : 15,"comment" : "OneSameMutability: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 10,"comment" : "OneSameMutability","filters" : [["IsListDefault"]]},{"rank" : 0,"comment" : "OneSameMutability: for an (immutable) object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseImmutable","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "InverseImmutable: system getter","filters" : [["IsAttributeStoringRep","Tester(InverseImmutable)"]]},{"rank" : 107,"comment" : "InverseImmutable: straight line program elements","filters" : [["IsStraightLineProgElm"]]},{"rank" : 15,"comment" : "InverseImmutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 7,"comment" : "InverseImmutable: for an identity element","filters" : [["IsMultiplicativeElementWithInverse","IsOne","Tester(IsOne)"]]},{"rank" : 6,"comment" : "InverseImmutable: for pcp elements","filters" : [["IsPcpElement"]]},{"rank" : 0,"comment" : "InverseImmutable: for any object (call `InverseOp' and make immutable)","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InverseImmutable)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InverseImmutable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InverseImmutable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InverseImmutable)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseMutable","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"]],[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 107,"comment" : "InverseMutable: objects with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 107,"comment" : "InverseMutable: straight line program elements","filters" : [["IsStraightLineProgElm"]]},{"rank" : 56,"comment" : "InverseMutable: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsMultiplicativeElementWithInverse","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 55,"comment" : "InverseMutable: for GF2 matrix","filters" : [["IsSmallList","Tester(IsSmallList)","IsMultiplicativeElementWithInverse","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsFFE))","IsGF2MatrixRep"]]},{"rank" : 54,"comment" : "InverseMutable: for plain list of GF2 vectors","filters" : [["IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 44,"comment" : "InverseMutable: for an ordinary matrix over a ring Z\/nZ","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]]},{"rank" : 44,"comment" : "InverseMutable: for default list whose rows are vectors of FFEs","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsListDefault"]]},{"rank" : 34,"comment" : "InverseMutable: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 31,"comment" : "InverseMutable: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 29,"comment" : "InverseMutable: for default list over a ring without zero divisors","filters" : [["CategoryCollections(CategoryCollections(IsZDFRE))","IsListDefault"]]},{"rank" : 23,"comment" : "InverseMutable: for a quaternion","filters" : [["IsQuaternion","IsSCAlgebraObj"]]},{"rank" : 17,"comment" : "InverseMutable","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "InverseMutable: BFElm","filters" : [["IsAlgBFRep"]]},{"rank" : 17,"comment" : "InverseMutable: AlgElm","filters" : [["IsKroneckerConstRep"]]},{"rank" : 17,"comment" : "InverseMutable: try to express as laurent polynomial","filters" : [["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 16,"comment" : "InverseMutable: Right cosets","filters" : [["IsRightCoset"]]},{"rank" : 16,"comment" : "InverseMutable: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"]]},{"rank" : 15,"comment" : "InverseMutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "InverseMutable: univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "InverseMutable: rational function","filters" : [["IsRationalFunctionsFamilyElement"]]},{"rank" : 15,"comment" : "InverseMutable: for a direct product element","filters" : [["IsDirectProductElement"]]},{"rank" : 14,"comment" : "InverseMutable","filters" : [["IsPadicExtensionNumber"]]},{"rank" : 14,"comment" : "InverseMutable","filters" : [["IsPurePadicNumber"]]},{"rank" : 13,"comment" : "InverseMutable: LAGUNA: for an element of modular group algebra","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]},{"rank" : 13,"comment" : "InverseMutable: zmodnze : for element in Z\/nZ(m) (ZModnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 12,"comment" : "InverseMutable: for binary relation on points and a set of integers","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 11,"comment" : "InverseMutable: for s. c. ring element","filters" : [["IsSCRingObj"]]},{"rank" : 11,"comment" : "InverseMutable: for Lie object","filters" : [["IsLieObject"]]},{"rank" : 11,"comment" : "InverseMutable: for s. c. algebra element","filters" : [["IsSCAlgebraObj"]]},{"rank" : 11,"comment" : "InverseMutable: for magma ring element","filters" : [["IsElementOfMagmaRingModuloRelations"]]},{"rank" : 10,"comment" : "InverseMutable: generic method for n bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 9,"comment" : "InverseMutable: assoc word in B letter rep","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord","IsBLetterAssocWordRep"]]},{"rank" : 9,"comment" : "InverseMutable: assoc word in W letter rep","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord","IsWLetterAssocWordRep"]]},{"rank" : 8,"comment" : "InverseMutable: for an assoc. word with inverse in syllable rep","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]]},{"rank" : 7,"comment" : "InverseMutable: for a transformation","filters" : [["IsTransformation"]]},{"rank" : 7,"comment" : "InverseMutable: for an element of an f.p. group","filters" : [["IsElementOfFpGroup"]]},{"rank" : 7,"comment" : "InverseMutable: wreath elements","filters" : [["IsWreathProductElement"]]},{"rank" : 7,"comment" : "InverseMutable: for an element in a magma by mult. table","filters" : [["IsMagmaByMultiplicationTableObj"]]},{"rank" : 7,"comment" : "InverseMutable: for a general mapping","filters" : [["IsGeneralMapping"]]},{"rank" : 7,"comment" : "InverseMutable: wrapped additive elements","filters" : [["IsMultiplicativeElementWithInverse","IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 7,"comment" : "InverseMutable: for a (non-copyable) identity element","filters" : [["IsMultiplicativeElementWithInverse","IsOne","Tester(IsOne)"]]},{"rank" : 6,"comment" : "InverseMutable: for pcp elements","filters" : [["IsPcpElement"]]},{"rank" : 6,"comment" : "InverseMutable: rws-element","filters" : [["IsMultiplicativeElementWithInverseByRws"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseSameMutability","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 56,"comment" : "InverseSameMutability: 8 bit matrix","filters" : [["IsTable","IsSmallList","Tester(IsSmallList)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsMultiplicativeElementWithInverse","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 55,"comment" : "InverseSameMutability: for GF2 matrix","filters" : [["IsSmallList","Tester(IsSmallList)","IsMultiplicativeElementWithInverse","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsFFE))","IsGF2MatrixRep"]]},{"rank" : 54,"comment" : "InverseSameMutability: for plain list of GF2 vectors","filters" : [["IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 44,"comment" : "InverseSameMutability: for an ordinary matrix over a ring Z\/nZ","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]]},{"rank" : 44,"comment" : "InverseSameMutability: for default list whose rows are vectors of FFEs","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsListDefault"]]},{"rank" : 29,"comment" : "InverseSameMutability: for default list over a ring without zero divisors","filters" : [["CategoryCollections(CategoryCollections(IsZDFRE))","IsListDefault"]]},{"rank" : 15,"comment" : "InverseSameMutability: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 7,"comment" : "InverseSameMutability: for a (non-copyable) identity element","filters" : [["IsMultiplicativeElementWithInverse","IsOne","Tester(IsOne)"]]},{"rank" : 0,"comment" : "InverseSameMutability: for an (immutable) object","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "\/","type" : "GAP_Operation","filters" : [[["IsExtRElement"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 129,"comment" : "\/: x with straight line perm","filters" : [["IsInt","IsPosRat"],["IsPerm","IsStraightLineProgElm"]]},{"rank" : 128,"comment" : "\/: integer and permutation with memory","filters" : [["IsInt"],["IsPerm","IsObjWithMemory"]]},{"rank" : 68,"comment" : "\/: generic method for two FLMLORs","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 66,"comment" : "\/: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 52,"comment" : "\/: generic method for two rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 51,"comment" : "\/: for two algebra modules","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsAlgebraModule","Tester(IsAlgebraModule)"],["IsAlgebraModule","Tester(IsAlgebraModule)"]]},{"rank" : 51,"comment" : "\/: for FLMLOR and empty list","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 50,"comment" : "\/: generic method for two vector spaces","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 49,"comment" : "\/: for char. table, and positions list (call `CharacterTableFactorGroup')","filters" : [["IsNearlyCharacterTable"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 47,"comment" : "\/: for a free group and an empty list of relators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 46,"comment" : "\/: for free groups and relators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsCollection"]]},{"rank" : 45,"comment" : "\/: for a semigroup and a congruence","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 40,"comment" : "\/: upol\/upol","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 36,"comment" : "\/: for internal FFE and element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 36,"comment" : "\/: for element in Z\/pZ (ModulusRep) and internal FFE","filters" : [["IsFFE","IsLogOrderedFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsInternalRep"]]},{"rank" : 36,"comment" : "\/: for FLMLOR and collection","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsCollection"]]},{"rank" : 34,"comment" : "\/: for integer and element in Z\/nZ (ModulusRep)","filters" : [["IsInt"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 34,"comment" : "\/: for element in Z\/nZ (ModulusRep) and integer","filters" : [["IsZmodnZObj","IsModulusRep"],["IsInt"]]},{"rank" : 33,"comment" : "\/: for rational and element in Z\/nZ (ModulusRep)","filters" : [["IsRat"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 33,"comment" : "\/: for element in Z\/nZ (ModulusRep) and rational","filters" : [["IsZmodnZObj","IsModulusRep"],["IsRat"]]},{"rank" : 32,"comment" : "\/: for two elements in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 32,"comment" : "\/: for unknown and cyclotomic","filters" : [["IsUnknown"],["IsCyc"]]},{"rank" : 30,"comment" : "\/","filters" : [["IsFFE"],["IsFFE"]]},{"rank" : 30,"comment" : "\/: univariate \/ univariate","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRationalFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 29,"comment" : "\/: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "\/: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 29,"comment" : "\/: for an algebra module and collection","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsAlgebraModule","Tester(IsAlgebraModule)"],["IsCollection"]]},{"rank" : 29,"comment" : "\/: for magma ring element, and integer","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsInt"]]},{"rank" : 28,"comment" : "\/","filters" : [["IsPurePadicNumber"],["IsPurePadicNumber"]]},{"rank" : 27,"comment" : "\/: method for vector space and collection","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsCollection"]]},{"rank" : 25,"comment" : "\/: for the empty set and a ring element (ResClasses)","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 25,"comment" : "\/: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 23,"comment" : "\/: for s. c. algebra element in dense vector rep. and scalar","filters" : [["IsSCAlgebraObj","IsDenseCoeffVectorRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 22,"comment" : "\/: for a checking plist vector and a scalar","filters" : [["IsPlistVectorRep","IsCheckingVector"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "\/: for a plist vector and a scalar","filters" : [["IsPlistVectorRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "\/: for s. c. algebra element and scalar","filters" : [["IsSCAlgebraObj"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 20,"comment" : "\/: generic method for n bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 19,"comment" : "\/: for residue class union and unit (ResClasses)","filters" : [["IsResidueClassUnion"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 19,"comment" : "\/: for magma ring element, and ring element","filters" : [["IsElementOfMagmaRingModuloRelations"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 18,"comment" : "\/: for multiplicative grvs which might not be IsExtRElement","filters" : [["IsMultiplicativeGeneralizedRowVector"],["IsMultiplicativeGeneralizedRowVector"]]},{"rank" : 16,"comment" : "\/: for empty list","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsFloat"]]},{"rank" : 16,"comment" : "\/: for a semigroup and an empty list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "\/: for semigroup and list of pairs","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : 14,"comment" : "\/: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "\/: for residue class union and ring element (ResClasses)","filters" : [["IsResidueClassUnion"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 12,"comment" : "\/: rws-element, rws-element","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 12,"comment" : "\/: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"],["IsMultiplicativeElementWithInverse","IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 11,"comment" : "\/: for element, and inj. & surj. general mapping","filters" : [[],["IsGeneralMapping","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)"]]},{"rank" : 9,"comment" : "\/: sliced perm","filters" : [[],["IsSlicedPerm"]]},{"rank" : 6,"comment" : "\/: for ext. r elm., and multiplicative-element-with-inverse","filters" : [["IsExtRElement"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftQuotient","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"],["IsExtLElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "LeftQuotient: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "LeftQuotient: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 25,"comment" : "LeftQuotient: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 20,"comment" : "LeftQuotient: generic method for n bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 18,"comment" : "LeftQuotient","filters" : [["IsMultiplicativeGeneralizedRowVector"],["IsMultiplicativeGeneralizedRowVector"]]},{"rank" : 12,"comment" : "LeftQuotient: rws-element, rws-element","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 9,"comment" : "LeftQuotient","filters" : [[],["IsMultiplicativeGeneralizedRowVector"]]},{"rank" : 9,"comment" : "LeftQuotient","filters" : [["IsMultiplicativeGeneralizedRowVector"],[]]},{"rank" : 6,"comment" : "LeftQuotient: for multiplicative-element-with-inverse, and ext. l elm.","filters" : [["IsMultiplicativeElementWithInverse"],["IsExtLElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "^","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],["IsMultiplicativeElement"]],[["IsListOrCollection"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10036,"comment" : "^: for zero mapping and positive integer","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],["IsInt","IsPosRat"]]},{"rank" : 10035,"comment" : "^: for identity mapping and integer","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],["IsInt"]]},{"rank" : 10034,"comment" : "^: for a pcp element and an integer","filters" : [["IsPcpElement"],["IsInt"]]},{"rank" : 128,"comment" : "^: integer and permutation with memory","filters" : [["IsInt"],["IsPerm","IsObjWithMemory"]]},{"rank" : 128,"comment" : "^: int with straight line perm","filters" : [["IsInt"],["IsPerm","IsStraightLineProgElm"]]},{"rank" : 125,"comment" : "^: objects with memory","filters" : [["IsObjWithMemory"],["IsInt"]]},{"rank" : 125,"comment" : "^: power straight line program elements","filters" : [["IsStraightLineProgElm"],["IsInt"]]},{"rank" : 80,"comment" : "^","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 80,"comment" : "^","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 66,"comment" : "^: conjugacy class of a subgroup of a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 64,"comment" : "^: for class function and group","filters" : [["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 62,"comment" : "^: for two class functions (conjugation, trivial action)","filters" : [["IsClassFunction"],["IsClassFunction"]]},{"rank" : 60,"comment" : "^: for empty matrix, and integer","filters" : [["IsTable","IsEmpty","Tester(IsEmpty)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt"]]},{"rank" : 59,"comment" : "^","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 55,"comment" : "^: for ring and list of integers (delegate to `FullMatrixModule')","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 52,"comment" : "^: for block matrix and integer","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"],["IsInt"]]},{"rank" : 51,"comment" : "^: for class function and nearly character table","filters" : [["IsClassFunction"],["IsNearlyCharacterTable"]]},{"rank" : 50,"comment" : "^: for group homomorphism and group (induction)","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "^: for class function and positive integer (pointwise powering)","filters" : [["IsClassFunction"],["IsInt","IsPosRat"]]},{"rank" : 50,"comment" : "^: using `PROD' for ring element list and ring element table","filters" : [["IsList","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 49,"comment" : "^: for matrices, use char. poly. for large exponents","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]},{"rank" : 44,"comment" : "^: for ANF automorphism and integer","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsInt"]]},{"rank" : 44,"comment" : "^: for a Frobenius automorphism, and an integer","filters" : [["IsFrobeniusAutomorphism"],["IsInt"]]},{"rank" : 44,"comment" : "^: for ring and integer (delegate to `FullRowModule')","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"]]},{"rank" : 40,"comment" : "^: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"],["IsInt"]]},{"rank" : 38,"comment" : "^: for class function and Galois automorphism","filters" : [["IsClassFunction"],["IsGeneralMapping"]]},{"rank" : 38,"comment" : "^: generic method for groups and element","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 37,"comment" : "^: for unknown and zero","filters" : [["IsUnknown"],["IsZeroCyc"]]},{"rank" : 36,"comment" : "^","filters" : [["IsMultiplicativeElementWithInverse"],["IsClassFunction"]]},{"rank" : 36,"comment" : "^: for class function and group element","filters" : [["IsClassFunction"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 36,"comment" : "^: conjugacy class of an element of a group","filters" : [["IsMultiplicativeElement"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 35,"comment" : "^: for unknown and positive integer","filters" : [["IsUnknown"],["IsInt","IsPosRat"]]},{"rank" : 34,"comment" : "^: for element in Z\/nZ (ModulusRep), and integer","filters" : [["IsZmodnZObj","IsModulusRep"],["IsInt"]]},{"rank" : 33,"comment" : "^: orbit of a point under the action of a group","filters" : [[],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "^: for binary relation on points and Zero","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsZeroCyc"]]},{"rank" : 33,"comment" : "^: for direct product element, and integer","filters" : [["IsDirectProductElement"],["IsInt"]]},{"rank" : 32,"comment" : "^: for a 32 bits assoc. word, and zero (in small integer rep)","filters" : [["IsMultiplicativeElementWithOne","Is32BitsAssocWord"],["IsZeroCyc","IsSmallIntRep"]]},{"rank" : 32,"comment" : "^: for a 16 bits assoc. word, and zero (in small integer rep)","filters" : [["IsMultiplicativeElementWithOne","Is16BitsAssocWord"],["IsZeroCyc","IsSmallIntRep"]]},{"rank" : 32,"comment" : "^: for an 8 bits assoc. word, and zero (in small integer rep)","filters" : [["IsMultiplicativeElementWithOne","Is8BitsAssocWord"],["IsZeroCyc","IsSmallIntRep"]]},{"rank" : 32,"comment" : "^: for Lie object in default representation, and positive integer","filters" : [["IsPackedElementDefaultRep","IsLieObject"],["IsInt","IsPosRat"]]},{"rank" : 31,"comment" : "^: for a 32 bits assoc. word, and a small negative integer","filters" : [["IsMultiplicativeElementWithInverse","Is32BitsAssocWord"],["IsInt","IsNegRat","IsSmallIntRep"]]},{"rank" : 31,"comment" : "^: for a 16 bits assoc. word, and a small negative integer","filters" : [["IsMultiplicativeElementWithInverse","Is16BitsAssocWord"],["IsInt","IsNegRat","IsSmallIntRep"]]},{"rank" : 31,"comment" : "^: for an 8 bits assoc. word, and a small negative integer","filters" : [["IsMultiplicativeElementWithInverse","Is8BitsAssocWord"],["IsInt","IsNegRat","IsSmallIntRep"]]},{"rank" : 31,"comment" : "^: for binary relation on points and a positive int","filters" : [["IsInt","IsPosRat"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 30,"comment" : "^: generic method for n bits pc word rep and small int","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"],["IsInt","IsSmallIntRep"]]},{"rank" : 29,"comment" : "^: for float and rational","filters" : [["IsFloat"],["IsRat"]]},{"rank" : 29,"comment" : "^: for rational and float","filters" : [["IsRat"],["IsFloat"]]},{"rank" : 29,"comment" : "^: for a 32 bits assoc. word, and a small positive integer","filters" : [["Is32BitsAssocWord"],["IsInt","IsPosRat","IsSmallIntRep"]]},{"rank" : 29,"comment" : "^: for a 16 bits assoc. word, and a small positive integer","filters" : [["Is16BitsAssocWord"],["IsInt","IsPosRat","IsSmallIntRep"]]},{"rank" : 29,"comment" : "^: for an 8 bits assoc. word, and a small positive integer","filters" : [["Is8BitsAssocWord"],["IsInt","IsPosRat","IsSmallIntRep"]]},{"rank" : 27,"comment" : "^: sliced perm","filters" : [["IsInt"],["IsSlicedPerm"]]},{"rank" : 26,"comment" : "^: assoc word in B letter rep and negative integer","filters" : [["IsAssociativeElement","IsWord","IsBLetterAssocWordRep"],["IsInt","IsNegRat"]]},{"rank" : 26,"comment" : "^: assoc word in B letter rep and positive integer","filters" : [["IsAssociativeElement","IsWord","IsBLetterAssocWordRep"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "^: assoc word in W letter rep and negative integer","filters" : [["IsAssociativeElement","IsWord","IsWLetterAssocWordRep"],["IsInt","IsNegRat"]]},{"rank" : 26,"comment" : "^: assoc word in W letter rep and positive integer","filters" : [["IsAssociativeElement","IsWord","IsWLetterAssocWordRep"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "^: for an assoc. word with inverse in syllable rep, and an integer","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsInt"]]},{"rank" : 25,"comment" : "^: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 25,"comment" : "^: for an assoc. word in syllable rep, and a positive integer","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsInt","IsPosRat"]]},{"rank" : 25,"comment" : "^: for mult. element-with-one, and zero","filters" : [["IsMultiplicativeElementWithOne"],["IsZeroCyc"]]},{"rank" : 24,"comment" : "^: rws-element ^ int","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsInt"]]},{"rank" : 24,"comment" : "^: for mult. element-with-inverse, and negative integer","filters" : [["IsMultiplicativeElementWithInverse"],["IsInt","IsNegRat"]]},{"rank" : 22,"comment" : "^: for mult. element, and positive integer","filters" : [["IsMultiplicativeElement"],["IsInt","IsPosRat"]]},{"rank" : 20,"comment" : "^: generic method for n bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 20,"comment" : "^: catch wrong root taking","filters" : [["IsMultiplicativeElement"],["IsRat"]]},{"rank" : 19,"comment" : "^: for an algebra element and an element of an algebra module","filters" : [["IsPackedElementDefaultRep","IsRightAlgebraModuleElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 19,"comment" : "^: for an algebra element and an element of an algebra module","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsLeftAlgebraModuleElement"]]},{"rank" : 18,"comment" : "^: for a Lie algebra element and a weight rep element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 17,"comment" : "^: sliced perm","filters" : [["IsPerm"],["IsSlicedPerm"]]},{"rank" : 14,"comment" : "^: for two general mappings","filters" : [["IsGeneralMapping"],["IsGeneralMapping"]]},{"rank" : 13,"comment" : "^: for binary relation on points and a set of integers","filters" : [["IsListOrCollection"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 12,"comment" : "^: for two pcp elements","filters" : [["IsPcpElement"],["IsPcpElement"]]},{"rank" : 12,"comment" : "^: rws-element ^ rws-element","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 12,"comment" : "^: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"],["IsMultiplicativeElementWithInverse","IsAdditiveElementAsMultiplicativeElementRep"]]},{"rank" : 10,"comment" : "^: for two mult.-elm.-with-inverse","filters" : [["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 9,"comment" : "^: sliced perm","filters" : [[],["IsSlicedPermInv"]]},{"rank" : 7,"comment" : "^: for element in the source, and general mapping","filters" : [[],["IsGeneralMapping"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Comm","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Comm: for arguments enclosed in list brackets (ResClasses)","filters" : [["IsList"]]}],"2args" : [{"rank" : 20,"comment" : "Comm: generic method for n bits pc word rep","filters" : [["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"],["IsMultiplicativeElementWithInverseByPolycyclicCollector","IsNBitsPcWordRep"]]},{"rank" : 12,"comment" : "Comm: for two pcp elements","filters" : [["IsPcpElement"],["IsPcpElement"]]},{"rank" : 12,"comment" : "Comm: rws-element, rws-element","filters" : [["IsMultiplicativeElementWithInverseByRws"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 10,"comment" : "Comm: for two mult.-elm.-with-inverse","filters" : [["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieBracket","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "LieBracket: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "mod","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 58,"comment" : "mod: for `Integers', and integer","filters" : [["IsIntegers"],["IsInt"]]},{"rank" : 49,"comment" : "mod: zmodnze : for RingOfIntegralCyclotomics and a positive integer","filters" : [["Tester(IsRingOfIntegralCyclotomics)"],["IsInt","IsPosRat"]]},{"rank" : 44,"comment" : "mod: two induced pcgs","filters" : [["IsInducedPcgs"],["IsInducedPcgs"]]},{"rank" : 43,"comment" : "mod: parent pcgs mod induced pcgs","filters" : [["IsPcgs"],["IsInducedPcgs"]]},{"rank" : 42,"comment" : "mod: for a vector and a lattice (ResClasses)","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 42,"comment" : "mod: two induced pcgs","filters" : [["IsPcgs"],["IsPcgs"]]},{"rank" : 42,"comment" : "mod: two parent pcgs","filters" : [["IsPcgs"],["IsPcgs"]]},{"rank" : 41,"comment" : "mod: for ord. char. table, and pos. integer (call `BrauerTable')","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "mod: two modulo pcgs","filters" : [["IsModuloPcgs"],["IsModuloPcgs"]]},{"rank" : 38,"comment" : "mod: laurent","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 37,"comment" : "mod: reduction of univariate rational polynomial at a prime","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsInt"]]},{"rank" : 34,"comment" : "mod: AlgElm","filters" : [["IsAlgebraicElement"],["IsInt","IsPosRat"]]},{"rank" : 34,"comment" : "mod","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 32,"comment" : "mod: reduction of general rational polynomial at a prime","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsInt"]]},{"rank" : 17,"comment" : "mod","filters" : [[],["IsSmallList","Tester(IsSmallList)","IsListDefault"]]},{"rank" : 17,"comment" : "mod","filters" : [["IsSmallList","Tester(IsSmallList)","IsListDefault"],[]]},{"rank" : 0,"comment" : "mod:  fallback method to test conditions","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Int","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "Int: system getter","filters" : [["IsAttributeStoringRep","Tester(Int)"]]},{"rank" : 20,"comment" : "Int","filters" : [["IsUnicodeCharacter"]]},{"rank" : 18,"comment" : "Int: for an integer","filters" : [["IsInt"]]},{"rank" : 17,"comment" : "Int: for a rational","filters" : [["IsRat"]]},{"rank" : 16,"comment" : "Int: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"]]},{"rank" : 16,"comment" : "Int: for a cyclotomic","filters" : [["IsCyc"]]},{"rank" : 15,"comment" : "Int: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 15,"comment" : "Int: for an FFE","filters" : [["IsFFE"]]},{"rank" : 5,"comment" : "Int: for strings","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Int)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Int): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Int): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Int)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Rat","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "Rat: system getter","filters" : [["IsAttributeStoringRep","Tester(Rat)"]]},{"rank" : 16,"comment" : "Rat: for float intervals","filters" : [["IsFloatInterval"]]},{"rank" : 13,"comment" : "Rat: for floats","filters" : [["IsFloat"]]},{"rank" : 5,"comment" : "Rat: for strings","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Rat)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Rat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Rat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Rat)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sqrt","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 17,"comment" : "Sqrt: for a rational","filters" : [["IsRat"]]},{"rank" : 15,"comment" : "Sqrt: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Root","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "Root: for two integers","filters" : [["IsInt"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Log","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],["IsMultiplicativeElement"]],[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "Log: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [{"rank" : 36,"comment" : "Log: for two integers","filters" : [["IsInt"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Characteristic","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "Characteristic: system getter","filters" : [["IsAttributeStoringRep","Tester(Characteristic)"]]},{"rank" : 43,"comment" : "Characteristic: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 30,"comment" : "Characteristic: for sc rings and their subrings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)","CategoryCollections(IsSCRingObj)"]]},{"rank" : 17,"comment" : "Characteristic: for local formation","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsSaturated","Tester(IsSaturated)","Tester(LocalDefinitionFunction)"]]},{"rank" : 17,"comment" : "Characteristic: for internal FFE","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 15,"comment" : "Characteristic: for formation product","filters" : [["IsFormationProductRep"]]},{"rank" : 15,"comment" : "Characteristic: for Schunck class w\/boundary","filters" : [["IsSchunckClass","Tester(IsSchunckClass)","Tester(BoundaryFunction)"]]},{"rank" : 15,"comment" : "Characteristic: for Fitting product","filters" : [["IsFittingProductRep"]]},{"rank" : 15,"comment" : "Characteristic: alg elm","filters" : [["IsAlgebraicElement"]]},{"rank" : 14,"comment" : "Characteristic: delegate to family (magma)","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 7,"comment" : "Characteristic: for union of group classes","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByUnionRep"]]},{"rank" : 7,"comment" : "Characteristic: for intersection of group classes","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByIntersectionRep"]]},{"rank" : 5,"comment" : "Characteristic: for an elements family of a magma ring quotient","filters" : [["IsElementOfMagmaRingModuloSpanOfZeroFamily"]]},{"rank" : 4,"comment" : "Characteristic: for generic grp class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 4,"comment" : "Characteristic: for an elements family of an fp subalgebra","filters" : [["CategoryFamily(IsElementOfFpAlgebra)"]]},{"rank" : 4,"comment" : "Characteristic: delegate to family (element)","filters" : [["IsNearAdditiveElementWithZero","IsAdditiveElement"]]},{"rank" : 2,"comment" : "Characteristic: for family delegate to elements family","filters" : [["IsFamily","Tester(ElementsFamily)"]]},{"rank" : 0,"comment" : "Characteristic: ask the family","filters" : [[]]},{"rank" : -10000,"comment" : "Characteristic: return fail","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Characteristic)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Characteristic): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Characteristic): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Characteristic)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Order","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "Order: system getter","filters" : [["IsAttributeStoringRep","Tester(Order)"]]},{"rank" : 117,"comment" : "Order: straight line program elements","filters" : [["IsStraightLineProgElm"]]},{"rank" : 107,"comment" : "Order: object with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 45,"comment" : "Order: ordinary matrix of finite field elements","filters" : [["IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 45,"comment" : "Order: for a matrix of cyclotomics, with Minkowski kernel","filters" : [["IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsCyclotomic))"]]},{"rank" : 33,"comment" : "Order: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 32,"comment" : "Order: generic method for ordinary matrices","filters" : [["IsOrdinaryMatrix"]]},{"rank" : 31,"comment" : "Order: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 17,"comment" : "Order: for automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 17,"comment" : "Order: for an internal FFE","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 16,"comment" : "Order: for element in Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"]]},{"rank" : 16,"comment" : "Order: for a cyclotomic","filters" : [["IsCyc"]]},{"rank" : 15,"comment" : "Order","filters" : [["IsFFE"]]},{"rank" : 15,"comment" : "Order: for a general FFE","filters" : [["IsFFE"]]},{"rank" : 8,"comment" : "Order: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "Order: for a transformation","filters" : [["IsTransformation"]]},{"rank" : 7,"comment" : "Order: fp group element","filters" : [["IsElementOfFpGroup"]]},{"rank" : 7,"comment" : "Order: method for a pc-element","filters" : [["IsMultiplicativeElementWithOne"]]},{"rank" : 7,"comment" : "Order: free group element","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]},{"rank" : 6,"comment" : "Order","filters" : [["IsPcpElement"]]},{"rank" : 4,"comment" : "Order: for a mult. element-with-one","filters" : [["IsMultiplicativeElementWithOne"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Order)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Order): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Order): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Order)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithOne"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormedRowVector","type" : "GAP_Operation","filters" : [[["IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElementWithInverse)","IsOddAdditiveNestingDepthObject"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "NormedRowVector: system getter","filters" : [["IsAttributeStoringRep","Tester(NormedRowVector)"]]},{"rank" : 32,"comment" : "NormedRowVector: for GF(2) vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElementWithInverse)","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 23,"comment" : "NormedRowVector: for a row vector of scalars","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElementWithInverse)","IsOddAdditiveNestingDepthObject"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormedRowVector)","type" : "GAP_Operation","filters" : [[["IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElementWithInverse)","IsOddAdditiveNestingDepthObject"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormedRowVector): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormedRowVector): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormedRowVector)","type" : "GAP_Operation","filters" : [[["IsHomogeneousList","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","CategoryCollections(IsMultiplicativeElementWithInverse)","IsOddAdditiveNestingDepthObject"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCommutativeFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsCommutativeFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCommutativeFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCommutativeFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCommutativeFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCommutativeFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCommutativeFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSkewFieldFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsSkewFieldFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSkewFieldFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSkewFieldFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSkewFieldFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSkewFieldFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSkewFieldFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUFDFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsUFDFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(IsUFDFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsUFDFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsUFDFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsUFDFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsUFDFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditiveElementsAsMultiplicativeElementsFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AdditiveElementsAsMultiplicativeElementsFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(AdditiveElementsAsMultiplicativeElementsFamily)"]]},{"rank" : 1,"comment" : "AdditiveElementsAsMultiplicativeElementsFamily: for families of additive elements","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdditiveElementsAsMultiplicativeElementsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdditiveElementsAsMultiplicativeElementsFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdditiveElementsAsMultiplicativeElementsFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdditiveElementsAsMultiplicativeElementsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditiveElementAsMultiplicativeElement","type" : "GAP_Operation","filters" : [[["IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "AdditiveElementAsMultiplicativeElement: system getter","filters" : [["IsAttributeStoringRep","Tester(AdditiveElementAsMultiplicativeElement)"]]},{"rank" : 5,"comment" : "AdditiveElementAsMultiplicativeElement: for additive elements with inverse","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement"]]},{"rank" : 4,"comment" : "AdditiveElementAsMultiplicativeElement: for additive elements with zero","filters" : [["IsNearAdditiveElementWithZero","IsAdditiveElement"]]},{"rank" : 3,"comment" : "AdditiveElementAsMultiplicativeElement: for additive elements","filters" : [["IsAdditiveElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdditiveElementAsMultiplicativeElement)","type" : "GAP_Operation","filters" : [[["IsAdditiveElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdditiveElementAsMultiplicativeElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdditiveElementAsMultiplicativeElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdditiveElementAsMultiplicativeElement)","type" : "GAP_Operation","filters" : [[["IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingElement","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 103,"comment" : "UnderlyingElement: using 16Bits_ExtRepOfObj","filters" : [["Is32BitsPcWordRep"]]},{"rank" : 103,"comment" : "UnderlyingElement: using 16Bits_ExtRepOfObj","filters" : [["Is16BitsPcWordRep"]]},{"rank" : 103,"comment" : "UnderlyingElement: using 8Bits_ExtRepOfObj","filters" : [["Is8BitsPcWordRep"]]},{"rank" : 9,"comment" : "UnderlyingElement: for an element of an f.p. group (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpGroup"]]},{"rank" : 8,"comment" : "UnderlyingElement: for an element of an fp monoid (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpMonoid"]]},{"rank" : 8,"comment" : "UnderlyingElement","filters" : [["IsPackedElementDefaultRep","IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 7,"comment" : "UnderlyingElement: for an element of an f.p. semigroup (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpSemigroup"]]},{"rank" : 7,"comment" : "UnderlyingElement: for an element of a free group","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]},{"rank" : 5,"comment" : "UnderlyingElement: wrapped additive elements","filters" : [["IsAdditiveElementAsMultiplicativeElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIdempotent","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "IsIdempotent: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIdempotent)"]]},{"rank" : 7,"comment" : "IsIdempotent: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "IsIdempotent: for a transformation","filters" : [["IsTransformation"]]},{"rank" : 5,"comment" : "IsIdempotent: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]},{"rank" : 3,"comment" : "IsIdempotent: multiplicative element","filters" : [["IsMultiplicativeElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIdempotent)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIdempotent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIdempotent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIdempotent)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LargeGaloisField","type" : "GAP_Operation","filters" : [[["IsInt"]],[["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "LargeGaloisField","filters" : [["IsInt","IsPosRat"]]}],"2args" : [{"rank" : 38,"comment" : "LargeGaloisField","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 38,"comment" : "LargeGaloisField","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeFFE","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "DegreeFFE: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeFFE)"]]},{"rank" : 43,"comment" : "DegreeFFE: for 8 bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)","Is8BitVectorRep"]]},{"rank" : 42,"comment" : "DegreeFFE: for a matrix of FFEs","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 40,"comment" : "DegreeFFE: for GF(2) vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)","IsGF2VectorRep"]]},{"rank" : 31,"comment" : "DegreeFFE: for a row vector of FFEs","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 18,"comment" : "DegreeFFE: for element in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 17,"comment" : "DegreeFFE","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "DegreeFFE: for internal FFE","filters" : [["IsFFE","IsInternalRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeFFE)","type" : "GAP_Operation","filters" : [[["IsFFE"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeFFE): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeFFE): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeFFE)","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LogFFE","type" : "GAP_Operation","filters" : [[["IsFFE"],["IsFFE"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "LogFFE: for two elements in Z\/pZ (ModulusRep)","filters" : [["IsFFE","IsZmodnZObj","IsModulusRep"],["IsFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 34,"comment" : "LogFFE","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE","IsInternalRep"]]},{"rank" : 34,"comment" : "LogFFE","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 34,"comment" : "LogFFE","filters" : [["IsFFE","IsCoeffsModConwayPolRep"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 34,"comment" : "LogFFE: for two internal FFEs","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]},{"rank" : 30,"comment" : "LogFFE: for two FFEs (in a prime field)","filters" : [["IsFFE"],["IsFFE"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntFFE","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IntFFE: system getter","filters" : [["IsAttributeStoringRep","Tester(IntFFE)"]]},{"rank" : 18,"comment" : "IntFFE","filters" : [["IsFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 17,"comment" : "IntFFE","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "IntFFE: for internal FFE","filters" : [["IsFFE","IsInternalRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IntFFE)","type" : "GAP_Operation","filters" : [[["IsFFE"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IntFFE): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IntFFE): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IntFFE)","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntFFESymm","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IntFFESymm: system getter","filters" : [["IsAttributeStoringRep","Tester(IntFFESymm)"]]},{"rank" : 31,"comment" : "IntFFESymm: vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 16,"comment" : "IntFFESymm: Z\/nZ (ModulusRep)","filters" : [["IsZmodnZObj","IsModulusRep"]]},{"rank" : 15,"comment" : "IntFFESymm: FFE","filters" : [["IsFFE"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IntFFESymm)","type" : "GAP_Operation","filters" : [[["IsFFE"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IntFFESymm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IntFFESymm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IntFFESymm)","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntVecFFE","type" : "GAP_Operation","filters" : [[["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 31,"comment" : "IntVecFFE: for a row vector of FFEs","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsInternalFFE","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "AsInternalFFE: system getter","filters" : [["IsAttributeStoringRep","Tester(AsInternalFFE)"]]},{"rank" : 17,"comment" : "AsInternalFFE","filters" : [["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 17,"comment" : "AsInternalFFE","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 16,"comment" : "AsInternalFFE","filters" : [["IsFFE","IsZmodnZObj"]]},{"rank" : 0,"comment" : "AsInternalFFE","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsInternalFFE)","type" : "GAP_Operation","filters" : [[["IsFFE"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsInternalFFE): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsInternalFFE): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsInternalFFE)","type" : "GAP_Operation","filters" : [[["IsFFE"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RootFFE","type" : "GAP_Operation","filters" : [[["IsFFE"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "RootFFE: for modulus rep, using RootMod","filters" : [["IsFFE","IsZmodnZObj","IsModulusRep"],["IsInt","IsPosRat"]]},{"rank" : 34,"comment" : "RootFFE: use LogFFE","filters" : [["IsFFE"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfDomain","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "GeneratorsOfDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfDomain)"]]},{"rank" : 8,"comment" : "GeneratorsOfDomain","filters" : [["IsAttributeStoringRep","IsCollection","Tester(AsList)","IsGeneralizedDomain"]]},{"rank" : 5,"comment" : "GeneratorsOfDomain: for a domain (delegate to `AsList')","filters" : [["IsCollection","IsGeneralizedDomain"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfDomain)","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "Setter(GeneratorsOfDomain): for an underlying relation and a list of direct product elements","filters" : [["IsAttributeStoringRep","IsCollection","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)","Tester(UnderlyingGeneralMapping)"],["CategoryCollections(IsDirectProductElement)"]]},{"rank" : 2,"comment" : "Setter(GeneratorsOfDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfDomain)","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DomainByGenerators","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "DomainByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 18,"comment" : "DomainByGenerators: for family and empty list","filters" : [["IsFamily"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 6,"comment" : "DomainByGenerators: for family and list & collection","filters" : [["IsFamily"],["IsList","IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParentAttr","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "ParentAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(ParentAttr)"]]},{"rank" : 17,"comment" : "ParentAttr: for a subsemigroup of a Rees 0-matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "ParentAttr: for a subsemigroup of a Rees matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ParentAttr)","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10,"comment" : "Setter(ParentAttr): method that calls 'UseSubsetRelation'","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 2,"comment" : "Setter(ParentAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ParentAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ParentAttr)","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIntegralCyclotomic","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsIntegralCyclotomic: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIntegralCyclotomic)"]]},{"rank" : 1,"comment" : "IsIntegralCyclotomic: for an internally represented cyclotomic","filters" : [["IsInternalRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIntegralCyclotomic)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIntegralCyclotomic): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIntegralCyclotomic): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIntegralCyclotomic)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Conductor","type" : "GAP_Operation","filters" : [[["IsCyc"]],[["CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20019,"comment" : "Conductor: system getter","filters" : [["Tester(CONDUCTOR)","IsAttributeStoringRep"]]},{"rank" : 65,"comment" : "Conductor: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 2,"comment" : "Conductor: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CONDUCTOR)","type" : "GAP_Operation","filters" : [[["IsCyc"],[]],[["CategoryCollections(IsCyclotomic)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CONDUCTOR): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CONDUCTOR): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CONDUCTOR)","type" : "GAP_Operation","filters" : [[["IsCyc"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GaloisCyc","type" : "GAP_Operation","filters" : [[["IsCyc"],["IsInt"]],[["CategoryCollections(IsCyclotomic)"],["IsInt"]],[["CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 56,"comment" : "GaloisCyc: for a class function, and an integer","filters" : [["CategoryCollections(IsCyclotomic)","IsClassFunction"],["IsInt"]]},{"rank" : 45,"comment" : "GaloisCyc: for a list of cyclotomics, and an integer","filters" : [["IsList","CategoryCollections(IsCyclotomic)"],["IsInt"]]},{"rank" : 44,"comment" : "GaloisCyc: for a list of lists of cyclotomics, and an integer","filters" : [["IsList","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsEqualSet","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "IsEqualSet: for two internally represented lists","filters" : [["IsList","IsInternalRep"],["IsList","IsInternalRep"]]},{"rank" : 4,"comment" : "IsEqualSet: for two lists","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubsetSet","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "IsSubsetSet: for two internally represented lists","filters" : [["IsList","IsInternalRep"],["IsList","IsInternalRep"]]},{"rank" : 4,"comment" : "IsSubsetSet: for two lists","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AddSet","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "AddSet: for mutable internally represented list, and object","filters" : [["IsMutable","IsList","IsInternalRep"],[]]},{"rank" : 4,"comment" : "AddSet: for mutable list, and object","filters" : [["IsMutable","IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RemoveSet","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "RemoveSet: for mutable internally represented list, and object","filters" : [["IsMutable","IsList","IsInternalRep"],[]]},{"rank" : 4,"comment" : "RemoveSet: for mutable list, and object","filters" : [["IsMutable","IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UniteSet","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 40,"comment" : "UniteSet: for two internally represented lists, the first being mutable","filters" : [["IsMutable","IsList","IsInternalRep"],["IsList","IsInternalRep"]]},{"rank" : 6,"comment" : "UniteSet: for two lists, the first being mutable","filters" : [["IsMutable","IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntersectSet","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 82,"comment" : "IntersectSet: for two ranges","filters" : [["IsMutable","IsRange","IsRangeRep"],["IsRange","IsRangeRep"]]},{"rank" : 40,"comment" : "IntersectSet: for two internally represented lists, the first being mutable","filters" : [["IsMutable","IsList","IsInternalRep"],["IsList","IsInternalRep"]]},{"rank" : 6,"comment" : "IntersectSet: for two lists, the first being mutable","filters" : [["IsMutable","IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubtractSet","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 40,"comment" : "SubtractSet: for two internally represented lists, the first being mutable","filters" : [["IsMutable","IsList","IsInternalRep"],["IsList","IsInternalRep"]]},{"rank" : 6,"comment" : "SubtractSet: for two lists, the first being mutable","filters" : [["IsMutable","IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : ".","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 65,"comment" : ".: generators of a free group containing the whole family","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : 61,"comment" : ".: generators of a s.c. algebra containing the whole family","filters" : [["Tester(GeneratorsOfLeftOperatorRing)","CategoryCollections(IsSCAlgebraObj)","IsFullSCAlgebra","Tester(IsFullSCAlgebra)"],["IsInt","IsPosRat"]]},{"rank" : 58,"comment" : ".: generators of a magma ring-with-one containing the whole family","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftOperatorRingWithOne)","IsMagmaRingModuloRelations"],["IsInt","IsPosRat"]]},{"rank" : 55,"comment" : ".: generators of a magma ring containing the whole family","filters" : [["Tester(GeneratorsOfLeftOperatorRing)","IsMagmaRingModuloRelations"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : ".: group generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 51,"comment" : ".: generators of a whole SC ring","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)","CategoryCollections(IsSCRingObj)"],["IsInt","IsPosRat"]]},{"rank" : 46,"comment" : ".: polynomial ring indeterminates","filters" : [["IsPolynomialRing"],["IsInt","IsPosRat"]]},{"rank" : 44,"comment" : ".: for an inverse monoid with generators and pos int","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseMonoid)"],["IsInt","IsPosRat"]]},{"rank" : 39,"comment" : ".: for an inverse semigroup with generators and pos int","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"],["IsInt","IsPosRat"]]},{"rank" : 38,"comment" : ".: for class names of a nearly character table","filters" : [["IsNearlyCharacterTable"],["IsInt"]]},{"rank" : 38,"comment" : ".: for a monoid with generators and pos int","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 37,"comment" : ".: generators of a free magma-with-one containing the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","CategoryCollections(IsWord)"],["IsInt","IsPosRat"]]},{"rank" : 34,"comment" : ".: generators of a free magma containing the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","Tester(GeneratorsOfMagma)","CategoryCollections(IsWord)"],["IsInt","IsPosRat"]]},{"rank" : 33,"comment" : ".: for a semigroup with generators and pos int","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 24,"comment" : ".: for a presentation in default representation","filters" : [["IsPresentation","IsPresentationDefaultRep"],["IsInt","IsPosRat"]]},{"rank" : 1,"comment" : ".: for a root system and a record component","filters" : [["IsRootSystem"],[]]},{"rank" : 0,"comment" : ".: catch error","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBound.","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 24,"comment" : "IsBound.: for a presentation in default representation","filters" : [["IsPresentation","IsPresentationDefaultRep"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "IsBound.: catch error","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : ".:=","type" : "GAP_Operation","filters" : [[[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 25,"comment" : ".:=: for a mutable presentation in default representation","filters" : [["IsMutable","IsPresentation","IsPresentationDefaultRep"],["IsInt","IsPosRat"],[]]},{"rank" : 0,"comment" : ".:=: catch error","filters" : [[],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Unbind.","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 25,"comment" : "Unbind.: for a mutable presentation in default representation","filters" : [["IsMutable","IsPresentation","IsPresentationDefaultRep"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "Unbind.: catch error","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RecNames","type" : "GAP_Operation","filters" : [[["IsRecord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "RecNames: system getter","filters" : [["IsAttributeStoringRep","Tester(RecNames)"]]},{"rank" : 2,"comment" : "RecNames: for a record in internal representation","filters" : [["IsRecord","IsInternalRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RecNames)","type" : "GAP_Operation","filters" : [[["IsRecord"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RecNames): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RecNames): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RecNames)","type" : "GAP_Operation","filters" : [[["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SUM_FFE_LARGE","type" : "GAP_Operation","filters" : [[["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "SUM_FFE_LARGE","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]},{"rank" : 30,"comment" : "SUM_FFE_LARGE","filters" : [["IsFFE"],["IsFFE"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DIFF_FFE_LARGE","type" : "GAP_Operation","filters" : [[["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "DIFF_FFE_LARGE","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]},{"rank" : 30,"comment" : "DIFF_FFE_LARGE","filters" : [["IsFFE"],["IsFFE"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PROD_FFE_LARGE","type" : "GAP_Operation","filters" : [[["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "PROD_FFE_LARGE","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]},{"rank" : 30,"comment" : "PROD_FFE_LARGE","filters" : [["IsFFE"],["IsFFE"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QUO_FFE_LARGE","type" : "GAP_Operation","filters" : [[["IsFFE"],["IsFFE"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "QUO_FFE_LARGE","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]},{"rank" : 34,"comment" : "QUO_FFE_LARGE","filters" : [["IsFFE","IsInternalRep"],["IsFFE","IsInternalRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZOp","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "ZOp","filters" : [["IsInt","IsPosRat"]]},{"rank" : 19,"comment" : "ZOp","filters" : [["IsInt","IsPosRat"]]}],"2args" : [{"rank" : 38,"comment" : "ZOp","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRectangularTable","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsRectangularTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRectangularTable)"]]},{"rank" : 22,"comment" : "IsRectangularTable: kernel method for a plain list","filters" : [["IsTable","IsPlistRep"]]},{"rank" : 2,"comment" : "IsRectangularTable: generic","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRectangularTable)","type" : "GAP_Operation","filters" : [[["IsList"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRectangularTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRectangularTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRectangularTable)","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SmallestGeneratorPerm","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "SmallestGeneratorPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(SmallestGeneratorPerm)"]]},{"rank" : 9,"comment" : "SmallestGeneratorPerm: for internally represented permutation","filters" : [["IsPerm","IsInternalRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SmallestGeneratorPerm)","type" : "GAP_Operation","filters" : [[["IsPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SmallestGeneratorPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SmallestGeneratorPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SmallestGeneratorPerm)","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SmallestMovedPoint","type" : "GAP_Operation","filters" : [[["IsPerm"]],[["CategoryCollections(IsPerm)"]],[["IsList","IsEmpty","Tester(IsEmpty)"]],[["IsTransformation"]],[["CategoryCollections(IsTransformation)"]],[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "SmallestMovedPoint: system getter","filters" : [["IsAttributeStoringRep","Tester(SmallestMovedPoint)"]]},{"rank" : 58,"comment" : "SmallestMovedPoint: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "SmallestMovedPoint: for a collection of permutations","filters" : [["CategoryCollections(IsPerm)"]]},{"rank" : 23,"comment" : "SmallestMovedPoint: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "SmallestMovedPoint: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "SmallestMovedPoint: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "SmallestMovedPoint: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 13,"comment" : "SmallestMovedPoint: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 8,"comment" : "SmallestMovedPoint: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "SmallestMovedPoint: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "SmallestMovedPoint: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SmallestMovedPoint)","type" : "GAP_Operation","filters" : [[["IsPerm"],[]],[["CategoryCollections(IsPerm)"],[]],[["IsList","IsEmpty","Tester(IsEmpty)"],[]],[["IsTransformation"],[]],[["CategoryCollections(IsTransformation)"],[]],[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SmallestMovedPoint): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SmallestMovedPoint): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SmallestMovedPoint)","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LargestMovedPoint","type" : "GAP_Operation","filters" : [[["IsPerm"]],[["CategoryCollections(IsPerm)"]],[["IsList","IsEmpty","Tester(IsEmpty)"]],[["IsTransformation"]],[["CategoryCollections(IsTransformation)"]],[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "LargestMovedPoint: system getter","filters" : [["IsAttributeStoringRep","Tester(LargestMovedPoint)"]]},{"rank" : 110,"comment" : "LargestMovedPoint: permutation with memory","filters" : [["IsPerm","IsObjWithMemory"]]},{"rank" : 110,"comment" : "LargestMovedPoint: straight line program permutation","filters" : [["IsPerm","IsStraightLineProgElm"]]},{"rank" : 58,"comment" : "LargestMovedPoint: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "LargestMovedPoint: for a collection of permutations","filters" : [["CategoryCollections(IsPerm)"]]},{"rank" : 23,"comment" : "LargestMovedPoint: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "LargestMovedPoint: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "LargestMovedPoint: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "LargestMovedPoint: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 13,"comment" : "LargestMovedPoint: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 9,"comment" : "LargestMovedPoint: for an internal permutation","filters" : [["IsPerm","IsInternalRep"]]},{"rank" : 7,"comment" : "LargestMovedPoint: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "LargestMovedPoint: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LargestMovedPoint)","type" : "GAP_Operation","filters" : [[["IsPerm"],[]],[["CategoryCollections(IsPerm)"],[]],[["IsList","IsEmpty","Tester(IsEmpty)"],[]],[["IsTransformation"],[]],[["CategoryCollections(IsTransformation)"],[]],[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LargestMovedPoint): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LargestMovedPoint): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LargestMovedPoint)","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrMovedPoints","type" : "GAP_Operation","filters" : [[["IsPerm"]],[["CategoryCollections(IsPerm)"]],[["IsList","IsEmpty","Tester(IsEmpty)"]],[["IsTransformation"]],[["CategoryCollections(IsTransformation)"]],[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "NrMovedPoints: system getter","filters" : [["IsAttributeStoringRep","Tester(NrMovedPoints)"]]},{"rank" : 58,"comment" : "NrMovedPoints: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "NrMovedPoints: for a collection of permutations","filters" : [["CategoryCollections(IsPerm)"]]},{"rank" : 23,"comment" : "NrMovedPoints: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "NrMovedPoints: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "NrMovedPoints: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "NrMovedPoints: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 13,"comment" : "NrMovedPoints: for a transformation coll","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 8,"comment" : "NrMovedPoints: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "NrMovedPoints: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "NrMovedPoints: for a tranformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrMovedPoints)","type" : "GAP_Operation","filters" : [[["IsPerm"],[]],[["CategoryCollections(IsPerm)"],[]],[["IsList","IsEmpty","Tester(IsEmpty)"],[]],[["IsTransformation"],[]],[["CategoryCollections(IsTransformation)"],[]],[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrMovedPoints): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrMovedPoints): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrMovedPoints)","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MovedPoints","type" : "GAP_Operation","filters" : [[["IsPerm"]],[["CategoryCollections(IsPerm)"]],[["IsList","IsEmpty","Tester(IsEmpty)"]],[["IsTransformation"]],[["CategoryCollections(IsTransformation)"]],[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "MovedPoints: system getter","filters" : [["IsAttributeStoringRep","Tester(MovedPoints)"]]},{"rank" : 58,"comment" : "MovedPoints: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "MovedPoints: for a collection of permutations","filters" : [["CategoryCollections(IsPerm)"]]},{"rank" : 23,"comment" : "MovedPoints: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "MovedPoints: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "MovedPoints: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "MovedPoints: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 13,"comment" : "MovedPoints: for a transformation coll","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 8,"comment" : "MovedPoints: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "MovedPoints: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "MovedPoints: for a tranformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MovedPoints)","type" : "GAP_Operation","filters" : [[["IsPerm"],[]],[["CategoryCollections(IsPerm)"],[]],[["IsList","IsEmpty","Tester(IsEmpty)"],[]],[["IsTransformation"],[]],[["CategoryCollections(IsTransformation)"],[]],[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MovedPoints): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MovedPoints): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MovedPoints)","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SignPerm","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "SignPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(SignPerm)"]]},{"rank" : 111,"comment" : "SignPerm: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"]]},{"rank" : 110,"comment" : "SignPerm: for a permutation with memory","filters" : [["IsPerm","IsObjWithMemory"]]},{"rank" : 9,"comment" : "SignPerm: for internally represented permutation","filters" : [["IsPerm","IsInternalRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SignPerm)","type" : "GAP_Operation","filters" : [[["IsPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SignPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SignPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SignPerm)","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CycleStructurePerm","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "CycleStructurePerm: system getter","filters" : [["IsAttributeStoringRep","Tester(CycleStructurePerm)"]]},{"rank" : 111,"comment" : "CycleStructurePerm: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"]]},{"rank" : 110,"comment" : "CycleStructurePerm: for a permutation with memory","filters" : [["IsPerm","IsObjWithMemory"]]},{"rank" : 9,"comment" : "CycleStructurePerm: internal","filters" : [["IsPerm","IsInternalRep"]]},{"rank" : 8,"comment" : "CycleStructurePerm: generic method","filters" : [["IsPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CycleStructurePerm)","type" : "GAP_Operation","filters" : [[["IsPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CycleStructurePerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CycleStructurePerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CycleStructurePerm)","type" : "GAP_Operation","filters" : [[["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedPerm","type" : "GAP_Operation","filters" : [[["IsPerm"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 112,"comment" : "RestrictedPerm: for a permutation with memory and a list of integers","filters" : [["IsPerm","IsObjWithMemory"],["IsList"]]},{"rank" : 11,"comment" : "RestrictedPerm: use kernel method, test","filters" : [["IsPerm","IsInternalRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedPermNC","type" : "GAP_Operation","filters" : [[["IsPerm"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 113,"comment" : "RestrictedPermNC: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"],["IsList"]]},{"rank" : 11,"comment" : "RestrictedPermNC: kernel method","filters" : [["IsPerm","IsInternalRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DistancePerms","type" : "GAP_Operation","filters" : [[["IsPerm"],["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 18,"comment" : "DistancePerms: for kernel permutations","filters" : [["IsPerm","IsInternalRep"],["IsPerm","IsInternalRep"]]},{"rank" : 16,"comment" : "DistancePerms: for general permutations","filters" : [["IsPerm"],["IsPerm"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AddRowVector","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"],["IsMultiplicativeElement"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsMutable","IsRowVectorObj"],["IsRowVectorObj"]],[["IsMutable","IsRowVectorObj"],["IsRowVectorObj"],[]],[["IsMutable","IsRowVectorObj"],["IsRowVectorObj"],[],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 86,"comment" : "AddRowVector: kernel method for vecffe (2 args)","filters" : [["IsMutable","IsHomogeneousList","IsPlistRep","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"],["IsHomogeneousList","IsPlistRep","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 82,"comment" : "AddRowVector: kernel method for plain lists of cyclotomics (2 args)","filters" : [["IsMutable","IsDenseList","IsPlistRep","IsSmallList","Tester(IsSmallList)","CategoryCollections(IsCyclotomic)"],["IsDenseList","IsPlistRep","CategoryCollections(IsCyclotomic)"]]},{"rank" : 50,"comment" : "AddRowVector: For 2 8 bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 45,"comment" : "AddRowVector: kernel method for GF2 (2 args)","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 25,"comment" : "AddRowVector: for two plist vectors","filters" : [["IsMutable","IsPlistVectorRep","IsIntVector"],["IsPlistVectorRep","IsIntVector"]]},{"rank" : 25,"comment" : "AddRowVector: for two checking plist vectors","filters" : [["IsMutable","IsPlistVectorRep","IsCheckingVector"],["IsPlistVectorRep","IsCheckingVector"]]},{"rank" : 23,"comment" : "AddRowVector: for two plist vectors","filters" : [["IsMutable","IsPlistVectorRep"],["IsPlistVectorRep"]]},{"rank" : 23,"comment" : "AddRowVector: kernel method for GF2 (2 args)","filters" : [["IsMutable","IsGF2VectorRep"],["IsGF2VectorRep"]]},{"rank" : 14,"comment" : "AddRowVector: kernel method for small lists (2 args)","filters" : [["IsMutable","IsDenseList","IsSmallList","Tester(IsSmallList)"],["IsDenseList"]]},{"rank" : 8,"comment" : "AddRowVector: generic method (2 args)","filters" : [["IsMutable","IsDenseList"],["IsDenseList"]]},{"rank" : 2,"comment" : "AddRowVector: error if immutable","filters" : [["IsList"],[]]}],"3args" : [{"rank" : 10008,"comment" : "AddRowVector: do nothing if mult is zero","filters" : [["IsList"],[],["IsZero","Tester(IsZero)"]]},{"rank" : 103,"comment" : "AddRowVector: kernel method for vecffe (3 args)","filters" : [["IsMutable","IsHomogeneousList","IsPlistRep","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"],["IsHomogeneousList","IsPlistRep","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"],["IsFFE","IsInternalRep"]]},{"rank" : 97,"comment" : "AddRowVector: kernel method for plain lists of cyclotomics(3 args)","filters" : [["IsMutable","IsDenseList","IsPlistRep","IsSmallList","Tester(IsSmallList)","CategoryCollections(IsCyclotomic)"],["IsDenseList","IsPlistRep","CategoryCollections(IsCyclotomic)"],["IsCyclotomic"]]},{"rank" : 67,"comment" : "AddRowVector: For 2 8 bit vectors and a field element","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE","IsInternalRep"]]},{"rank" : 40,"comment" : "AddRowVector: kernel method for GF2 (3 args)","filters" : [["IsMutable","IsGF2VectorRep"],["IsGF2VectorRep"],["IsFFE","IsInternalRep"]]},{"rank" : 25,"comment" : "AddRowVector: for two plist vectors, and a scalar","filters" : [["IsMutable","IsPlistVectorRep","IsIntVector"],["IsPlistVectorRep","IsIntVector"],[]]},{"rank" : 25,"comment" : "AddRowVector: for two checking plist vectors, and a scalar","filters" : [["IsMutable","IsPlistVectorRep","IsCheckingVector"],["IsPlistVectorRep","IsCheckingVector"],[]]},{"rank" : 23,"comment" : "AddRowVector: for two plist vectors, and a scalar","filters" : [["IsMutable","IsPlistVectorRep"],["IsPlistVectorRep"],[]]},{"rank" : 17,"comment" : "AddRowVector: kernel method for small lists (3 args)","filters" : [["IsMutable","IsDenseList","IsSmallList","Tester(IsSmallList)"],["IsDenseList"],["IsMultiplicativeElement"]]},{"rank" : 11,"comment" : "AddRowVector: generic method 3 args","filters" : [["IsMutable","IsDenseList"],["IsDenseList"],["IsMultiplicativeElement"]]},{"rank" : 2,"comment" : "AddRowVector: error if immutable","filters" : [["IsList"],[],[]]}],"4args" : [],"5args" : [{"rank" : 141,"comment" : "AddRowVector: kernel method for vecffe (5 args -- ignores last 2)","filters" : [["IsMutable","IsHomogeneousList","IsPlistRep","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"],["IsHomogeneousList","IsPlistRep","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"],["IsFFE","IsInternalRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 135,"comment" : "AddRowVector: kernel method for plain lists of cyclotomics","filters" : [["IsMutable","IsDenseList","IsPlistRep","IsSmallList","Tester(IsSmallList)","CategoryCollections(IsCyclotomic)"],["IsDenseList","IsPlistRep","CategoryCollections(IsCyclotomic)"],["IsCyclotomic"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 105,"comment" : "AddRowVector: For 2 8 bit vectors and a field element and from and to","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE","IsInternalRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 76,"comment" : "AddRowVector: kernel method for GF2 (5 args, last 2 ignored)","filters" : [["IsMutable","IsGF2VectorRep"],["IsGF2VectorRep"],["IsFFE"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "AddRowVector: for two integer plist vectors, a scalar, and two positions","filters" : [["IsMutable","IsPlistVectorRep","IsIntVector"],["IsPlistVectorRep","IsIntVector"],[],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "AddRowVector: for two checking plist vectors, a scalar, and two positions","filters" : [["IsMutable","IsPlistVectorRep","IsCheckingVector"],["IsPlistVectorRep","IsCheckingVector"],[],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 61,"comment" : "AddRowVector: for two plist vectors, a scalar, and two positions","filters" : [["IsMutable","IsPlistVectorRep"],["IsPlistVectorRep"],[],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 55,"comment" : "AddRowVector: kernel method for small lists","filters" : [["IsMutable","IsDenseList","IsSmallList","Tester(IsSmallList)"],["IsDenseList"],["IsMultiplicativeElement"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 49,"comment" : "AddRowVector: generic method","filters" : [["IsMutable","IsDenseList"],["IsDenseList"],["IsMultiplicativeElement"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "AddRowVector: error if immutable","filters" : [["IsList"],[],[],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"6args" : []}},{"name" : "AddCoeffs","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"],["IsList"],["IsList"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 50,"comment" : "AddCoeffs: two 8 bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 47,"comment" : "AddCoeffs: GF2 vector and 8 bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 47,"comment" : "AddCoeffs: 8 bit vector and GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 45,"comment" : "AddCoeffs: for GF2 vectors","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 41,"comment" : "AddCoeffs: for empty list, GF2 vector","filters" : [["IsMutable","IsList","IsEmpty","Tester(IsEmpty)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 22,"comment" : "AddCoeffs: generic method (2nd arg empty)","filters" : [["IsMutable","IsDenseList"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 8,"comment" : "AddCoeffs: generic method (2 args)","filters" : [["IsMutable","IsDenseList"],["IsDenseList"]]},{"rank" : 2,"comment" : "AddCoeffs: error if immutable","filters" : [["IsList"],[]]}],"3args" : [{"rank" : 65,"comment" : "AddCoeffs: two 8 bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE"]]},{"rank" : 62,"comment" : "AddCoeffs: GF2 vector and 8 bit vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE"]]},{"rank" : 62,"comment" : "AddCoeffs: 8 bit vector and GF2 vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE"]]},{"rank" : 60,"comment" : "AddCoeffs: for GF2 vectors and FFE","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE"]]},{"rank" : 56,"comment" : "AddCoeffs: for empty list, GF2 vector and FFE","filters" : [["IsMutable","IsList","IsEmpty","Tester(IsEmpty)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE"]]},{"rank" : 11,"comment" : "AddCoeffs: generic method 3args","filters" : [["IsMutable","IsDenseList"],["IsDenseList"],["IsMultiplicativeElement"]]},{"rank" : 2,"comment" : "AddCoeffs: error if immutable","filters" : [["IsList"],[],[]]}],"4args" : [],"5args" : [{"rank" : 17,"comment" : "AddCoeffs: generic method (5 args)","filters" : [["IsMutable","IsDenseList"],["IsDenseList"],["IsDenseList"],["IsDenseList"],["IsMultiplicativeElement"]]},{"rank" : 2,"comment" : "AddCoeffs: error if immutable","filters" : [["IsList"],[],[],[],[]]}],"6args" : []}},{"name" : "MultRowVector","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"],["IsList"],["IsList"],["IsMultiplicativeElement"]],[["IsMutable","IsRowVectorObj"],[]],[["IsMutable","IsRowVectorObj"],["IsList"],["IsRowVectorObj"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 59,"comment" : "MultRowVector: kernel method for vecffe (2 args)","filters" : [["IsMutable","IsHomogeneousList","IsPlistRep","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"],["IsFFE"]]},{"rank" : 57,"comment" : "MultRowVector: Two argument kernel method for plain list of cyclotomics and an integer","filters" : [["IsMutable","IsDenseList","IsPlistRep","IsSmallList","Tester(IsSmallList)","CategoryCollections(IsCyclotomic)"],["IsCyclotomic"]]},{"rank" : 42,"comment" : "MultRowVector: For an 8 bit vector and an ffe","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE","IsInternalRep"]]},{"rank" : 38,"comment" : "MultRowVector: for GF(2) vector and char 2 scalar","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE"]]},{"rank" : 14,"comment" : "MultRowVector: Two argument kernel method for small list","filters" : [["IsMutable","IsDenseList","IsSmallList","Tester(IsSmallList)"],["IsMultiplicativeElement"]]},{"rank" : 13,"comment" : "MultRowVector: for a plist vector, and a scalar","filters" : [["IsMutable","IsPlistVectorRep","IsIntVector"],[]]},{"rank" : 13,"comment" : "MultRowVector: for a checking plist vector, and a scalar","filters" : [["IsMutable","IsPlistVectorRep","IsCheckingVector"],[]]},{"rank" : 12,"comment" : "MultRowVector: for a plist vector, and a scalar","filters" : [["IsMutable","IsPlistVectorRep"],[]]},{"rank" : 8,"comment" : "MultRowVector: two argument generic method","filters" : [["IsMutable","IsDenseList"],["IsMultiplicativeElement"]]},{"rank" : 2,"comment" : "MultRowVector: error if immutable","filters" : [["IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [{"rank" : 29,"comment" : "MultRowVector: for a checking plist vector, a list, a ch. plist vector, a list, a scalar","filters" : [["IsMutable","IsPlistVectorRep","IsCheckingVector"],["IsList"],["IsPlistVectorRep","IsCheckingVector"],["IsList"],[]]},{"rank" : 27,"comment" : "MultRowVector: for a plist vector, a list, a plist vector, a list, and a scalar","filters" : [["IsMutable","IsPlistVectorRep"],["IsList"],["IsPlistVectorRep"],["IsList"],[]]},{"rank" : 17,"comment" : "MultRowVector: generic method","filters" : [["IsMutable","IsDenseList"],["IsDenseList"],["IsDenseList"],["IsDenseList"],["IsMultiplicativeElement"]]},{"rank" : 2,"comment" : "MultRowVector: error if immutable","filters" : [["IsList"],[],[],[],[]]}],"6args" : []}},{"name" : "CoeffsMod","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "CoeffsMod","filters" : [["IsDenseList"],["IsInt"]]}],"3args" : [{"rank" : 39,"comment" : "CoeffsMod: call `ReduceCoeffsMod'","filters" : [["IsDenseList"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MultCoeffs","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsList"],["IsInt"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 46,"comment" : "MultCoeffs: generic method","filters" : [["IsMutable","IsList"],["IsDenseList"],["IsInt"],["IsDenseList"],["IsInt"]]},{"rank" : 38,"comment" : "MultCoeffs: error if immutable","filters" : [["IsList"],[],["IsInt"],[],["IsInt"]]}],"6args" : []}},{"name" : "PowerModCoeffs","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"],["IsInt"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 24,"comment" : "PowerModCoeffs: default, 3 argt","filters" : [["IsDenseList"],["IsInt"],["IsDenseList"]]}],"4args" : [],"5args" : [{"rank" : 105,"comment" : "PowerModCoeffs: for 8 bit vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"],["IsInt","IsPosRat"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"]]},{"rank" : 99,"comment" : "PowerModCoeffs: for gf2vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"],["IsInt","IsPosRat"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"]]},{"rank" : 60,"comment" : "PowerModCoeffs: default five argt method","filters" : [["IsDenseList"],["IsInt"],["IsInt"],["IsDenseList"],["IsInt"]]}],"6args" : []}},{"name" : "ProductCoeffs","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 50,"comment" : "ProductCoeffs: 8 bit vectors, kernel method (2 arg)","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 44,"comment" : "ProductCoeffs: Gf2 vectors, kernel method (2 arg)","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 6,"comment" : "ProductCoeffs: call PRODUCT_COEFFS_GENERIC_LISTS with lengths","filters" : [["IsDenseList"],["IsDenseList"]]}],"3args" : [],"4args" : [{"rank" : 86,"comment" : "ProductCoeffs: 8 bit vectors, kernel method","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"]]},{"rank" : 80,"comment" : "ProductCoeffs: GF2 vectors, kernel method","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"]]},{"rank" : 42,"comment" : "ProductCoeffs: call PRODUCT_COEFFS_GENERIC_LISTS","filters" : [["IsDenseList"],["IsInt"],["IsDenseList"],["IsInt"]]}],"5args" : [],"6args" : []}},{"name" : "ReduceCoeffs","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsInt"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "ReduceCoeffs: 8 bit vectors, kernel method (2 arg)","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 45,"comment" : "ReduceCoeffs: Gf2 vectors, kernel method (2 arg)","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 8,"comment" : "ReduceCoeffs","filters" : [["IsMutable","IsDenseList"],["IsDenseList"]]},{"rank" : 2,"comment" : "ReduceCoeffs: error if immutable","filters" : [["IsList"],[]]}],"3args" : [],"4args" : [{"rank" : 87,"comment" : "ReduceCoeffs: 8 bit vectors, kernel method","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"]]},{"rank" : 81,"comment" : "ReduceCoeffs: GF2 vectors, kernel method","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"]]},{"rank" : 72,"comment" : "ReduceCoeffs: for float vectors","filters" : [["CategoryCollections(IsFloat)"],["IsInt"],["CategoryCollections(IsFloat)"],["IsInt"]]},{"rank" : 44,"comment" : "ReduceCoeffs: generic method","filters" : [["IsMutable","IsDenseList"],["IsInt"],["IsDenseList"],["IsInt"]]},{"rank" : 38,"comment" : "ReduceCoeffs: error if immutable","filters" : [["IsList"],["IsInt"],[],["IsInt"]]}],"5args" : [],"6args" : []}},{"name" : "ReduceCoeffsMod","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsInt"],["IsList"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "ReduceCoeffsMod","filters" : [["IsMutable","IsDenseList"],["IsInt"]]},{"rank" : 20,"comment" : "ReduceCoeffsMod: error if immutable","filters" : [["IsList"],["IsInt"]]}],"3args" : [{"rank" : 41,"comment" : "ReduceCoeffsMod: generic: list, int,int","filters" : [["IsMutable","IsDenseList"],["IsInt"],["IsInt"]]},{"rank" : 38,"comment" : "ReduceCoeffsMod: error if immutable","filters" : [["IsList"],["IsInt"],["IsInt"]]},{"rank" : 26,"comment" : "ReduceCoeffsMod: generic: list,list,int","filters" : [["IsMutable","IsDenseList"],["IsDenseList"],["IsInt"]]},{"rank" : 20,"comment" : "ReduceCoeffsMod: error if immutable","filters" : [["IsList"],[],["IsInt"]]}],"4args" : [],"5args" : [{"rank" : 62,"comment" : "ReduceCoeffsMod: generic method (5 args)","filters" : [["IsMutable","IsDenseList"],["IsInt"],["IsDenseList"],["IsInt"],["IsInt"]]},{"rank" : 56,"comment" : "ReduceCoeffsMod: error if immutable","filters" : [["IsList"],["IsInt"],[],["IsInt"],["IsInt"]]}],"6args" : []}},{"name" : "QuotRemCoeffs","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "QuotRemCoeffs: 8 bit vectors, kernel method (2 arg)","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 6,"comment" : "QuotRemCoeffs: generic, use list lengths","filters" : [["IsDenseList"],["IsDenseList"]]}],"3args" : [],"4args" : [{"rank" : 87,"comment" : "QuotRemCoeffs: 8 bit vectors, kernel method","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt"]]},{"rank" : 80,"comment" : "QuotRemCoeffs: GF2 vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt"]]},{"rank" : 40,"comment" : "QuotRemCoeffs: generic","filters" : [["IsList"],["IsInt"],["IsList"],["IsInt"]]}],"5args" : [],"6args" : []}},{"name" : "ValuePol","type" : "GAP_Operation","filters" : [[["IsList"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 19,"comment" : "ValuePol: special code for rational values","filters" : [["IsList"],["IsRat"]]},{"rank" : 10,"comment" : "ValuePol: generic","filters" : [["IsList"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RemoveOuterCoeffs","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 43,"comment" : "RemoveOuterCoeffs: vec8bit and zero","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsFFE","IsZero","Tester(IsZero)"]]},{"rank" : 40,"comment" : "RemoveOuterCoeffs: gf2vec and zero","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsFFE","IsZero","Tester(IsZero)"]]},{"rank" : 5,"comment" : "RemoveOuterCoeffs: generic method","filters" : [["IsMutable","IsDenseList"],[]]},{"rank" : 2,"comment" : "RemoveOuterCoeffs: error if immutable","filters" : [["IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ShiftedCoeffs","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "ShiftedCoeffs: empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsInt"]]},{"rank" : 21,"comment" : "ShiftedCoeffs: call ShiftRowVektor","filters" : [["IsDenseList"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftShiftRowVector","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10024,"comment" : "LeftShiftRowVector","filters" : [["IsDenseList"],["IsInt","IsZeroCyc"]]},{"rank" : 45,"comment" : "LeftShiftRowVector: 8bit vector","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 42,"comment" : "LeftShiftRowVector: gf2 vector","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt","IsPosRat"]]},{"rank" : 24,"comment" : "LeftShiftRowVector: generic method","filters" : [["IsMutable","IsDenseList"],["IsInt","IsPosRat"]]},{"rank" : 2,"comment" : "LeftShiftRowVector: error if immutable","filters" : [["IsList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightShiftRowVector","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "RightShiftRowVector: error if immutable","filters" : [["IsList"],[]]}],"3args" : [{"rank" : 10023,"comment" : "RightShiftRowVector","filters" : [["IsList"],["IsInt","IsZeroCyc"],[]]},{"rank" : 62,"comment" : "RightShiftRowVector: 8bit vector, fill with zeros","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt","IsPosRat"],["IsFFE","IsZero","Tester(IsZero)"]]},{"rank" : 59,"comment" : "RightShiftRowVector: gf2 vector, fill with zeros","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt","IsPosRat"],["IsFFE","IsZero","Tester(IsZero)"]]},{"rank" : 23,"comment" : "RightShiftRowVector: generic method","filters" : [["IsMutable","IsList"],["IsInt","IsPosRat"],[]]},{"rank" : 2,"comment" : "RightShiftRowVector: error if immutable","filters" : [["IsList"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ShrinkRowVector","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "ShrinkRowVector: 8 bit vector","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 23,"comment" : "ShrinkRowVector: GF2 vector","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 4,"comment" : "ShrinkRowVector: generic method","filters" : [["IsMutable","IsList"]]},{"rank" : 2,"comment" : "ShrinkRowVector: error if immutable","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PadCoeffs","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"],["IsInt","IsPosRat"],[]],[["IsMutable","IsList","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsAdditiveElement)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 49,"comment" : "PadCoeffs: 8 bit vector","filters" : [["IsMutable","IsHomogeneousList","CategoryCollections(IsNearAdditiveElementWithZero)","IsNearAdditiveElementWithInverse","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 46,"comment" : "PadCoeffs: for GF2 vector","filters" : [["IsMutable","IsHomogeneousList","CategoryCollections(IsNearAdditiveElementWithZero)","IsNearAdditiveElementWithInverse","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"],["IsInt","IsPosRat"]]},{"rank" : 34,"comment" : "PadCoeffs: pad with zero","filters" : [["IsMutable","IsList","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsAdditiveElement)"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 23,"comment" : "PadCoeffs: pad with supplied value","filters" : [["IsMutable","IsList"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WeightVecFFE","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "WeightVecFFE: gf2 vectors","filters" : [["IsList","IsGF2VectorRep"]]},{"rank" : 2,"comment" : "WeightVecFFE: generic","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DistanceVecFFE","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 50,"comment" : "DistanceVecFFE: 8bit-vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 42,"comment" : "DistanceVecFFE: gf2 vectors","filters" : [["IsList","IsGF2VectorRep"],["IsList","IsGF2VectorRep"]]},{"rank" : 4,"comment" : "DistanceVecFFE: generic","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DistancesDistributionVecFFEsVecFFE","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 4,"comment" : "DistancesDistributionVecFFEsVecFFE: generic","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DistancesDistributionMatFFEVecFFE","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["CategoryCollections(IsFFE)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 114,"comment" : "DistancesDistributionMatFFEVecFFE: generic","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AClosestVectorCombinationsMatFFEVecFFE","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["CategoryCollections(IsFFE)"],["IsList"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 150,"comment" : "AClosestVectorCombinationsMatFFEVecFFE: generic","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList"],["IsInt"],["IsInt"]]}],"6args" : []}},{"name" : "AClosestVectorCombinationsMatFFEVecFFECoords","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["CategoryCollections(IsFFE)"],["IsList"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 150,"comment" : "AClosestVectorCombinationsMatFFEVecFFECoords: generic","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList"],["IsInt"],["IsInt"]]}],"6args" : []}},{"name" : "CosetLeadersMatFFE","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["CategoryCollections(IsFFE)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 112,"comment" : "CosetLeadersMatFFE: generic","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AddToListEntries","type" : "GAP_Operation","filters" : [[["IsMutable","IsList","CategoryCollections(IsExtAElement)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsExtAElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 100,"comment" : "AddToListEntries: fast kernel method","filters" : [["IsMutable","IsList","IsPlistRep","CategoryCollections(IsCyclotomic)"],["IsRange","IsRangeRep"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewInfoClass","type" : "GAP_Operation","filters" : [[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "NewInfoClass","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetInfoLevel","type" : "GAP_Operation","filters" : [[["IsInfoClass"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 24,"comment" : "SetInfoLevel","filters" : [["IsInfoClass","IsInfoClassListRep"],["IsZeroCyc"]]},{"rank" : 22,"comment" : "SetInfoLevel","filters" : [["IsInfoClass","IsInfoClassListRep"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InfoLevel","type" : "GAP_Operation","filters" : [[["IsInfoClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "InfoLevel","filters" : [["IsInfoClass","IsInfoClassListRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Directory","type" : "GAP_Operation","filters" : [[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "Directory: string","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Filename","type" : "GAP_Operation","filters" : [[["IsDirectory"],["IsString"]],[["IsList"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "Filename: for a list and a string","filters" : [["IsList"],["IsString"]]},{"rank" : 6,"comment" : "Filename: for a directory and a string","filters" : [["IsDirectory"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExternalFilename","type" : "GAP_Operation","filters" : [[["IsDirectory"],["IsString"]],[["IsList"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "ExternalFilename: for a directory list and a string","filters" : [["IsList"],["IsString"]]},{"rank" : 6,"comment" : "ExternalFilename: for a directory and a string","filters" : [["IsDirectory"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Read","type" : "GAP_Operation","filters" : [[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "Read: string","filters" : [["IsString"]]},{"rank" : 2,"comment" : "Read: input stream","filters" : [["IsInputStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReadAsFunction","type" : "GAP_Operation","filters" : [[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "ReadAsFunction: string","filters" : [["IsString"]]},{"rank" : 2,"comment" : "ReadAsFunction: input stream","filters" : [["IsInputStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsEndOfStream","type" : "GAP_Operation","filters" : [[["IsInputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "IsEndOfStream: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 6,"comment" : "IsEndOfStream: input text none","filters" : [["IsInputTextNone","IsInputTextNoneRep"]]},{"rank" : 5,"comment" : "IsEndOfStream: input text string","filters" : [["IsInputTextStringRep","IsInputTextStream"]]},{"rank" : 4,"comment" : "IsEndOfStream: input text file","filters" : [["IsInputStream","IsInputTextFileRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionStream","type" : "GAP_Operation","filters" : [[["IsInputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "PositionStream: input text none","filters" : [["IsInputTextNone","IsInputTextNoneRep"]]},{"rank" : 5,"comment" : "PositionStream: input text file","filters" : [["IsInputTextStream","IsInputTextFileRep"]]},{"rank" : 5,"comment" : "PositionStream: input text string","filters" : [["IsInputTextStringRep","IsInputTextStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReadAll","type" : "GAP_Operation","filters" : [[["IsInputStream"]],[["IsInputStream"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "ReadAll: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 6,"comment" : "ReadAll: input text none","filters" : [["IsInputTextNone","IsInputTextNoneRep"]]},{"rank" : 5,"comment" : "ReadAll: input text file","filters" : [["IsInputTextStream","IsInputTextFileRep"]]},{"rank" : 5,"comment" : "ReadAll: input text string","filters" : [["IsInputTextStringRep","IsInputTextStream"]]},{"rank" : 2,"comment" : "ReadAll: input stream","filters" : [["IsInputStream"]]}],"2args" : [{"rank" : 24,"comment" : "ReadAll: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"],["IsInt"]]},{"rank" : 24,"comment" : "ReadAll: input text none and limit","filters" : [["IsInputTextNone","IsInputTextNoneRep"],["IsInt"]]},{"rank" : 23,"comment" : "ReadAll: input text file and limit","filters" : [["IsInputTextStream","IsInputTextFileRep"],["IsInt"]]},{"rank" : 23,"comment" : "ReadAll: input text string and limit","filters" : [["IsInputTextStringRep","IsInputTextStream"],["IsInt"]]},{"rank" : 20,"comment" : "ReadAll: input stream, length limit","filters" : [["IsInputStream"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReadByte","type" : "GAP_Operation","filters" : [[["IsInputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "ReadByte: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 6,"comment" : "ReadByte: input text none","filters" : [["IsInputTextNone","IsInputTextNoneRep"]]},{"rank" : 5,"comment" : "ReadByte: input text file","filters" : [["IsInputTextStream","IsInputTextFileRep"]]},{"rank" : 5,"comment" : "ReadByte: input text string","filters" : [["IsInputTextStringRep","IsInputTextStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReadLine","type" : "GAP_Operation","filters" : [[["IsInputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "ReadLine: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 6,"comment" : "ReadLine: input text none","filters" : [["IsInputTextNone","IsInputTextNoneRep"]]},{"rank" : 5,"comment" : "ReadLine: input text file","filters" : [["IsInputTextStream","IsInputTextFileRep"]]},{"rank" : 5,"comment" : "ReadLine: input text string","filters" : [["IsInputTextStringRep","IsInputTextStream"]]},{"rank" : 2,"comment" : "ReadLine: generic, call ReadByte","filters" : [["IsInputStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReadAllLine","type" : "GAP_Operation","filters" : [[["IsInputStream"],["IsBool"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "ReadAllLine: iostream","filters" : [["IsInputOutputStream"]]},{"rank" : 2,"comment" : "ReadAllLine: stream","filters" : [["IsInputStream"]]}],"2args" : [{"rank" : 5,"comment" : "ReadAllLine: iostream,function","filters" : [["IsInputOutputStream"],["IsFunction"]]},{"rank" : 5,"comment" : "ReadAllLine: iostream,boolean","filters" : [["IsInputOutputStream"],["IsBool"]]},{"rank" : 3,"comment" : "ReadAllLine: stream,function","filters" : [["IsInputStream"],["IsFunction"]]},{"rank" : 3,"comment" : "ReadAllLine: stream,boolean","filters" : [["IsInputStream"],["IsBool"]]}],"3args" : [{"rank" : 6,"comment" : "ReadAllLine: iostream,boolean,function","filters" : [["IsInputOutputStream"],["IsBool"],["IsFunction"]]},{"rank" : 4,"comment" : "ReadAllLine: stream,boolean,function","filters" : [["IsInputStream"],["IsBool"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RewindStream","type" : "GAP_Operation","filters" : [[["IsInputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "RewindStream: input text none","filters" : [["IsInputTextNone","IsInputTextNoneRep"]]},{"rank" : 5,"comment" : "RewindStream: input text string","filters" : [["IsInputTextStringRep","IsInputTextStream"]]},{"rank" : 3,"comment" : "RewindStream: input text stream","filters" : [["IsInputTextStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SeekPositionStream","type" : "GAP_Operation","filters" : [[["IsInputStream"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 24,"comment" : "SeekPositionStream: input text none","filters" : [["IsInputTextNone","IsInputTextNoneRep"],["IsInt"]]},{"rank" : 23,"comment" : "SeekPositionStream: input text file","filters" : [["IsInputTextStream","IsInputTextFileRep"],["IsInt"]]},{"rank" : 23,"comment" : "SeekPositionStream: input text string","filters" : [["IsInputTextStringRep","IsInputTextStream"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WriteAll","type" : "GAP_Operation","filters" : [[["IsOutputStream"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "WriteAll: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"],["IsString"]]},{"rank" : 11,"comment" : "WriteAll: output text none","filters" : [["IsOutputTextNone","IsOutputTextNoneRep"],["IsString"]]},{"rank" : 10,"comment" : "WriteAll: output text file","filters" : [["IsOutputTextStream","IsOutputTextFileRep"],["IsString"]]},{"rank" : 10,"comment" : "WriteAll: output text string","filters" : [["IsOutputTextStream","IsOutputTextStringRep"],["IsString"]]},{"rank" : 7,"comment" : "WriteAll: output stream","filters" : [["IsOutputStream"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WriteByte","type" : "GAP_Operation","filters" : [[["IsOutputStream"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 24,"comment" : "WriteByte: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"],["IsInt"]]},{"rank" : 24,"comment" : "WriteByte: output text none","filters" : [["IsOutputTextNone","IsOutputTextNoneRep"],["IsInt"]]},{"rank" : 23,"comment" : "WriteByte: output text file","filters" : [["IsOutputTextStream","IsOutputTextFileRep"],["IsInt"]]},{"rank" : 23,"comment" : "WriteByte: output text string","filters" : [["IsOutputTextStream","IsOutputTextStringRep"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WriteLine","type" : "GAP_Operation","filters" : [[["IsOutputStream"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "WriteLine: output stream","filters" : [["IsOutputStream"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CloseStream","type" : "GAP_Operation","filters" : [[["IsStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "CloseStream: iostream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 4,"comment" : "CloseStream: output text file","filters" : [["IsOutputStream","IsOutputTextFileRep"]]},{"rank" : 4,"comment" : "CloseStream: input text file","filters" : [["IsInputStream","IsInputTextFileRep"]]},{"rank" : 2,"comment" : "CloseStream: non-process streams","filters" : [["IsPositionalObjectRep","IsStream"]]},{"rank" : 2,"comment" : "CloseStream: non-process streams","filters" : [["IsComponentObjectRep","IsStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InputTextString","type" : "GAP_Operation","filters" : [[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "InputTextString: input text stream from string","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InputTextFile","type" : "GAP_Operation","filters" : [[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "InputTextFile: input text stream from file","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OutputTextString","type" : "GAP_Operation","filters" : [[["IsList"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [{"rank" : -9995,"comment" : "OutputTextString: error catching method, append not given","filters" : [["IsString"]]}],"2args" : [{"rank" : 3,"comment" : "OutputTextString: output text stream from string","filters" : [["IsList"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OutputTextFile","type" : "GAP_Operation","filters" : [[["IsString"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [{"rank" : -9995,"comment" : "OutputTextFile: error catching method, append not given","filters" : [["IsString"]]}],"2args" : [{"rank" : 6,"comment" : "OutputTextFile: output text stream from file","filters" : [["IsString"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPrintFormattingStatus","type" : "GAP_Operation","filters" : [[["IsOutputStream"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "SetPrintFormattingStatus: output text none","filters" : [["IsOutputTextNone","IsOutputTextNoneRep"],["IsBool"]]},{"rank" : 6,"comment" : "SetPrintFormattingStatus: for stdout","filters" : [["IsString"],["IsBool"]]},{"rank" : 6,"comment" : "SetPrintFormattingStatus: output text file","filters" : [["IsOutputTextStream","IsOutputTextFileRep"],["IsBool"]]},{"rank" : 6,"comment" : "SetPrintFormattingStatus: output text string","filters" : [["IsOutputTextStream","IsOutputTextStringRep"],["IsBool"]]},{"rank" : 3,"comment" : "SetPrintFormattingStatus: for non-text output stream","filters" : [["IsOutputStream"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrintFormattingStatus","type" : "GAP_Operation","filters" : [[["IsOutputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "PrintFormattingStatus: output text none","filters" : [["IsOutputTextNone","IsOutputTextNoneRep"]]},{"rank" : 5,"comment" : "PrintFormattingStatus: for stdout","filters" : [["IsString"]]},{"rank" : 5,"comment" : "PrintFormattingStatus: output text file","filters" : [["IsOutputTextStream","IsOutputTextFileRep"]]},{"rank" : 5,"comment" : "PrintFormattingStatus: output text string","filters" : [["IsOutputTextStream","IsOutputTextStringRep"]]},{"rank" : 2,"comment" : "PrintFormattingStatus: for non-text output stream","filters" : [["IsOutputStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LogTo","type" : "GAP_Operation","filters" : [[["IsOutputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "LogTo: for output file","filters" : [["IsString"]]},{"rank" : 3,"comment" : "LogTo: for output stream","filters" : [["IsOutputTextStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InputLogTo","type" : "GAP_Operation","filters" : [[["IsOutputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "InputLogTo: for output file","filters" : [["IsString"]]},{"rank" : 3,"comment" : "InputLogTo: for output stream","filters" : [["IsOutputTextStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OutputLogTo","type" : "GAP_Operation","filters" : [[["IsOutputStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "OutputLogTo: for output file","filters" : [["IsString"]]},{"rank" : 3,"comment" : "OutputLogTo: for output stream","filters" : [["IsOutputTextStream"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FileDescriptorOfStream","type" : "GAP_Operation","filters" : [[["IsStream"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "FileDescriptorOfStream","filters" : [["IsInputOutputStream","IsInputOutputStreamByPtyRep"]]},{"rank" : 5,"comment" : "FileDescriptorOfStream","filters" : [["IsOutputTextStream","IsOutputTextFileRep"]]},{"rank" : 5,"comment" : "FileDescriptorOfStream","filters" : [["IsInputTextStream","IsInputTextFileRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImmutableMatrix","type" : "GAP_Operation","filters" : [[[],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "ImmutableMatrix: field,gf2","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsGF2MatrixRep"]]},{"rank" : 67,"comment" : "ImmutableMatrix: field,8bit","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["Is8BitMatrixRep"]]},{"rank" : 34,"comment" : "ImmutableMatrix: fieldsize,gf2","filters" : [["IsInt","IsPosRat"],["IsGF2MatrixRep"]]},{"rank" : 34,"comment" : "ImmutableMatrix: fieldsize,8bit","filters" : [["IsInt","IsPosRat"],["Is8BitMatrixRep"]]},{"rank" : 30,"comment" : "ImmutableMatrix: general,2","filters" : [[],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "ImmutableMatrix: empty","filters" : [[],["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "ImmutableMatrix: transposed empty","filters" : [[],["IsList"]]}],"3args" : [{"rank" : 31,"comment" : "ImmutableMatrix: general,3","filters" : [[],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumberFFVector","type" : "GAP_Operation","filters" : [[["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 62,"comment" : "NumberFFVector: 8bit-vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)","Is8BitVectorRep"],["IsInt","IsPosRat"]]},{"rank" : 59,"comment" : "NumberFFVector: GF2-Vector","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)","IsGF2VectorRep"],["IsInt","IsPosRat"]]},{"rank" : 50,"comment" : "NumberFFVector: uncompressed vecffe","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "State","type" : "GAP_Operation","filters" : [[["IsRandomSource"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "State: for a real random source","filters" : [["IsRealRandomSource"]]},{"rank" : 3,"comment" : "State","filters" : [["IsMersenneTwister"]]},{"rank" : 3,"comment" : "State","filters" : [["IsGAPRandomSource"]]},{"rank" : 3,"comment" : "State","filters" : [["IsGlobalRandomSource"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Reset","type" : "GAP_Operation","filters" : [[["IsRandomSource"]],[["IsRandomSource"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "Reset: for a real random source","filters" : [["IsRealRandomSource"]]},{"rank" : 2,"comment" : "Reset","filters" : [["IsRandomSource"]]}],"2args" : [{"rank" : 3,"comment" : "Reset: for a real random source and an object","filters" : [["IsRealRandomSource"],[]]},{"rank" : 3,"comment" : "Reset","filters" : [["IsMersenneTwister"],[]]},{"rank" : 3,"comment" : "Reset","filters" : [["IsGAPRandomSource"],[]]},{"rank" : 3,"comment" : "Reset","filters" : [["IsGlobalRandomSource"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Init","type" : "GAP_Operation","filters" : [[["IsRandomSource"]],[["IsRandomSource"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "Init: for a real random source","filters" : [["IsRealRandomSource"],["IsString"]]},{"rank" : 3,"comment" : "Init","filters" : [["IsMersenneTwister"],[]]},{"rank" : 3,"comment" : "Init","filters" : [["IsGAPRandomSource"],[]]},{"rank" : 3,"comment" : "Init","filters" : [["IsGlobalRandomSource"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RandomSource","type" : "GAP_Operation","filters" : [[["IsOperation"]],[["IsOperation"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "RandomSource","filters" : [["IsOperation"]]}],"2args" : [{"rank" : 2,"comment" : "RandomSource","filters" : [["IsOperation"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SplitString","type" : "GAP_Operation","filters" : [[["IsString"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10,"comment" : "SplitString: for two strings","filters" : [["IsString"],["IsString"]]},{"rank" : 6,"comment" : "SplitString: for a string and a character","filters" : [["IsString"],["IsChar"]]}],"3args" : [{"rank" : 15,"comment" : "SplitString: for three strings","filters" : [["IsString"],["IsString"],["IsString"]]},{"rank" : 11,"comment" : "SplitString: for a string, a character and a string","filters" : [["IsString"],["IsChar"],["IsString"]]},{"rank" : 11,"comment" : "SplitString: for two strings and a character","filters" : [["IsString"],["IsString"],["IsChar"]]},{"rank" : 7,"comment" : "SplitString: for a string and two characters","filters" : [["IsString"],["IsChar"],["IsChar"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewFloat","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -15,"comment" : "NewFloat: for IsIEEE754FloatRep and string","filters" : [["IsIEEE754FloatRep"],["IsString"]]},{"rank" : -15,"comment" : "NewFloat: for IsIEEE754FloatRep and integer","filters" : [["IsIEEE754FloatRep"],["IsInt"]]},{"rank" : -16,"comment" : "NewFloat","filters" : [["IsIEEE754FloatRep"],["IsIEEE754FloatRep"]]},{"rank" : -16,"comment" : "NewFloat","filters" : [["IsIEEE754FloatRep"],["IsList"]]},{"rank" : -16,"comment" : "NewFloat","filters" : [["IsIEEE754FloatRep"],["IsInfinity"]]},{"rank" : -16,"comment" : "NewFloat","filters" : [["IsIEEE754FloatRep"],["IsRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MakeFloat","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "MakeFloat: for IsIEEE754FloatRep and integer","filters" : [["IsIEEE754FloatRep"],["IsInt"]]},{"rank" : 31,"comment" : "MakeFloat","filters" : [["IsIEEE754FloatRep"],["IsRat"]]},{"rank" : 30,"comment" : "MakeFloat","filters" : [["IsIEEE754FloatRep"],["IsInfinity"]]},{"rank" : 29,"comment" : "MakeFloat","filters" : [["IsIEEE754FloatRep"],["IsIEEE754FloatRep"]]},{"rank" : 20,"comment" : "MakeFloat: for IsIEEE754FloatRep and string","filters" : [["IsIEEE754FloatRep"],["IsString"]]},{"rank" : 16,"comment" : "MakeFloat","filters" : [["IsIEEE754FloatRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cos","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Cos: system getter","filters" : [["IsAttributeStoringRep","Tester(Cos)"]]},{"rank" : 15,"comment" : "Cos: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Cos)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Cos): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Cos): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Cos)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sin","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Sin: system getter","filters" : [["IsAttributeStoringRep","Tester(Sin)"]]},{"rank" : 15,"comment" : "Sin: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Sin)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Sin): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Sin): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Sin)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tan","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Tan: system getter","filters" : [["IsAttributeStoringRep","Tester(Tan)"]]},{"rank" : 15,"comment" : "Tan: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Tan)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Tan): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Tan): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Tan)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sec","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Sec: system getter","filters" : [["IsAttributeStoringRep","Tester(Sec)"]]},{"rank" : 12,"comment" : "Sec: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Sec)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Sec): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Sec): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Sec)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Csc","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Csc: system getter","filters" : [["IsAttributeStoringRep","Tester(Csc)"]]},{"rank" : 12,"comment" : "Csc: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Csc)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Csc): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Csc): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Csc)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cot","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Cot: system getter","filters" : [["IsAttributeStoringRep","Tester(Cot)"]]},{"rank" : 12,"comment" : "Cot: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Cot)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Cot): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Cot): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Cot)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Asin","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Asin: system getter","filters" : [["IsAttributeStoringRep","Tester(Asin)"]]},{"rank" : 15,"comment" : "Asin: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Asin)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Asin): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Asin): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Asin)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Acos","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Acos: system getter","filters" : [["IsAttributeStoringRep","Tester(Acos)"]]},{"rank" : 15,"comment" : "Acos: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Acos)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Acos): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Acos): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Acos)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Atan","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Atan: system getter","filters" : [["IsAttributeStoringRep","Tester(Atan)"]]},{"rank" : 15,"comment" : "Atan: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Atan)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Atan): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Atan): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Atan)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cosh","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Cosh: system getter","filters" : [["IsAttributeStoringRep","Tester(Cosh)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Cosh)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Cosh): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Cosh): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Cosh)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sinh","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Sinh: system getter","filters" : [["IsAttributeStoringRep","Tester(Sinh)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Sinh)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Sinh): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Sinh): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Sinh)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tanh","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Tanh: system getter","filters" : [["IsAttributeStoringRep","Tester(Tanh)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Tanh)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Tanh): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Tanh): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Tanh)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sech","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Sech: system getter","filters" : [["IsAttributeStoringRep","Tester(Sech)"]]},{"rank" : 12,"comment" : "Sech: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Sech)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Sech): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Sech): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Sech)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Csch","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Csch: system getter","filters" : [["IsAttributeStoringRep","Tester(Csch)"]]},{"rank" : 12,"comment" : "Csch: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Csch)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Csch): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Csch): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Csch)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Coth","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Coth: system getter","filters" : [["IsAttributeStoringRep","Tester(Coth)"]]},{"rank" : 12,"comment" : "Coth: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Coth)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Coth): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Coth): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Coth)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Asinh","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Asinh: system getter","filters" : [["IsAttributeStoringRep","Tester(Asinh)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Asinh)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Asinh): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Asinh): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Asinh)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Acosh","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Acosh: system getter","filters" : [["IsAttributeStoringRep","Tester(Acosh)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Acosh)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Acosh): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Acosh): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Acosh)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Atanh","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Atanh: system getter","filters" : [["IsAttributeStoringRep","Tester(Atanh)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Atanh)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Atanh): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Atanh): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Atanh)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Log2","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Log2: system getter","filters" : [["IsAttributeStoringRep","Tester(Log2)"]]},{"rank" : 12,"comment" : "Log2: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Log2)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Log2): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Log2): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Log2)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Log10","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Log10: system getter","filters" : [["IsAttributeStoringRep","Tester(Log10)"]]},{"rank" : 12,"comment" : "Log10: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Log10)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Log10): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Log10): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Log10)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Log1p","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Log1p: system getter","filters" : [["IsAttributeStoringRep","Tester(Log1p)"]]},{"rank" : 12,"comment" : "Log1p: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Log1p)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Log1p): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Log1p): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Log1p)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Exp","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Exp: system getter","filters" : [["IsAttributeStoringRep","Tester(Exp)"]]},{"rank" : 15,"comment" : "Exp: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Exp)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Exp): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Exp): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Exp)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Exp2","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Exp2: system getter","filters" : [["IsAttributeStoringRep","Tester(Exp2)"]]},{"rank" : 12,"comment" : "Exp2: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Exp2)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Exp2): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Exp2): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Exp2)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Exp10","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Exp10: system getter","filters" : [["IsAttributeStoringRep","Tester(Exp10)"]]},{"rank" : 12,"comment" : "Exp10: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Exp10)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Exp10): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Exp10): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Exp10)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Expm1","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Expm1: system getter","filters" : [["IsAttributeStoringRep","Tester(Expm1)"]]},{"rank" : 12,"comment" : "Expm1: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Expm1)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Expm1): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Expm1): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Expm1)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CubeRoot","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "CubeRoot: system getter","filters" : [["IsAttributeStoringRep","Tester(CubeRoot)"]]},{"rank" : 12,"comment" : "CubeRoot: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CubeRoot)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CubeRoot): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CubeRoot): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CubeRoot)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Square","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Square: system getter","filters" : [["IsAttributeStoringRep","Tester(Square)"]]},{"rank" : 12,"comment" : "Square: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Square)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Square): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Square): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Square)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Ceil","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Ceil: system getter","filters" : [["IsAttributeStoringRep","Tester(Ceil)"]]},{"rank" : 15,"comment" : "Ceil: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 12,"comment" : "Ceil: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Ceil)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Ceil): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Ceil): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Ceil)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Floor","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Floor: system getter","filters" : [["IsAttributeStoringRep","Tester(Floor)"]]},{"rank" : 15,"comment" : "Floor: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Floor)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Floor): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Floor): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Floor)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Round","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Round: system getter","filters" : [["IsAttributeStoringRep","Tester(Round)"]]},{"rank" : 15,"comment" : "Round: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 12,"comment" : "Round: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Round)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Round): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Round): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Round)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Trunc","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Trunc: system getter","filters" : [["IsAttributeStoringRep","Tester(Trunc)"]]},{"rank" : 12,"comment" : "Trunc: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Trunc)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Trunc): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Trunc): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Trunc)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Atan2","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "Atan2: for macfloats","filters" : [["IsIEEE754FloatRep"],["IsIEEE754FloatRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FrExp","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "FrExp: system getter","filters" : [["IsAttributeStoringRep","Tester(FrExp)"]]},{"rank" : 15,"comment" : "FrExp: for macfloat","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 12,"comment" : "FrExp: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FrExp)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FrExp): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FrExp): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FrExp)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LdExp","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "LdExp: for macfloat,int","filters" : [["IsIEEE754FloatRep"],["IsInt"]]},{"rank" : 30,"comment" : "LdExp: for floats","filters" : [["IsFloat"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Argument","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Argument: system getter","filters" : [["IsAttributeStoringRep","Tester(Argument)"]]},{"rank" : 12,"comment" : "Argument: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Argument)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Argument): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Argument): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Argument)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbsoluteValue","type" : "GAP_Operation","filters" : [[["IsFloat"]],[["IsCyclotomic"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AbsoluteValue: system getter","filters" : [["IsAttributeStoringRep","Tester(AbsoluteValue)"]]},{"rank" : 17,"comment" : "AbsoluteValue: rationals","filters" : [["IsRat"]]},{"rank" : 15,"comment" : "AbsoluteValue: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 12,"comment" : "AbsoluteValue: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AbsoluteValue)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]],[["IsCyclotomic"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AbsoluteValue): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AbsoluteValue): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AbsoluteValue)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Hypothenuse","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "Hypothenuse: for macfloats","filters" : [["IsIEEE754FloatRep"],["IsIEEE754FloatRep"]]},{"rank" : 25,"comment" : "Hypothenuse: for floats","filters" : [["IsFloat"],["IsFloat"]]},{"rank" : 25,"comment" : "Hypothenuse: for floats","filters" : [["IsFloat"],["IsFloat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Frac","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Frac: system getter","filters" : [["IsAttributeStoringRep","Tester(Frac)"]]},{"rank" : 12,"comment" : "Frac: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Frac)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Frac): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Frac): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Frac)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SinCos","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "SinCos: system getter","filters" : [["IsAttributeStoringRep","Tester(SinCos)"]]},{"rank" : 12,"comment" : "SinCos: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SinCos)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SinCos): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SinCos): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SinCos)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Erf","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Erf: system getter","filters" : [["IsAttributeStoringRep","Tester(Erf)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Erf)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Erf): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Erf): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Erf)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Zeta","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Zeta: system getter","filters" : [["IsAttributeStoringRep","Tester(Zeta)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Zeta)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Zeta): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Zeta): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Zeta)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Gamma","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Gamma: system getter","filters" : [["IsAttributeStoringRep","Tester(Gamma)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Gamma)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Gamma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Gamma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Gamma)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComplexI","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "ComplexI: system getter","filters" : [["IsAttributeStoringRep","Tester(ComplexI)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComplexI)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComplexI): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComplexI): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComplexI)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrecisionFloat","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "PrecisionFloat: system getter","filters" : [["IsAttributeStoringRep","Tester(PrecisionFloat)"]]},{"rank" : 15,"comment" : "PrecisionFloat: for macfloats","filters" : [["IsIEEE754FloatRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrecisionFloat)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrecisionFloat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrecisionFloat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrecisionFloat)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SignFloat","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "SignFloat: system getter","filters" : [["IsAttributeStoringRep","Tester(SignFloat)"]]},{"rank" : 12,"comment" : "SignFloat: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SignFloat)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SignFloat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SignFloat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SignFloat)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sup","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Sup: system getter","filters" : [["IsAttributeStoringRep","Tester(Sup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Sup)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Sup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Sup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Sup)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Inf","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Inf: system getter","filters" : [["IsAttributeStoringRep","Tester(Inf)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Inf)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Inf): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Inf): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Inf)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Mid","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Mid: system getter","filters" : [["IsAttributeStoringRep","Tester(Mid)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Mid)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Mid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Mid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Mid)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbsoluteDiameter","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AbsoluteDiameter: system getter","filters" : [["IsAttributeStoringRep","Tester(AbsoluteDiameter)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AbsoluteDiameter)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AbsoluteDiameter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AbsoluteDiameter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AbsoluteDiameter)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelativeDiameter","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "RelativeDiameter: system getter","filters" : [["IsAttributeStoringRep","Tester(RelativeDiameter)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelativeDiameter)","type" : "GAP_Operation","filters" : [[["IsFloat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RelativeDiameter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelativeDiameter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelativeDiameter)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Overlaps","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsDisjoint","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EqFloat","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "EqFloat: for macfloats","filters" : [["IsIEEE754FloatRep"],["IsIEEE754FloatRep"]]},{"rank" : 25,"comment" : "EqFloat: for floats","filters" : [["IsFloat"],["IsFloat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IncreaseInterval","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BlowupInterval","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BisectInterval","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPInfinity","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsPInfinity: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPInfinity)"]]},{"rank" : 12,"comment" : "IsPInfinity: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPInfinity)","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPInfinity): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPInfinity): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPInfinity)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNInfinity","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsNInfinity: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNInfinity)"]]},{"rank" : 12,"comment" : "IsNInfinity: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNInfinity)","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNInfinity): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNInfinity): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNInfinity)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsXInfinity","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsXInfinity: system getter","filters" : [["IsAttributeStoringRep","Tester(IsXInfinity)"]]},{"rank" : 12,"comment" : "IsXInfinity: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsXInfinity)","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsXInfinity): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsXInfinity): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsXInfinity)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNaN","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsNaN: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNaN)"]]},{"rank" : 12,"comment" : "IsNaN: for floats","filters" : [["IsFloat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNaN)","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNaN): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNaN): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNaN)","type" : "GAP_Operation","filters" : [[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cyc","type" : "GAP_Operation","filters" : [[["IsFloat"],["IsInt","IsPosRat"]],[["IsFloat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "Cyc: for intervals","filters" : [["IsFloatInterval"]]},{"rank" : 12,"comment" : "Cyc: for floats","filters" : [["IsFloat"]]}],"2args" : [{"rank" : 34,"comment" : "Cyc: for intervals, degree","filters" : [["IsFloatInterval"],["IsInt","IsPosRat"]]},{"rank" : 31,"comment" : "Cyc: for floats, degree","filters" : [["IsFloat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Process","type" : "GAP_Operation","filters" : [[["IsDirectory"],["IsString"],["IsInputStream"],["IsOutputStream"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 20,"comment" : "Process","filters" : [["IsDirectory","IsDirectoryRep"],["IsString"],["IsInputTextStream","IsInputTextFileRep"],["IsOutputTextStream","IsOutputTextFileRep"],["IsList"]]},{"rank" : 19,"comment" : "Process","filters" : [["IsDirectory","IsDirectoryRep"],["IsString"],["IsInputTextNone"],["IsOutputTextStream","IsOutputTextFileRep"],["IsList"]]},{"rank" : 19,"comment" : "Process","filters" : [["IsDirectory","IsDirectoryRep"],["IsString"],["IsInputTextStream","IsInputTextFileRep"],["IsOutputTextNone"],["IsList"]]},{"rank" : 18,"comment" : "Process","filters" : [["IsDirectory","IsDirectoryRep"],["IsString"],["IsInputTextNone"],["IsOutputTextNone"],["IsList"]]},{"rank" : 16,"comment" : "Process","filters" : [["IsDirectory","IsDirectoryRep"],["IsString"],["IsInputTextStream"],["IsOutputTextStream"],["IsList"]]}],"6args" : []}},{"name" : "DirectProductElementsFamily","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 17,"comment" : "DirectProductElementsFamily: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "DirectProductElementsFamily: for a collection (of families)","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComponentsOfDirectProductElementsFamily","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsDirectProductElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "ComponentsOfDirectProductElementsFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(ComponentsOfDirectProductElementsFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComponentsOfDirectProductElementsFamily)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsDirectProductElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComponentsOfDirectProductElementsFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComponentsOfDirectProductElementsFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComponentsOfDirectProductElementsFamily)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsDirectProductElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectProductElement","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "DirectProductElement: for a list","filters" : [["IsList"]]}],"2args" : [{"rank" : 6,"comment" : "DirectProductElement: for a direct product elements family, and a list","filters" : [["CategoryFamily(IsDirectProductElement)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectProductElementNC","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsDirectProductElement)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 6,"comment" : "DirectProductElementNC: for a direct product elements family, and a list","filters" : [["CategoryFamily(IsDirectProductElement)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EmptyRowVector","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "EmptyRowVector: system getter","filters" : [["IsAttributeStoringRep","Tester(EmptyRowVector)"]]},{"rank" : 1,"comment" : "EmptyRowVector: for a family","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EmptyRowVector)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EmptyRowVector): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EmptyRowVector): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EmptyRowVector)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfExtASet","type" : "GAP_Operation","filters" : [[["IsExtASet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "GeneratorsOfExtASet: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfExtASet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfExtASet)","type" : "GAP_Operation","filters" : [[["IsExtASet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfExtASet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfExtASet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfExtASet)","type" : "GAP_Operation","filters" : [[["IsExtASet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditivelyActingDomain","type" : "GAP_Operation","filters" : [[["IsExtASet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "AdditivelyActingDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(AdditivelyActingDomain)"]]},{"rank" : 10014,"comment" : "AdditivelyActingDomain: for additive coset in default repres.","filters" : [["IsAdditiveCoset","IsAdditiveCosetDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdditivelyActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtASet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdditivelyActingDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdditivelyActingDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdditivelyActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtASet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftActedOnByDivisionRing","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsLeftActedOnByRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsLeftActedOnByDivisionRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLeftActedOnByDivisionRing)"]]},{"rank" : 7,"comment" : "IsLeftActedOnByDivisionRing: method for external left set that is left acted on by a ring","filters" : [["IsExtLSet","IsLeftActedOnByRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLeftActedOnByDivisionRing)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsLeftActedOnByRing"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLeftActedOnByDivisionRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLeftActedOnByDivisionRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLeftActedOnByDivisionRing)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsLeftActedOnByRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfExtLSet","type" : "GAP_Operation","filters" : [[["IsExtLSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "GeneratorsOfExtLSet: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfExtLSet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfExtLSet)","type" : "GAP_Operation","filters" : [[["IsExtLSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfExtLSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfExtLSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfExtLSet)","type" : "GAP_Operation","filters" : [[["IsExtLSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftActingDomain","type" : "GAP_Operation","filters" : [[["IsExtLSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "LeftActingDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(LeftActingDomain)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeftActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtLSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "Setter(LeftActingDomain): method to set also 'IsLeftActedOnByDivisionRing'","filters" : [["IsAttributeStoringRep","IsLeftActedOnByRing"],[]]},{"rank" : 2,"comment" : "Setter(LeftActingDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeftActingDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeftActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtLSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfExtRSet","type" : "GAP_Operation","filters" : [[["IsExtRSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "GeneratorsOfExtRSet: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfExtRSet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfExtRSet)","type" : "GAP_Operation","filters" : [[["IsExtRSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfExtRSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfExtRSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfExtRSet)","type" : "GAP_Operation","filters" : [[["IsExtRSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightActingDomain","type" : "GAP_Operation","filters" : [[["IsExtRSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "RightActingDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(RightActingDomain)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RightActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtRSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RightActingDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RightActingDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RightActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtRSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfExtUSet","type" : "GAP_Operation","filters" : [[["IsExtUSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "GeneratorsOfExtUSet: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfExtUSet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfExtUSet)","type" : "GAP_Operation","filters" : [[["IsExtUSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfExtUSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfExtUSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfExtUSet)","type" : "GAP_Operation","filters" : [[["IsExtUSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UpperActingDomain","type" : "GAP_Operation","filters" : [[["IsExtRSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "UpperActingDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(UpperActingDomain)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UpperActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtRSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UpperActingDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UpperActingDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UpperActingDomain)","type" : "GAP_Operation","filters" : [[["IsExtRSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KnowsDictionary","type" : "GAP_Operation","filters" : [[["IsDictionary"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10,"comment" : "KnowsDictionary: for lookup sort dictionaries","filters" : [["IsSortLookupDictionary"],[]]},{"rank" : 8,"comment" : "KnowsDictionary: for list lookup dictionaries","filters" : [["IsListLookupDictionary"],[]]},{"rank" : 6,"comment" : "KnowsDictionary: for position dictionaries","filters" : [["IsPositionDictionary"],[]]},{"rank" : 6,"comment" : "KnowsDictionary: for list dictionaries","filters" : [["IsListDictionary"],[]]},{"rank" : 5,"comment" : "KnowsDictionary: for hash tables","filters" : [["IsHash"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AddDictionary","type" : "GAP_Operation","filters" : [[["IsMutable","IsDictionary"],[]],[["IsMutable","IsDictionary"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "AddDictionary: for sort dictionaries","filters" : [["IsMutable","IsSortDictionary"],[]]},{"rank" : 8,"comment" : "AddDictionary: for position dictionaries","filters" : [["IsMutable","IsPositionDictionary"],[]]},{"rank" : 8,"comment" : "AddDictionary: for list dictionaries","filters" : [["IsMutable","IsListDictionary"],[]]},{"rank" : 7,"comment" : "AddDictionary: for hash tables, no value given","filters" : [["IsMutable","IsHash"],[]]}],"3args" : [{"rank" : 12,"comment" : "AddDictionary: for lookup sort dictionaries","filters" : [["IsMutable","IsSortLookupDictionary"],[],[]]},{"rank" : 10,"comment" : "AddDictionary: for hash tables","filters" : [["IsMutable","IsHash","TableHasIntKeyFun","IsSparseHashRep"],[],[]]},{"rank" : 10,"comment" : "AddDictionary: for lookup position dictionaries","filters" : [["IsMutable","IsPositionDictionary"],[],[]]},{"rank" : 10,"comment" : "AddDictionary: for lookup list dictionaries","filters" : [["IsMutable","IsListLookupDictionary"],[],[]]},{"rank" : 9,"comment" : "AddDictionary: for hash tables","filters" : [["IsMutable","IsHash","IsSparseHashRep"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RemoveDictionary","type" : "GAP_Operation","filters" : [[["IsMutable","IsDictionary"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10,"comment" : "RemoveDictionary: for lookup list dictionaries","filters" : [["IsMutable","IsListLookupDictionary"],[]]},{"rank" : 8,"comment" : "RemoveDictionary: for list dictionaries","filters" : [["IsMutable","IsListDictionary"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LookupDictionary","type" : "GAP_Operation","filters" : [[["IsDictionary"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10,"comment" : "LookupDictionary: for lookup sort dictionaries","filters" : [["IsSortLookupDictionary"],[]]},{"rank" : 8,"comment" : "LookupDictionary: for hash tables that know their int key","filters" : [["IsHash","TableHasIntKeyFun","IsSparseHashRep"],[]]},{"rank" : 8,"comment" : "LookupDictionary: for position dictionaries","filters" : [["IsPositionDictionary"],[]]},{"rank" : 8,"comment" : "LookupDictionary: for list dictionaries","filters" : [["IsListLookupDictionary"],[]]},{"rank" : 7,"comment" : "LookupDictionary: for hash tables","filters" : [["IsHash","IsSparseHashRep"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ListKeyEnumerator","type" : "GAP_Operation","filters" : [[["IsListDictionary"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "ListKeyEnumerator: for list dictionaries","filters" : [["IsListDictionary"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrintHashWithNames","type" : "GAP_Operation","filters" : [[["IsHash"],["IsString"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 17,"comment" : "PrintHashWithNames: for sparse hash tables","filters" : [["IsSparseHashRep"],["IsString"],["IsString"]]},{"rank" : 17,"comment" : "PrintHashWithNames: for dense hash tables","filters" : [["IsDenseHashRep"],["IsString"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RandomHashKey","type" : "GAP_Operation","filters" : [[["IsHash"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 107,"comment" : "RandomHashKey: for sparse hash tables","filters" : [["IsHash","IsSparseHashRep"]]},{"rank" : 107,"comment" : "RandomHashKey: for dense hash tables","filters" : [["IsHash","IsDenseHashRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HashKeyEnumerator","type" : "GAP_Operation","filters" : [[["IsHash"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "HashKeyEnumerator: for sparse hash tables","filters" : [["IsHash","IsSparseHashRep"]]},{"rank" : 7,"comment" : "HashKeyEnumerator: for dense hash tables","filters" : [["IsDenseHashRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DenseIntKey","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 19,"comment" : "DenseIntKey: integers","filters" : [[],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "DenseIntKey: default fail","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SparseIntKey","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "SparseIntKey: for finite Gaussian row spaces","filters" : [["CategoryCollections(CategoryCollections(IsFFE))","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"],[]]},{"rank" : 42,"comment" : "SparseIntKey: pcgs element lists: i.e. pcgs","filters" : [[],["IsList","CategoryCollections(IsElementFinitePolycyclicGroup)"]]},{"rank" : 42,"comment" : "SparseIntKey: for matrices over finite field vector spaces","filters" : [[],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 29,"comment" : "SparseIntKey: for row spaces over finite fields","filters" : [[],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)"]]},{"rank" : 28,"comment" : "SparseIntKey: for vector listsover finite field vector spaces","filters" : [[],["IsList","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 25,"comment" : "SparseIntKey: for lists of vectors","filters" : [["CategoryCollections(CategoryCollections(IsFFE))"],[]]},{"rank" : 9,"comment" : "SparseIntKey: kernel pc group elements","filters" : [[],["IsDataObjectRep","IsElementFinitePolycyclicGroup","IsNBitsPcWordRep"]]},{"rank" : 9,"comment" : "SparseIntKey: permutations, arbitrary domain","filters" : [[],["IsPerm","IsInternalRep"]]},{"rank" : 7,"comment" : "SparseIntKey: for an object and transformation","filters" : [[],["IsTransformation"]]},{"rank" : 0,"comment" : "SparseIntKey: defaults to DenseIntKey","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetHashEntryAtLastIndex","type" : "GAP_Operation","filters" : [[["IsHash"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetHashEntryAtLastIndex","type" : "GAP_Operation","filters" : [[["IsMutable","IsHash"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetHashEntry","type" : "GAP_Operation","filters" : [[["IsMutable","IsHash"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FamilyRange","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FamilyRange: system getter","filters" : [["IsAttributeStoringRep","Tester(FamilyRange)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FamilyRange)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsGeneralMapping)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FamilyRange): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FamilyRange): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FamilyRange)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FamilySource","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FamilySource: system getter","filters" : [["IsAttributeStoringRep","Tester(FamilySource)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FamilySource)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsGeneralMapping)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FamilySource): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FamilySource): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FamilySource)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FamiliesOfGeneralMappingsAndRanges","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "FamiliesOfGeneralMappingsAndRanges: system getter","filters" : [["IsAttributeStoringRep","Tester(FamiliesOfGeneralMappingsAndRanges)"]]},{"rank" : 1,"comment" : "FamiliesOfGeneralMappingsAndRanges: for a family (return empty list)","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FamiliesOfGeneralMappingsAndRanges)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FamiliesOfGeneralMappingsAndRanges): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FamiliesOfGeneralMappingsAndRanges): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FamiliesOfGeneralMappingsAndRanges)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsConstantTimeAccessGeneralMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsConstantTimeAccessGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(IsConstantTimeAccessGeneralMapping)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsConstantTimeAccessGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsConstantTimeAccessGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsConstantTimeAccessGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsConstantTimeAccessGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsEndoGeneralMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsEndoGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(IsEndoGeneralMapping)"]]},{"rank" : 7,"comment" : "IsEndoGeneralMapping: for general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsEndoGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsEndoGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsEndoGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsEndoGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTotal","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsTotal: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTotal)"]]},{"rank" : 10013,"comment" : "IsTotal: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 23,"comment" : "IsTotal: for ring g.m.b.i.","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 18,"comment" : "IsTotal: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 10,"comment" : "IsTotal: for a composition mapping","filters" : [["IsCompositionMappingRep"]]},{"rank" : 9,"comment" : "IsTotal: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]},{"rank" : 8,"comment" : "IsTotal","filters" : [["IsGeneralMapping","Tester(InverseGeneralMapping)"]]},{"rank" : 7,"comment" : "IsTotal: for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTotal)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTotal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTotal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTotal)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSingleValued","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsSingleValued: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSingleValued)"]]},{"rank" : 10013,"comment" : "IsSingleValued: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 31,"comment" : "IsSingleValued: map from whole fp group or free group to perm, std. gens: test relators","filters" : [["IsToPermGroupGeneralMappingByImages","IsFromFpGroupStdGensGeneralMappingByImages"]]},{"rank" : 30,"comment" : "IsSingleValued: for group general mappings of free groups","filters" : [["Tester(MappingGeneratorsImages)","IsFromFpGroupGeneralMappingByImages"]]},{"rank" : 30,"comment" : "IsSingleValued: map from whole fp group or free group, given on std. gens: test relators","filters" : [["IsFromFpGroupStdGensGeneralMappingByImages"]]},{"rank" : 30,"comment" : "IsSingleValued: map from fp group or free group on arbitrary gens: rewrite","filters" : [["Tester(MappingGeneratorsImages)","IsFromFpGroupGeneralMappingByImages"]]},{"rank" : 26,"comment" : "IsSingleValued: for algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsPolynomialRingDefaultGeneratorMapping"]]},{"rank" : 25,"comment" : "IsSingleValued: for algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 24,"comment" : "IsSingleValued: for sc ring g.m.b.i.","filters" : [["IsGeneralMapping","IsSCRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "IsSingleValued: for left module g.m.b.i.","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 19,"comment" : "IsSingleValued","filters" : [["IsPermGroupGeneralMappingByImages"]]},{"rank" : 18,"comment" : "IsSingleValued: for GMBPCGS: test relations","filters" : [["IsGroupGeneralMappingByPcgs"]]},{"rank" : 18,"comment" : "IsSingleValued: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 13,"comment" : "IsSingleValued: method for a gen. mapping that respects add. and add. inverses","filters" : [["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 13,"comment" : "IsSingleValued: method for a gen. mapping that respects mult. and inverses","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 10,"comment" : "IsSingleValued: for a composition mapping","filters" : [["IsCompositionMappingRep"]]},{"rank" : 9,"comment" : "IsSingleValued: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]},{"rank" : 8,"comment" : "IsSingleValued","filters" : [["IsGeneralMapping","Tester(InverseGeneralMapping)"]]},{"rank" : 7,"comment" : "IsSingleValued: for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSingleValued)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSingleValued): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSingleValued): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSingleValued)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInjective","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsInjective: system getter","filters" : [["IsAttributeStoringRep","Tester(IsInjective)"]]},{"rank" : 10013,"comment" : "IsInjective: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 41,"comment" : "IsInjective: for PcpGHBI","filters" : [["IsFromPcpGHBI","IsToPcpGHBI"]]},{"rank" : 25,"comment" : "IsInjective: for algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "IsInjective: for a linear action homomorphism","filters" : [["IsLinearActionHomomorphism"]]},{"rank" : 23,"comment" : "IsInjective: method for homs from pc group","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcGroupGeneralMappingByImages"]]},{"rank" : 23,"comment" : "IsInjective: for a field homomorphism","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]]},{"rank" : 23,"comment" : "IsInjective: for ring g.m.b.i.","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "IsInjective: for left module m.b.m.","filters" : [["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 23,"comment" : "IsInjective: for left module g.m.b.i.","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 18,"comment" : "IsInjective: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "IsInjective: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "IsInjective: for zero mapping","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"]]},{"rank" : 13,"comment" : "IsInjective: method for a gen. mapping that respects add. and add. inverses","filters" : [["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 13,"comment" : "IsInjective: method for a gen. mapping that respects mult. and one","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 11,"comment" : "IsInjective: for a mapping","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 10,"comment" : "IsInjective: for a composition mapping","filters" : [["IsCompositionMappingRep"]]},{"rank" : 9,"comment" : "IsInjective: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]},{"rank" : 8,"comment" : "IsInjective","filters" : [["IsGeneralMapping","Tester(InverseGeneralMapping)"]]},{"rank" : 7,"comment" : "IsInjective: for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsInjective)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsInjective): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsInjective): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsInjective)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSurjective","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsSurjective: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSurjective)"]]},{"rank" : 10013,"comment" : "IsSurjective: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 23,"comment" : "IsSurjective: for a field homomorphism","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]]},{"rank" : 18,"comment" : "IsSurjective: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "IsSurjective: for zero mapping","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"]]},{"rank" : 10,"comment" : "IsSurjective: for a composition mapping","filters" : [["IsCompositionMappingRep"]]},{"rank" : 9,"comment" : "IsSurjective: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]},{"rank" : 8,"comment" : "IsSurjective","filters" : [["IsGeneralMapping","Tester(InverseGeneralMapping)"]]},{"rank" : 7,"comment" : "IsSurjective: for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSurjective)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSurjective): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSurjective): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSurjective)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Range","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "Range: for default general mapping","filters" : [["IsGeneralMapping","IsDefaultGeneralMappingRep"]]},{"rank" : 20010,"comment" : "Range: system getter","filters" : [["IsAttributeStoringRep","Tester(Range)"]]},{"rank" : 29,"comment" : "Range: for operation algebra homomorphism (set full matrix FLMLOR)","filters" : [["IsOperationAlgebraHomomorphismDefaultRep"]]},{"rank" : 25,"comment" : "Range: surjective blocks homomorphism","filters" : [["IsSurjective","Tester(IsSurjective)","IsBlocksHomomorphism"]]},{"rank" : 25,"comment" : "Range: surjective constituent homomorphism","filters" : [["IsSurjective","Tester(IsSurjective)","IsActionHomomorphism","IsConstituentHomomorphism"]]},{"rank" : 24,"comment" : "Range: surjective action homomorphism","filters" : [["IsSurjective","Tester(IsSurjective)","IsActionHomomorphism"]]},{"rank" : 23,"comment" : "Range: perm subdirect product projection","filters" : [["IsProjectionSubdirectProductPermGroup"]]},{"rank" : 23,"comment" : "Range: perm direct product projection","filters" : [["IsProjectionDirectProductPermGroup"]]},{"rank" : 22,"comment" : "Range: ophom: S(domain)","filters" : [["IsActionHomomorphism"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Range)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Range): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Range): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Range)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Source","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "Source: for default general mapping","filters" : [["IsGeneralMapping","IsDefaultGeneralMappingRep"]]},{"rank" : 20010,"comment" : "Source: system getter","filters" : [["IsAttributeStoringRep","Tester(Source)"]]},{"rank" : 23,"comment" : "Source: perm wreath product embedding","filters" : [["IsEmbeddingWreathProductPermGroup"]]},{"rank" : 23,"comment" : "Source: perm direct product embedding","filters" : [["IsEmbeddingDirectProductPermGroup"]]},{"rank" : 22,"comment" : "Source: action homomorphism","filters" : [["IsActionHomomorphism"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Source)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Source): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Source): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Source)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingRelation","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "UnderlyingRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingRelation)"]]},{"rank" : 7,"comment" : "UnderlyingRelation: for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingRelation)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingRelation)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingGeneralMapping","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "UnderlyingGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingGeneralMapping)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "Setter(UnderlyingGeneralMapping): for an underlying relation and a general mapping","filters" : [["IsAttributeStoringRep","IsCollection","IsGeneralizedDomain","Tester(GeneratorsOfDomain)","CategoryCollections(IsDirectProductElement)"],["IsGeneralMapping"]]},{"rank" : 29,"comment" : "Setter(UnderlyingGeneralMapping): for an underlying relation and a general mapping","filters" : [["IsAttributeStoringRep","IsCollection","Tester(AsList)","IsGeneralizedDomain","CategoryCollections(IsDirectProductElement)"],["IsGeneralMapping"]]},{"rank" : 2,"comment" : "Setter(UnderlyingGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdentityMapping","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IdentityMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(IdentityMapping)"]]},{"rank" : 2,"comment" : "IdentityMapping: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdentityMapping)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdentityMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdentityMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdentityMapping)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseGeneralMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "InverseGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(InverseGeneralMapping)"]]},{"rank" : 10022,"comment" : "InverseGeneralMapping: for nilpotent Lie algebra automorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 10022,"comment" : "InverseGeneralMapping: for group automorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]},{"rank" : 27,"comment" : "InverseGeneralMapping: for inner automorphism","filters" : [["IsInnerAutomorphism","Tester(IsInnerAutomorphism)"]]},{"rank" : 26,"comment" : "InverseGeneralMapping: for ANF automorphism","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"]]},{"rank" : 26,"comment" : "InverseGeneralMapping: for a Frobenius automorphism","filters" : [["IsFrobeniusAutomorphism"]]},{"rank" : 25,"comment" : "InverseGeneralMapping: for conjugator automorphism","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 25,"comment" : "InverseGeneralMapping: for bijective GHBI","filters" : [["IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsGroupGeneralMappingByImages"]]},{"rank" : 23,"comment" : "InverseGeneralMapping: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 23,"comment" : "InverseGeneralMapping: for an ring g.m.b.i.","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 21,"comment" : "InverseGeneralMapping: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"]]},{"rank" : 19,"comment" : "InverseGeneralMapping: for mapping by function","filters" : [["IsMappingByFunctionWithInverseRep"]]},{"rank" : 13,"comment" : "InverseGeneralMapping: via generators\/images","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 10,"comment" : "InverseGeneralMapping","filters" : [["IsAttributeStoringRep","Tester(InverseImmutable)","IsGeneralMapping"]]},{"rank" : 7,"comment" : "InverseGeneralMapping: for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InverseGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "Setter(InverseGeneralMapping): transfer the AsGHBI","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages","Tester(AsGroupGeneralMappingByImages)"],["IsGeneralMapping"]]},{"rank" : 2,"comment" : "Setter(InverseGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InverseGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InverseGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImagesSource","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ImagesSource: system getter","filters" : [["IsAttributeStoringRep","Tester(ImagesSource)"]]},{"rank" : 10017,"comment" : "ImagesSource: for zero mapping","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"]]},{"rank" : 10017,"comment" : "ImagesSource: for identity mapping","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"]]},{"rank" : 10013,"comment" : "ImagesSource: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 10009,"comment" : "ImagesSource: for surjective general mapping (delegate to `Range')","filters" : [["IsGeneralMapping","IsSurjective","Tester(IsSurjective)"]]},{"rank" : 25,"comment" : "ImagesSource: for an algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "ImagesSource: actionHomomorphismByBase","filters" : [["IsActionHomomorphismByBase"]]},{"rank" : 23,"comment" : "ImagesSource: perm direct product embedding","filters" : [["IsEmbeddingDirectProductPermGroup"]]},{"rank" : 23,"comment" : "ImagesSource: blocks homomorphism","filters" : [["IsBlocksHomomorphism"]]},{"rank" : 23,"comment" : "ImagesSource: constituent homomorphism","filters" : [["IsActionHomomorphism","IsConstituentHomomorphism"]]},{"rank" : 23,"comment" : "ImagesSource: for an ring g.m.b.i.","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "ImagesSource: for a linear g.m.b.i.","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 21,"comment" : "ImagesSource: for group homomorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 18,"comment" : "ImagesSource: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "ImagesSource: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 7,"comment" : "ImagesSource: for general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImagesSource)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImagesSource): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImagesSource): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImagesSource)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImagesRange","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "PreImagesRange: system getter","filters" : [["IsAttributeStoringRep","Tester(PreImagesRange)"]]},{"rank" : 10013,"comment" : "PreImagesRange: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 10009,"comment" : "PreImagesRange: for total general mapping (delegate to `Source')","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)"]]},{"rank" : 25,"comment" : "PreImagesRange: for an algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "PreImagesRange: for an ring g.m.b.i.","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "PreImagesRange: for a linear g.m.b.i.","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 18,"comment" : "PreImagesRange: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "PreImagesRange: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 7,"comment" : "PreImagesRange: for general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PreImagesRange)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PreImagesRange): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PreImagesRange): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PreImagesRange)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImagesElm","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10017,"comment" : "ImagesElm: for zero mapping and object","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],[]]},{"rank" : 10017,"comment" : "ImagesElm: for identity mapping and object","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],[]]},{"rank" : 36,"comment" : "ImagesElm: for ANF automorphism and scalar","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 33,"comment" : "ImagesElm: for embedding of ring into magma ring, and ring element","filters" : [["IsEmbeddingRingMagmaRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 31,"comment" : "ImagesElm: for binary relations over [1..n] with images list","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "ImagesElm: for Frobenius automorphism and source element","filters" : [["IsFrobeniusAutomorphism"],[]]},{"rank" : 26,"comment" : "ImagesElm: for magma congruence and element","filters" : [["IsMagmaCongruence"],[]]},{"rank" : 22,"comment" : "ImagesElm: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"],[]]},{"rank" : 22,"comment" : "ImagesElm: for a Green's equivalence","filters" : [["IsGreensRelation"],[]]},{"rank" : 22,"comment" : "ImagesElm: for embedding of magma into magma ring, and mult. element","filters" : [["IsEmbeddingMagmaMagmaRing"],["IsMultiplicativeElement"]]},{"rank" : 22,"comment" : "ImagesElm: for magma congruence and element","filters" : [["IsRightMagmaCongruence"],[]]},{"rank" : 22,"comment" : "ImagesElm: for magma congruence and element","filters" : [["IsLeftMagmaCongruence"],[]]},{"rank" : 22,"comment" : "ImagesElm: for equivalence relation with partition and element","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","Tester(EquivalenceRelationPartition)"],[]]},{"rank" : 20,"comment" : "ImagesElm: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"],["IsMultiplicativeElement"]]},{"rank" : 16,"comment" : "ImagesElm: IsTransformationRepOfEndo","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"],[]]},{"rank" : 14,"comment" : "ImagesElm: method for s.p. gen. mapping respecting add. & add.inv., and element","filters" : [["IsSPGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],[]]},{"rank" : 14,"comment" : "ImagesElm: method for s.p. general mapping respecting mult. & inv., and element","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],[]]},{"rank" : 14,"comment" : "ImagesElm: for mapping by function","filters" : [["IsMappingByFunctionRep"],[]]},{"rank" : 10,"comment" : "ImagesElm: for Lie embedding and object","filters" : [["IsGeneralMapping","IsLieEmbeddingRep"],[]]},{"rank" : 10,"comment" : "ImagesElm: for a restricted mapping, and an element","filters" : [["IsGeneralRestrictedMappingRep"],[]]},{"rank" : 10,"comment" : "ImagesElm: for a composition mapping, and an element","filters" : [["IsCompositionMappingRep"],[]]},{"rank" : 9,"comment" : "ImagesElm: for an inverse mapping and an element","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"],[]]},{"rank" : 9,"comment" : "ImagesElm: for constant time access general mapping, and element","filters" : [["IsGeneralMapping","IsConstantTimeAccessGeneralMapping","Tester(IsConstantTimeAccessGeneralMapping)"],[]]},{"rank" : 8,"comment" : "ImagesElm: for non s.p. general mapping, and element","filters" : [["IsNonSPGeneralMapping"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImagesRepresentative","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10017,"comment" : "ImagesRepresentative: for zero mapping and object","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],[]]},{"rank" : 10017,"comment" : "ImagesRepresentative: for identity mapping and object","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],[]]},{"rank" : 125,"comment" : "ImagesRepresentative: for total GGMBPCGS, and mult.-elm.-with-inverse","filters" : [["IsTotal","Tester(IsTotal)","IsGroupGeneralMappingByPcgs"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 59,"comment" : "ImagesRepresentative: for homomorphisms of free groups","filters" : [["IsFromFpGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]},{"rank" : 47,"comment" : "ImagesRepresentative: for a blow up isomorphism, and a matrix in the source","filters" : [["IsBlowUpIsomorphism"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 37,"comment" : "ImagesRepresentative: for an alg. hom. from f. p. algebra, and an element","filters" : [["IsAlgebraHomomorphismFromFpRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 37,"comment" : "ImagesRepresentative: for an operation algebra homomorphism, and an element","filters" : [["IsOperationAlgebraHomomorphismDefaultRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 36,"comment" : "ImagesRepresentative: for ANF automorphism and scalar","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 35,"comment" : "ImagesRepresentative: for FromPcpGHBI","filters" : [["IsFromPcpGHBI"],["IsPcpElement"]]},{"rank" : 35,"comment" : "ImagesRepresentative: simple tests on equal words to check whether the `generators' are mapped","filters" : [["IsGroupGeneralMappingByImages","IsFromFpGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 35,"comment" : "ImagesRepresentative: map from fp group or free group, use 'MappedWord'","filters" : [["IsFromFpGroupStdGensGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 34,"comment" : "ImagesRepresentative: map from (sub)fp group, rewrite","filters" : [["IsGroupGeneralMappingByImages","IsFromFpGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 33,"comment" : "ImagesRepresentative: for embedding of ring into magma ring, and ring element","filters" : [["IsEmbeddingRingMagmaRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 31,"comment" : "ImagesRepresentative: for Fp to SCA mapping, and element","filters" : [["IsFptoSCAMorphism"],["IsElementOfFpAlgebra"]]},{"rank" : 30,"comment" : "ImagesRepresentative","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcgsToPcgsGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 29,"comment" : "ImagesRepresentative: using `RepresentativeAction'","filters" : [["Tester(ImagesSource)","IsActionHomomorphismByBase"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 29,"comment" : "ImagesRepresentative: imprim perm wreath product embedding","filters" : [["IsEmbeddingImprimitiveWreathProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: for isom by finite matrix groups (Polenta)","filters" : [["IsGroupGeneralMappingByImages","IsIsomorphismByFinitePolycyclicMatrixGroup","Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: for isom by matrix groups (Polenta)","filters" : [["IsGroupGeneralMappingByImages","IsIsomorphismByPolycyclicMatrixGroup","Tester(IsIsomorphismByPolycyclicMatrixGroup)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: for group by field elems isom","filters" : [["IsGroupGeneralMappingByImages","IsMultGroupByFieldElemsIsomorphism","Tester(IsMultGroupByFieldElemsIsomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: for unit groups","filters" : [["IsGroupGeneralMappingByImages","IsUnitGroupIsomorphism","Tester(IsUnitGroupIsomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: restricted perm","filters" : [["IsActionHomomorphismSubset"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: for action hom that is `ByAsGroup'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages","IsActionHomomorphism"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: imprim matrix wreath product embedding","filters" : [["IsEmbeddingImprimitiveWreathProductMatrixGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: matrix direct product projection","filters" : [["IsProjectionDirectProductMatrixGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: matrix direct product embedding","filters" : [["IsEmbeddingDirectProductMatrixGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: perm subdirect product projection","filters" : [["IsProjectionSubdirectProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: perm direct product projection","filters" : [["IsProjectionDirectProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: perm direct product embedding","filters" : [["IsEmbeddingDirectProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: blocks homomorphism","filters" : [["IsBlocksHomomorphism"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: Constituent homomorphism","filters" : [["IsConstituentHomomorphism"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "ImagesRepresentative: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 27,"comment" : "ImagesRepresentative: for action hom","filters" : [["IsActionHomomorphism"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 26,"comment" : "ImagesRepresentative: for Frobenius automorphism and source element","filters" : [["IsFrobeniusAutomorphism"],[]]},{"rank" : 26,"comment" : "ImagesRepresentative: for polring g.m.b.i., and element","filters" : [["IsGeneralMapping","IsPolynomialRingDefaultGeneratorMapping"],[]]},{"rank" : 25,"comment" : "ImagesRepresentative: for algebra g.m.b.i., and element","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"],[]]},{"rank" : 24,"comment" : "ImagesRepresentative","filters" : [["IsGroupGeneralMappingByImages","IsFromAffineCrystGroupToPcpGroup","Tester(IsFromAffineCrystGroupToPcpGroup)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 24,"comment" : "ImagesRepresentative","filters" : [["IsGroupGeneralMappingByImages","IsFromAffineCrystGroupToFpGroup","Tester(IsFromAffineCrystGroupToFpGroup)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 24,"comment" : "ImagesRepresentative","filters" : [["IsGroupGeneralMappingByImages","IsPointHomomorphism","Tester(IsPointHomomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 24,"comment" : "ImagesRepresentative: word decomp hom","filters" : [["IsGroupGeneralMappingByImages","IsWordDecompHomomorphism","Tester(IsWordDecompHomomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 24,"comment" : "ImagesRepresentative: perm group hom","filters" : [["IsPermGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 24,"comment" : "ImagesRepresentative: for SC ring g.m.b.i., and element","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsSCRingGeneralMappingByImagesDefaultRep"],[]]},{"rank" : 23,"comment" : "ImagesRepresentative: for `ByAsGroupGeneralMapping' hom","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 23,"comment" : "ImagesRepresentative: for left module m.b.m., and element","filters" : [["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"],[]]},{"rank" : 23,"comment" : "ImagesRepresentative: for left module g.m.b.i., and element","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"],[]]},{"rank" : 22,"comment" : "ImagesRepresentative: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"],[]]},{"rank" : 22,"comment" : "ImagesRepresentative: for group automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"],[]]},{"rank" : 22,"comment" : "ImagesRepresentative: parallel enumeration of source and range","filters" : [["IsGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 22,"comment" : "ImagesRepresentative: for embedding of magma into magma ring, and mult. element","filters" : [["IsEmbeddingMagmaMagmaRing"],["IsMultiplicativeElement"]]},{"rank" : 21,"comment" : "ImagesRepresentative: equivalence relations","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]},{"rank" : 20,"comment" : "ImagesRepresentative: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"],["IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "ImagesRepresentative: for mapping by function","filters" : [["IsMappingByFunctionRep"],[]]},{"rank" : 10,"comment" : "ImagesRepresentative: for a restricted mapping, and an element","filters" : [["IsGeneralRestrictedMappingRep"],[]]},{"rank" : 10,"comment" : "ImagesRepresentative: for a composition mapping, and an element","filters" : [["IsCompositionMappingRep"],[]]},{"rank" : 9,"comment" : "ImagesRepresentative: for an inverse mapping and an element","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"],[]]},{"rank" : 8,"comment" : "ImagesRepresentative: for non s.p. general mapping, and element","filters" : [["IsNonSPGeneralMapping"],[]]},{"rank" : 8,"comment" : "ImagesRepresentative: for s.p. general mapping, and element","filters" : [["IsSPGeneralMapping"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImagesSet","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10019,"comment" : "ImagesSet: for zero mapping and collection","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],["IsCollection"]]},{"rank" : 10019,"comment" : "ImagesSet: for identity mapping and collection","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],["IsCollection"]]},{"rank" : 79,"comment" : "ImagesSet: constituent homomorphism","filters" : [["IsConstituentHomomorphism"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(StabChainMutable)"]]},{"rank" : 78,"comment" : "ImagesSet: for blocks homomorphism and perm. group","filters" : [["IsBlocksHomomorphism"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 78,"comment" : "ImagesSet: for ANF automorphism and field","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 78,"comment" : "ImagesSet: for Frobenius automorphism and field contained in the source","filters" : [["IsFrobeniusAutomorphism"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 75,"comment" : "ImagesSet: for field homomorphism and field","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 56,"comment" : "ImagesSet: for conjugator isomorphism, and group","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 56,"comment" : "ImagesSet: method for algebra-with-one hom. and FLMLOR-with-one","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 52,"comment" : "ImagesSet: for polring g.m.b.i., and ring","filters" : [["IsGeneralMapping","IsPolynomialRingDefaultGeneratorMapping"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 52,"comment" : "ImagesSet: method for algebra hom. and FLMLOR","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 52,"comment" : "ImagesSet: method for injective s.p. mapping respecting mult. & inv., and group","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "ImagesSet: method for s.p. general mapping respecting mult. & inv., and group","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 38,"comment" : "ImagesSet: method for linear mapping and left module","filters" : [["IsSPGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 30,"comment" : "ImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group","filters" : [["IsSPGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 24,"comment" : "ImagesSet: for general mapping, and empty list","filters" : [["IsGeneralMapping"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 12,"comment" : "ImagesSet: for a restricted mapping, and an collection","filters" : [["IsGeneralRestrictedMappingRep"],["IsCollection"]]},{"rank" : 12,"comment" : "ImagesSet: for a composition mapping, and an collection","filters" : [["IsCompositionMappingRep"],["IsCollection"]]},{"rank" : 11,"comment" : "ImagesSet: for an inverse mapping and a collection","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"],["IsCollection"]]},{"rank" : 9,"comment" : "ImagesSet: for general mapping, and finite collection","filters" : [["IsGeneralMapping"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImageElm","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10017,"comment" : "ImageElm: for zero mapping and object","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],[]]},{"rank" : 10017,"comment" : "ImageElm: for identity mapping and object","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],[]]},{"rank" : 42,"comment" : "ImageElm: for ANF automorphism and scalar","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsCyc"]]},{"rank" : 31,"comment" : "ImageElm: for Fp to SCA mapping, and element","filters" : [["IsFptoSCAMorphism"],["IsElementOfFpAlgebra"]]},{"rank" : 26,"comment" : "ImageElm: for Frobenius automorphism and source element","filters" : [["IsFrobeniusAutomorphism"],[]]},{"rank" : 14,"comment" : "ImageElm: for mapping by function","filters" : [["IsMappingByFunctionRep"],[]]},{"rank" : 13,"comment" : "ImageElm: for an inverse mapping and an element","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInverseGeneralMappingRep"],[]]},{"rank" : 11,"comment" : "ImageElm: for mapping, and element","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],[]]},{"rank" : 7,"comment" : "ImageElm: for general mapping, and element","filters" : [["IsGeneralMapping"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImagesElm","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10017,"comment" : "PreImagesElm: for zero mapping and object","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],[]]},{"rank" : 10017,"comment" : "PreImagesElm: for identity mapping and object","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],[]]},{"rank" : 37,"comment" : "PreImagesElm: for embedding of ring into magma ring, and free magma ring element","filters" : [["IsEmbeddingRingMagmaRing"],["IsElementOfFreeMagmaRing"]]},{"rank" : 36,"comment" : "PreImagesElm: for ANF automorphism and scalar","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 31,"comment" : "PreImagesElm: for embedding of magma into magma ring, and free magma ring element","filters" : [["IsEmbeddingMagmaMagmaRing"],["IsElementOfFreeMagmaRing"]]},{"rank" : 31,"comment" : "PreImagesElm: for binary rels over [1..n] with images list","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"],["IsInt","IsPosRat"]]},{"rank" : 23,"comment" : "PreImagesElm: for field homomorphism and element","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"],[]]},{"rank" : 23,"comment" : "PreImagesElm: for Lie embedding and Lie object in default representation","filters" : [["IsGeneralMapping","IsLieEmbeddingRep"],["IsPackedElementDefaultRep","IsLieObject"]]},{"rank" : 22,"comment" : "PreImagesElm: equivalence relations with parition and element","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","Tester(EquivalenceRelationPartition)"],[]]},{"rank" : 19,"comment" : "PreImagesElm: for mapping by function","filters" : [["IsMappingByFunctionWithInverseRep"],[]]},{"rank" : 14,"comment" : "PreImagesElm: method for s.p. gen. mapping respecting add. & add.inv., and element","filters" : [["IsSPGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],[]]},{"rank" : 14,"comment" : "PreImagesElm: method for s.p. general mapping respecting mult. & inv., and element","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],[]]},{"rank" : 10,"comment" : "PreImagesElm: for a restricted mapping, and an element","filters" : [["IsGeneralRestrictedMappingRep"],[]]},{"rank" : 10,"comment" : "PreImagesElm: for a composition mapping, and an element","filters" : [["IsCompositionMappingRep"],[]]},{"rank" : 9,"comment" : "PreImagesElm: for an inverse mapping and an element","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"],[]]},{"rank" : 9,"comment" : "PreImagesElm: for constant time access general mapping, and element","filters" : [["IsGeneralMapping","IsConstantTimeAccessGeneralMapping","Tester(IsConstantTimeAccessGeneralMapping)"],[]]},{"rank" : 7,"comment" : "PreImagesElm: for general mapping with finite source, and element","filters" : [["IsGeneralMapping"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImageElm","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10017,"comment" : "PreImageElm: for identity mapping and object","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],[]]},{"rank" : 40,"comment" : "PreImageElm: for ANF automorphism and scalar","filters" : [["IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 19,"comment" : "PreImageElm: for mapping by function","filters" : [["IsMappingByFunctionWithInverseRep"],[]]},{"rank" : 13,"comment" : "PreImageElm: for an inj. & surj. inverse mapping, and an element","filters" : [["IsGeneralMapping","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsInverseGeneralMappingRep"],[]]},{"rank" : 11,"comment" : "PreImageElm: for inj. & surj. general mapping, and element","filters" : [["IsGeneralMapping","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)"],[]]},{"rank" : 7,"comment" : "PreImageElm: for general mapping, and element","filters" : [["IsGeneralMapping"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImagesRepresentative","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10017,"comment" : "PreImagesRepresentative: for zero mapping and object","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],[]]},{"rank" : 10017,"comment" : "PreImagesRepresentative: for identity mapping and object","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],[]]},{"rank" : 59,"comment" : "PreImagesRepresentative: for an alg. hom. from f. p. algebra, and an element","filters" : [["IsAlgebraHomomorphismFromFpRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 59,"comment" : "PreImagesRepresentative: for an operation algebra homomorphism, and an element","filters" : [["IsOperationAlgebraHomomorphismDefaultRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 47,"comment" : "PreImagesRepresentative: for a blow up isomorphism, and a matrix in the range","filters" : [["IsBlowUpIsomorphism"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 37,"comment" : "PreImagesRepresentative: for embedding of ring into magma ring, and free magma ring element","filters" : [["IsEmbeddingRingMagmaRing"],["IsElementOfFreeMagmaRing"]]},{"rank" : 36,"comment" : "PreImagesRepresentative: for ANF automorphism and scalar","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 35,"comment" : "PreImagesRepresentative: for ToPcpGHBI","filters" : [["IsToPcpGHBI"],["IsPcpElement"]]},{"rank" : 33,"comment" : "PreImagesRepresentative: for Fp to SCA mapping, and element","filters" : [["IsFptoSCAMorphism"],["IsSCAlgebraObj"]]},{"rank" : 32,"comment" : "PreImagesRepresentative: AutomGroup Niceomorphism","filters" : [["IsActionHomomorphismAutomGroup"],["IsPerm"]]},{"rank" : 31,"comment" : "PreImagesRepresentative: IsProjectiveActionHomomorphism","filters" : [["IsProjectiveActionHomomorphism"],["IsPerm"]]},{"rank" : 31,"comment" : "PreImagesRepresentative: IsLinearActionHomomorphism","filters" : [["IsLinearActionHomomorphism"],["IsPerm"]]},{"rank" : 31,"comment" : "PreImagesRepresentative: constituent homomorphism","filters" : [["IsConstituentHomomorphism"],["IsPerm"]]},{"rank" : 31,"comment" : "PreImagesRepresentative: for embedding of magma into magma ring, and free magma ring element","filters" : [["IsEmbeddingMagmaMagmaRing"],["IsElementOfFreeMagmaRing"]]},{"rank" : 30,"comment" : "PreImagesRepresentative","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcgsToPcgsGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 29,"comment" : "PreImagesRepresentative: imprim perm wreath product embedding","filters" : [["IsEmbeddingImprimitiveWreathProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: hom. to standard generators of fp group, using 'MappedWord'","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsToFpGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: imprim matrix wreath product embedding","filters" : [["IsEmbeddingImprimitiveWreathProductMatrixGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: matrix direct product projection","filters" : [["IsProjectionDirectProductMatrixGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: matrix direct product embedding","filters" : [["IsEmbeddingDirectProductMatrixGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: perm subdirect product projection","filters" : [["IsProjectionSubdirectProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: perm direct product projection","filters" : [["IsProjectionDirectProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: perm direct product embedding","filters" : [["IsEmbeddingDirectProductPermGroup"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: blocks homomorphism","filters" : [["IsBlocksHomomorphism"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "PreImagesRepresentative: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 27,"comment" : "PreImagesRepresentative: method for pcgs hom","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsToPcGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 26,"comment" : "PreImagesRepresentative: for algebra g.m.b.i. knowing inverse, and element","filters" : [["IsGeneralMapping","Tester(InverseGeneralMapping)","IsAlgebraGeneralMappingByImagesDefaultRep"],[]]},{"rank" : 25,"comment" : "PreImagesRepresentative: for homomorphisms of free groups","filters" : [["IsToFpGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]},{"rank" : 25,"comment" : "PreImagesRepresentative: for algebra g.m.b.i., and element","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"],[]]},{"rank" : 24,"comment" : "PreImagesRepresentative","filters" : [["IsGroupGeneralMappingByImages","IsPointHomomorphism","Tester(IsPointHomomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 23,"comment" : "PreImagesRepresentative: for PBG-Niceo","filters" : [["IsPreimagesByAsGroupGeneralMappingByImages","IsNiceMonomorphism"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 23,"comment" : "PreImagesRepresentative","filters" : [["IsToPermGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 23,"comment" : "PreImagesRepresentative: for ring g.m.b.i., and element","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","IsRingGeneralMappingByImagesDefaultRep"],[]]},{"rank" : 23,"comment" : "PreImagesRepresentative: for left module m.b.m., and element","filters" : [["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"],[]]},{"rank" : 23,"comment" : "PreImagesRepresentative: for left module g.m.b.i., and element","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"],[]]},{"rank" : 22,"comment" : "PreImagesRepresentative: for GHBI and mult.-elm.-with-inverse","filters" : [["IsGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 22,"comment" : "PreImagesRepresentative: for PBG-Hom","filters" : [["IsPreimagesByAsGroupGeneralMappingByImages"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "PreImagesRepresentative: equivalence relations","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]},{"rank" : 20,"comment" : "PreImagesRepresentative: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"],["IsMultiplicativeElement"]]},{"rank" : 19,"comment" : "PreImagesRepresentative: for mapping by function with inverse","filters" : [["IsMappingByFunctionWithInverseRep"],[]]},{"rank" : 14,"comment" : "PreImagesRepresentative: for mapping by function","filters" : [["IsMappingByFunctionRep"],[]]},{"rank" : 10,"comment" : "PreImagesRepresentative: for a restricted mapping, and an element","filters" : [["IsGeneralRestrictedMappingRep"],[]]},{"rank" : 10,"comment" : "PreImagesRepresentative: for a composition mapping, and an element","filters" : [["IsCompositionMappingRep"],[]]},{"rank" : 9,"comment" : "PreImagesRepresentative: for an inverse mapping and an element","filters" : [["IsInverseGeneralMappingRep"],[]]},{"rank" : 8,"comment" : "PreImagesRepresentative: for total non-s.p. general mapping, and element","filters" : [["IsNonSPGeneralMapping"],[]]},{"rank" : 8,"comment" : "PreImagesRepresentative: for s.p. general mapping, and element","filters" : [["IsSPGeneralMapping"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImagesSet","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10019,"comment" : "PreImagesSet: for zero mapping and collection","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],["IsCollection"]]},{"rank" : 10019,"comment" : "PreImagesSet: for identity mapping and collection","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],["IsCollection"]]},{"rank" : 89,"comment" : "PreImagesSet: for PcpGHBI","filters" : [["IsFromPcpGHBI","IsToPcpGHBI"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 78,"comment" : "PreImagesSet","filters" : [["IsBlocksHomomorphism"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 78,"comment" : "PreImagesSet: constituent homomorphism","filters" : [["IsConstituentHomomorphism"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 78,"comment" : "PreImagesSet: for ANF automorphism and scalar","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 75,"comment" : "PreImagesSet: for field homomorphism and field","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 61,"comment" : "PreImagesSet: map from (sub)group of fp group","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsFromFpGroupGeneralMapping"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 56,"comment" : "PreImagesSet: for conjugator isomorphism, and group","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 56,"comment" : "PreImagesSet: method for algebra-with-one hom. and FLMLOR-with-one","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 52,"comment" : "PreImagesSet: method for algebra hom. and FLMLOR","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 52,"comment" : "PreImagesSet: method for injective s.p. mapping respecting mult. & inv., and group","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 51,"comment" : "PreImagesSet: method for permgroup homs","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPermGroupGeneralMapping"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "PreImagesSet: method for s.p. general mapping respecting mult. & inv., and group","filters" : [["IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 38,"comment" : "PreImagesSet: method for linear mapping and left module","filters" : [["IsSPGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 30,"comment" : "PreImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group","filters" : [["IsSPGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"],["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 24,"comment" : "PreImagesSet: for general mapping, and empty list","filters" : [["IsGeneralMapping"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 12,"comment" : "PreImagesSet: for a restricted mapping, and an collection","filters" : [["IsGeneralRestrictedMappingRep"],["IsCollection"]]},{"rank" : 12,"comment" : "PreImagesSet: for a composition mapping, and an collection","filters" : [["IsCompositionMappingRep"],["IsCollection"]]},{"rank" : 11,"comment" : "PreImagesSet: for an inverse mapping and a collection","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"],["IsCollection"]]},{"rank" : 9,"comment" : "PreImagesSet: for general mapping, and finite collection","filters" : [["IsGeneralMapping"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CompositionMapping2","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10028,"comment" : "CompositionMapping2: for zero mapping and single-valued gen. mapping that resp. zero","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping"],["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 10025,"comment" : "CompositionMapping2: for identity mapping and general mapping","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping"],["IsGeneralMapping"]]},{"rank" : 10025,"comment" : "CompositionMapping2: for general mapping and identity mapping","filters" : [["IsGeneralMapping"],["IsOne","Tester(IsOne)","IsGeneralMapping"]]},{"rank" : 10024,"comment" : "CompositionMapping2: for general mapping and zero mapping","filters" : [["IsGeneralMapping"],["IsZero","Tester(IsZero)","IsGeneralMapping"]]},{"rank" : 56,"comment" : "CompositionMapping2: method for two pc group automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsPcGroupGeneralMappingByImages","IsToPcGroupGeneralMappingByImages"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsPcGroupGeneralMappingByImages","IsToPcGroupGeneralMappingByImages"]]},{"rank" : 54,"comment" : "CompositionMapping2: for two inner automorphisms","filters" : [["IsInnerAutomorphism","Tester(IsInnerAutomorphism)"],["IsInnerAutomorphism","Tester(IsInnerAutomorphism)"]]},{"rank" : 52,"comment" : "CompositionMapping2: for two ANF automorphisms","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"],["IsFieldHomomorphism","Tester(IsFieldHomomorphism)","IsANFAutomorphismRep"]]},{"rank" : 52,"comment" : "CompositionMapping2: for two Frobenius automorphisms","filters" : [["IsFrobeniusAutomorphism"],["IsFrobeniusAutomorphism"]]},{"rank" : 51,"comment" : "CompositionMapping2: for gp. hom. and fp. hom, transferring the coset table","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsFromFpGroupGeneralMappingByImages","Tester(CosetTableFpHom)"]]},{"rank" : 50,"comment" : "CompositionMapping2: for two conjugator automorphisms","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"],["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 47,"comment" : "CompositionMapping2: fp hom. with perm group hom.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsToFpGroupGeneralMappingByImages"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsPermGroupGeneralMappingByImages"]]},{"rank" : 46,"comment" : "CompositionMapping2: for two conjugator isomorphisms","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"],["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 46,"comment" : "CompositionMapping2: for left module hom. and algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 46,"comment" : "CompositionMapping2: for left module hom. and linear m.b.m.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 45,"comment" : "CompositionMapping2: for action homomorphism with blocks homomorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsBlocksHomomorphism"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsActionHomomorphism"]]},{"rank" : 44,"comment" : "CompositionMapping2: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 44,"comment" : "CompositionMapping2: for group automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]},{"rank" : 44,"comment" : "CompositionMapping2: for left module hom. and algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 42,"comment" : "CompositionMapping2: for left module hom. and linear g.m.b.i.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"],["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 40,"comment" : "CompositionMapping2: group hom. with perm group hom.","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsPermGroupGeneralMappingByImages"]]},{"rank" : 39,"comment" : "CompositionMapping2: method for hom2 from pc group","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsGroupGeneralMappingByPcgs"]]},{"rank" : 34,"comment" : "CompositionMapping2: for semigroup homomorphism by images","filters" : [["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"],["IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupHomomorphismByImagesRep"]]},{"rank" : 32,"comment" : "CompositionMapping2: IsTransformationRepOfEndo, IsTransformationRepOfEndo","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"]]},{"rank" : 30,"comment" : "CompositionMapping2: for gp. hom. and gp. gen. mapp., using `MappingGeneratorsImages'","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 29,"comment" : "CompositionMapping2: IsTransformationRepOfEndo, IsEndoMapping","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 29,"comment" : "CompositionMapping2: IsEndoMapping, IsTransformationRepOfEndo","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"]]},{"rank" : 14,"comment" : "CompositionMapping2: for two general mappings","filters" : [["IsGeneralMapping"],["IsGeneralMapping"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroMapping","type" : "GAP_Operation","filters" : [[["IsCollection"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "ZeroMapping: for collection and additive-magma-with-zero","filters" : [["IsCollection"],["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10046,"comment" : "RestrictedMapping: try if restriction is proper","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 10015,"comment" : "RestrictedMapping: for mapping that is already restricted","filters" : [["IsGeneralMapping","IsGeneralRestrictedMappingRep"],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 55,"comment" : "RestrictedMapping: action homomorphism","filters" : [["IsActionHomomorphism"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 52,"comment" : "RestrictedMapping: injective case: use GeneralRestrictedMapping","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "RestrictedMapping: create new GHBI","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 12,"comment" : "RestrictedMapping: use GeneralRestrictedMapping","filters" : [["IsGeneralMapping"],["IsCollection","IsGeneralizedDomain"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Embedding","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 78,"comment" : "Embedding: generic method for perm semidirect products","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SemidirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 78,"comment" : "Embedding: perm wreath product","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 78,"comment" : "Embedding: perm direct product","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 75,"comment" : "Embedding: LAGUNA: from group to pc-presented normalized unit group of group ring","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]},{"rank" : 68,"comment" : "Embedding: pcp wreath product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : 68,"comment" : "Embedding","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : 66,"comment" : "Embedding: of semidirect pc group and integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)","Tester(SemidirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 66,"comment" : "Embedding: of pc group and integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "Embedding: matrix wreath product","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "Embedding: matrix direct product","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 62,"comment" : "Embedding: for ring and magma ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFreeMagmaRing"]]},{"rank" : 59,"comment" : "Embedding: generic wreath product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)","CategoryCollections(IsWreathProductElement)"],["IsInt","IsPosRat"]]},{"rank" : 56,"comment" : "Embedding: LAGUNA: from a group to the Lie algebra of the group ring","filters" : [["IsMagma"],["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 53,"comment" : "Embedding: free products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FreeProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "Embedding: vectorspace semidirect products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SemidirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "Embedding: of semidirect product and integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SemidirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "Embedding: group direct product and integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 47,"comment" : "Embedding: for magma and magma ring","filters" : [["IsMagma"],["IsFreeMagmaRing"]]},{"rank" : 3,"comment" : "Embedding: for two families, the first with known Lie family","filters" : [["IsFamily","Tester(LieFamily)"],["IsFamily"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Projection","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 59,"comment" : "Projection: generic method for perm semidirect products","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SemidirectProductInfo)"]]},{"rank" : 59,"comment" : "Projection: perm wreath product","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)"]]},{"rank" : 47,"comment" : "Projection: of semidirect pc group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)","Tester(SemidirectProductInfo)"]]},{"rank" : 44,"comment" : "Projection: matrix wreath product","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)"]]},{"rank" : 40,"comment" : "Projection: generic wreath product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(WreathProductInfo)","CategoryCollections(IsWreathProductElement)"]]},{"rank" : 34,"comment" : "Projection: of semidirect product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SemidirectProductInfo)"]]}],"2args" : [{"rank" : 78,"comment" : "Projection: perm subdirect product","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SubdirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 78,"comment" : "Projection: perm direct product","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 68,"comment" : "Projection","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : 66,"comment" : "Projection: of pc group and integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "Projection: matrix direct product","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "Projection: pc subdirect product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SubdirectProductInfo)"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "Projection: group direct product and integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MappingGeneratorsImages","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "MappingGeneratorsImages: system getter","filters" : [["IsAttributeStoringRep","Tester(MappingGeneratorsImages)"]]},{"rank" : 23,"comment" : "MappingGeneratorsImages: for action hom that is `ByAsGroup'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages","IsActionHomomorphism"]]},{"rank" : 23,"comment" : "MappingGeneratorsImages: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 17,"comment" : "MappingGeneratorsImages: for group homomorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 0,"comment" : "MappingGeneratorsImages:  fallback method to test conditions","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MappingGeneratorsImages)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MappingGeneratorsImages): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MappingGeneratorsImages): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MappingGeneratorsImages)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RespectsMultiplication","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RespectsMultiplication: system getter","filters" : [["IsAttributeStoringRep","Tester(RespectsMultiplication)"]]},{"rank" : 7,"comment" : "RespectsMultiplication: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RespectsMultiplication)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RespectsMultiplication): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RespectsMultiplication): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RespectsMultiplication)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RespectsOne","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RespectsOne: system getter","filters" : [["IsAttributeStoringRep","Tester(RespectsOne)"]]},{"rank" : 7,"comment" : "RespectsOne: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RespectsOne)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RespectsOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RespectsOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RespectsOne)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RespectsInverses","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RespectsInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(RespectsInverses)"]]},{"rank" : 7,"comment" : "RespectsInverses: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RespectsInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RespectsInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RespectsInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RespectsInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KernelOfMultiplicativeGeneralMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "KernelOfMultiplicativeGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(KernelOfMultiplicativeGeneralMapping)"]]},{"rank" : 10013,"comment" : "KernelOfMultiplicativeGeneralMapping: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 10013,"comment" : "KernelOfMultiplicativeGeneralMapping: method for an injective gen. mapping that respects mult. and one","filters" : [["IsGeneralMapping","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)"]]},{"rank" : 41,"comment" : "KernelOfMultiplicativeGeneralMapping: for PcpGHBI","filters" : [["IsFromPcpGHBI","IsToPcpGHBI"]]},{"rank" : 29,"comment" : "KernelOfMultiplicativeGeneralMapping: from fp\/free group, std. gens., to perm group","filters" : [["IsToPermGroupGeneralMappingByImages","IsFromFpGroupGeneralMapping"]]},{"rank" : 24,"comment" : "KernelOfMultiplicativeGeneralMapping: hom from fp grp","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsFromFpGroupGeneralMapping"]]},{"rank" : 24,"comment" : "KernelOfMultiplicativeGeneralMapping: method for homs from pc group into pc group or perm group","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcGroupGeneralMappingByImages","IsToPcGroupGeneralMappingByImages"]]},{"rank" : 23,"comment" : "KernelOfMultiplicativeGeneralMapping: matrix direct product projection","filters" : [["IsProjectionDirectProductMatrixGroup"]]},{"rank" : 23,"comment" : "KernelOfMultiplicativeGeneralMapping: perm subdirect product projection","filters" : [["IsProjectionSubdirectProductPermGroup"]]},{"rank" : 23,"comment" : "KernelOfMultiplicativeGeneralMapping: perm direct product projection","filters" : [["IsProjectionDirectProductPermGroup"]]},{"rank" : 23,"comment" : "KernelOfMultiplicativeGeneralMapping: blocks homomorphism","filters" : [["IsBlocksHomomorphism"]]},{"rank" : 23,"comment" : "KernelOfMultiplicativeGeneralMapping: for constituent homomorphism","filters" : [["IsConstituentHomomorphism"]]},{"rank" : 23,"comment" : "KernelOfMultiplicativeGeneralMapping: method for homs from pc group","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPcGroupGeneralMappingByImages"]]},{"rank" : 22,"comment" : "KernelOfMultiplicativeGeneralMapping: for action homomorphism","filters" : [["IsActionHomomorphism"]]},{"rank" : 20,"comment" : "KernelOfMultiplicativeGeneralMapping: for perm to perm group homs, compute stab chain, try again","filters" : [["IsPermGroupGeneralMappingByImages","IsToPermGroupGeneralMappingByImages"]]},{"rank" : 20,"comment" : "KernelOfMultiplicativeGeneralMapping: hom by function","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsMappingByFunctionRep"]]},{"rank" : 19,"comment" : "KernelOfMultiplicativeGeneralMapping","filters" : [["IsGroupGeneralMappingByImages","IsPointHomomorphism","Tester(IsPointHomomorphism)"]]},{"rank" : 18,"comment" : "KernelOfMultiplicativeGeneralMapping: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "KernelOfMultiplicativeGeneralMapping: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 16,"comment" : "KernelOfMultiplicativeGeneralMapping: for a restricted mapping that resp. mult. and inv.","filters" : [["IsGeneralMapping","IsGeneralRestrictedMappingRep","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 16,"comment" : "KernelOfMultiplicativeGeneralMapping: for a composition mapping that resp. mult. and inv.","filters" : [["IsGeneralMapping","IsCompositionMappingRep","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 11,"comment" : "KernelOfMultiplicativeGeneralMapping: method for a finite general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)"]]},{"rank" : 9,"comment" : "KernelOfMultiplicativeGeneralMapping: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KernelOfMultiplicativeGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KernelOfMultiplicativeGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KernelOfMultiplicativeGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KernelOfMultiplicativeGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoKernelOfMultiplicativeGeneralMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "CoKernelOfMultiplicativeGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(CoKernelOfMultiplicativeGeneralMapping)"]]},{"rank" : 10013,"comment" : "CoKernelOfMultiplicativeGeneralMapping: get delayed set attribute values","filters" : [["Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 10013,"comment" : "CoKernelOfMultiplicativeGeneralMapping: method for a single-valued gen. mapping that respects mult. and one","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)"]]},{"rank" : 29,"comment" : "CoKernelOfMultiplicativeGeneralMapping: for PcpGHBI","filters" : [["IsFromPcpGHBI"]]},{"rank" : 29,"comment" : "CoKernelOfMultiplicativeGeneralMapping: GHBI from fp grp","filters" : [["IsGroupGeneralMappingByImages","IsFromFpGroupGeneralMappingByImages"]]},{"rank" : 20,"comment" : "CoKernelOfMultiplicativeGeneralMapping","filters" : [["IsPermGroupGeneralMappingByImages","IsToPermGroupGeneralMappingByImages"]]},{"rank" : 19,"comment" : "CoKernelOfMultiplicativeGeneralMapping","filters" : [["IsGroupGeneralMappingByImages","IsPointHomomorphism","Tester(IsPointHomomorphism)"]]},{"rank" : 19,"comment" : "CoKernelOfMultiplicativeGeneralMapping","filters" : [["IsPermGroupGeneralMappingByImages"]]},{"rank" : 18,"comment" : "CoKernelOfMultiplicativeGeneralMapping: for GMBPCGS: evaluate relations","filters" : [["IsGroupGeneralMappingByPcgs"]]},{"rank" : 18,"comment" : "CoKernelOfMultiplicativeGeneralMapping: via `AsGroupGeneralMappingByImages'","filters" : [["IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]]},{"rank" : 17,"comment" : "CoKernelOfMultiplicativeGeneralMapping: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 16,"comment" : "CoKernelOfMultiplicativeGeneralMapping: for a restricted mapping that resp. mult. and inv.","filters" : [["IsGeneralMapping","IsGeneralRestrictedMappingRep","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 16,"comment" : "CoKernelOfMultiplicativeGeneralMapping: for a composition mapping that resp. mult. and inv.","filters" : [["IsGeneralMapping","IsCompositionMappingRep","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 11,"comment" : "CoKernelOfMultiplicativeGeneralMapping: method for a finite general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)"]]},{"rank" : 9,"comment" : "CoKernelOfMultiplicativeGeneralMapping: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoKernelOfMultiplicativeGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoKernelOfMultiplicativeGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoKernelOfMultiplicativeGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoKernelOfMultiplicativeGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RespectsAddition","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RespectsAddition: system getter","filters" : [["IsAttributeStoringRep","Tester(RespectsAddition)"]]},{"rank" : 7,"comment" : "RespectsAddition: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RespectsAddition)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RespectsAddition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RespectsAddition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RespectsAddition)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RespectsZero","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RespectsZero: system getter","filters" : [["IsAttributeStoringRep","Tester(RespectsZero)"]]},{"rank" : 7,"comment" : "RespectsZero: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RespectsZero)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RespectsZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RespectsZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RespectsZero)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RespectsAdditiveInverses","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RespectsAdditiveInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(RespectsAdditiveInverses)"]]},{"rank" : 7,"comment" : "RespectsAdditiveInverses: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RespectsAdditiveInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RespectsAdditiveInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RespectsAdditiveInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RespectsAdditiveInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KernelOfAdditiveGeneralMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "KernelOfAdditiveGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(KernelOfAdditiveGeneralMapping)"]]},{"rank" : 10021,"comment" : "KernelOfAdditiveGeneralMapping: method for zero mapping","filters" : [["IsZero","Tester(IsZero)","IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 10013,"comment" : "KernelOfAdditiveGeneralMapping: method for an injective gen. mapping that respects add. and zero","filters" : [["IsGeneralMapping","IsInjective","Tester(IsInjective)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 29,"comment" : "KernelOfAdditiveGeneralMapping: for operation algebra hom. with fin. dim. source","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsOperationAlgebraHomomorphismDefaultRep"]]},{"rank" : 25,"comment" : "KernelOfAdditiveGeneralMapping: for algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "KernelOfAdditiveGeneralMapping: for a field homomorphism","filters" : [["IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]]},{"rank" : 23,"comment" : "KernelOfAdditiveGeneralMapping: for ring g.m.b.i.","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "KernelOfAdditiveGeneralMapping: for left module m.b.m.","filters" : [["IsGeneralMapping","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 23,"comment" : "KernelOfAdditiveGeneralMapping: for left module g.m.b.i.","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 16,"comment" : "KernelOfAdditiveGeneralMapping: for a restricted mapping that resp. add. and add.inv.","filters" : [["IsGeneralMapping","IsGeneralRestrictedMappingRep","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 16,"comment" : "KernelOfAdditiveGeneralMapping: for a composition mapping that resp. add. and add.inv.","filters" : [["IsGeneralMapping","IsCompositionMappingRep","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 15,"comment" : "KernelOfAdditiveGeneralMapping: method for a finite linear mapping","filters" : [["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 11,"comment" : "KernelOfAdditiveGeneralMapping: method for a finite general mapping","filters" : [["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 9,"comment" : "KernelOfAdditiveGeneralMapping: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KernelOfAdditiveGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KernelOfAdditiveGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KernelOfAdditiveGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KernelOfAdditiveGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoKernelOfAdditiveGeneralMapping","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "CoKernelOfAdditiveGeneralMapping: system getter","filters" : [["IsAttributeStoringRep","Tester(CoKernelOfAdditiveGeneralMapping)"]]},{"rank" : 10013,"comment" : "CoKernelOfAdditiveGeneralMapping: method for a single-valued gen. mapping that respects add. and zero","filters" : [["IsGeneralMapping","IsSingleValued","Tester(IsSingleValued)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 25,"comment" : "CoKernelOfAdditiveGeneralMapping: for algebra g.m.b.i.","filters" : [["IsGeneralMapping","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "CoKernelOfAdditiveGeneralMapping: for ring g.m.b.i.","filters" : [["IsGeneralMapping","IsRingGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "CoKernelOfAdditiveGeneralMapping: for left module g.m.b.i.","filters" : [["IsGeneralMapping","IsLinearGeneralMappingByImagesDefaultRep"]]},{"rank" : 16,"comment" : "CoKernelOfAdditiveGeneralMapping: for a restricted mapping that resp. add. and add.inv.","filters" : [["IsGeneralMapping","IsGeneralRestrictedMappingRep","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 16,"comment" : "CoKernelOfAdditiveGeneralMapping: for a composition mapping that resp. add. and add.inv.","filters" : [["IsGeneralMapping","IsCompositionMappingRep","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]]},{"rank" : 15,"comment" : "CoKernelOfAdditiveGeneralMapping: method for a finite linear mapping","filters" : [["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]},{"rank" : 11,"comment" : "CoKernelOfAdditiveGeneralMapping: method for a finite general mapping","filters" : [["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)"]]},{"rank" : 9,"comment" : "CoKernelOfAdditiveGeneralMapping: for an inverse mapping","filters" : [["IsGeneralMapping","IsInverseGeneralMappingRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoKernelOfAdditiveGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoKernelOfAdditiveGeneralMapping): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoKernelOfAdditiveGeneralMapping): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoKernelOfAdditiveGeneralMapping)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RespectsScalarMultiplication","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RespectsScalarMultiplication: system getter","filters" : [["IsAttributeStoringRep","Tester(RespectsScalarMultiplication)"]]},{"rank" : 7,"comment" : "RespectsScalarMultiplication: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RespectsScalarMultiplication)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RespectsScalarMultiplication): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RespectsScalarMultiplication): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RespectsScalarMultiplication)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLinearMapping","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFieldHomomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsFieldHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFieldHomomorphism)"]]},{"rank" : 7,"comment" : "IsFieldHomomorphism","filters" : [["IsGeneralMapping"]]},{"rank" : 7,"comment" : "IsFieldHomomorphism: method for a general mapping","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFieldHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFieldHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFieldHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFieldHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformsMultiplicationIntoAddition","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "TransformsMultiplicationIntoAddition: system getter","filters" : [["IsAttributeStoringRep","Tester(TransformsMultiplicationIntoAddition)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransformsMultiplicationIntoAddition)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransformsMultiplicationIntoAddition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransformsMultiplicationIntoAddition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransformsMultiplicationIntoAddition)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TranformsOneIntoZero","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "TranformsOneIntoZero: system getter","filters" : [["IsAttributeStoringRep","Tester(TranformsOneIntoZero)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TranformsOneIntoZero)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TranformsOneIntoZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TranformsOneIntoZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TranformsOneIntoZero)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformsInversesIntoAdditiveInverses","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "TransformsInversesIntoAdditiveInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(TransformsInversesIntoAdditiveInverses)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransformsInversesIntoAdditiveInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransformsInversesIntoAdditiveInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransformsInversesIntoAdditiveInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransformsInversesIntoAdditiveInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformsAdditionIntoMultiplication","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "TransformsAdditionIntoMultiplication: system getter","filters" : [["IsAttributeStoringRep","Tester(TransformsAdditionIntoMultiplication)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransformsAdditionIntoMultiplication)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransformsAdditionIntoMultiplication): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransformsAdditionIntoMultiplication): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransformsAdditionIntoMultiplication)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformsZeroIntoOne","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "TransformsZeroIntoOne: system getter","filters" : [["IsAttributeStoringRep","Tester(TransformsZeroIntoOne)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransformsZeroIntoOne)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransformsZeroIntoOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransformsZeroIntoOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransformsZeroIntoOne)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformsAdditiveInversesIntoInverses","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "TransformsAdditiveInversesIntoInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(TransformsAdditiveInversesIntoInverses)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransformsAdditiveInversesIntoInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransformsAdditiveInversesIntoInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransformsAdditiveInversesIntoInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransformsAdditiveInversesIntoInverses)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Successors","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "Successors: system getter","filters" : [["IsAttributeStoringRep","Tester(Successors)"]]},{"rank" : 22,"comment" : "Successors: for a Green's equivalence","filters" : [["IsGreensRelation"]]},{"rank" : 9,"comment" : "Successors: for a generic relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "Successors: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Successors)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Successors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Successors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Successors)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOfBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "DegreeOfBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOfBinaryRelation)"]]},{"rank" : 0,"comment" : "DegreeOfBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOfBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOfBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOfBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOfBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsReflexiveBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsReflexiveBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsReflexiveBinaryRelation)"]]},{"rank" : 12,"comment" : "IsReflexiveBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "IsReflexiveBinaryRelation: reflexive test binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsReflexiveBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsReflexiveBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsReflexiveBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsReflexiveBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsReflexiveBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSymmetricBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsSymmetricBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSymmetricBinaryRelation)"]]},{"rank" : 12,"comment" : "IsSymmetricBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "IsSymmetricBinaryRelation: symmetric test binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsSymmetricBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSymmetricBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSymmetricBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSymmetricBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSymmetricBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTransitiveBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsTransitiveBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTransitiveBinaryRelation)"]]},{"rank" : 12,"comment" : "IsTransitiveBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "IsTransitiveBinaryRelation: transitive test binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsTransitiveBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTransitiveBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTransitiveBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTransitiveBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTransitiveBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAntisymmetricBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsAntisymmetricBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAntisymmetricBinaryRelation)"]]},{"rank" : 12,"comment" : "IsAntisymmetricBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "IsAntisymmetricBinaryRelation: test for Antisymmetry of a binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsAntisymmetricBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAntisymmetricBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAntisymmetricBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAntisymmetricBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAntisymmetricBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPreOrderBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsPreOrderBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPreOrderBinaryRelation)"]]},{"rank" : 12,"comment" : "IsPreOrderBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "IsPreOrderBinaryRelation: test for whether a binary relation is a preorder","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsPreOrderBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPreOrderBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPreOrderBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPreOrderBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPreOrderBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPartialOrderBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsPartialOrderBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPartialOrderBinaryRelation)"]]},{"rank" : 12,"comment" : "IsPartialOrderBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "IsPartialOrderBinaryRelation: test for whether a binary relation is a partial order","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsPartialOrderBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPartialOrderBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPartialOrderBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPartialOrderBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPartialOrderBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLatticeOrderBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsLatticeOrderBinaryRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLatticeOrderBinaryRelation)"]]},{"rank" : 9,"comment" : "IsLatticeOrderBinaryRelation: test for whether a binary relation is a lattice order","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsLatticeOrderBinaryRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLatticeOrderBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLatticeOrderBinaryRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLatticeOrderBinaryRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLatticeOrderBinaryRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsEquivalenceRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsEquivalenceRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsEquivalenceRelation)"]]},{"rank" : 12,"comment" : "IsEquivalenceRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "IsEquivalenceRelation: test for equivalence relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]},{"rank" : 0,"comment" : "IsEquivalenceRelation: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsEquivalenceRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsEquivalenceRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsEquivalenceRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsEquivalenceRelation)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReflexiveClosureBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 12,"comment" : "ReflexiveClosureBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "ReflexiveClosureBinaryRelation: for binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymmetricClosureBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 12,"comment" : "SymmetricClosureBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "SymmetricClosureBinaryRelation: for binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransitiveClosureBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 12,"comment" : "TransitiveClosureBinaryRelation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 9,"comment" : "TransitiveClosureBinaryRelation: for binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasseDiagramBinaryRelation","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 9,"comment" : "HasseDiagramBinaryRelation: for binary relation","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsHasseDiagram","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsHasseDiagram: system getter","filters" : [["IsAttributeStoringRep","Tester(IsHasseDiagram)"]]},{"rank" : 0,"comment" : "IsHasseDiagram: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsHasseDiagram)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsHasseDiagram): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsHasseDiagram): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsHasseDiagram)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PartialOrderOfHasseDiagram","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "PartialOrderOfHasseDiagram: system getter","filters" : [["IsAttributeStoringRep","Tester(PartialOrderOfHasseDiagram)"]]},{"rank" : 0,"comment" : "PartialOrderOfHasseDiagram: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PartialOrderOfHasseDiagram)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PartialOrderOfHasseDiagram): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PartialOrderOfHasseDiagram): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PartialOrderOfHasseDiagram)","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StronglyConnectedComponents","type" : "GAP_Operation","filters" : [[["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 9,"comment" : "StronglyConnectedComponents: for general binary relations","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EquivalenceRelationPartition","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "EquivalenceRelationPartition: system getter","filters" : [["IsAttributeStoringRep","Tester(EquivalenceRelationPartition)"]]},{"rank" : 26,"comment" : "EquivalenceRelationPartition: for a congruence on a magma","filters" : [["IsMagmaCongruence"]]},{"rank" : 22,"comment" : "EquivalenceRelationPartition: for a Green's equivalence","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation"]]},{"rank" : 22,"comment" : "EquivalenceRelationPartition: for a right congruence on a magma","filters" : [["IsRightMagmaCongruence"]]},{"rank" : 22,"comment" : "EquivalenceRelationPartition: for a left congruence on a magma","filters" : [["IsLeftMagmaCongruence"]]},{"rank" : 21,"comment" : "EquivalenceRelationPartition: compute the partition for an arbitrary equiv rel","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]},{"rank" : 0,"comment" : "EquivalenceRelationPartition: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EquivalenceRelationPartition)","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EquivalenceRelationPartition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EquivalenceRelationPartition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EquivalenceRelationPartition)","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfEquivalenceRelationPartition","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "GeneratorsOfEquivalenceRelationPartition: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfEquivalenceRelationPartition)"]]},{"rank" : 21,"comment" : "GeneratorsOfEquivalenceRelationPartition: generators for an equivalence with a partition","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]},{"rank" : 0,"comment" : "GeneratorsOfEquivalenceRelationPartition: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfEquivalenceRelationPartition)","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfEquivalenceRelationPartition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfEquivalenceRelationPartition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfEquivalenceRelationPartition)","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "JoinEquivalenceRelations","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "JoinEquivalenceRelations: join of two equivalence relations","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MeetEquivalenceRelations","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "MeetEquivalenceRelations: meet of two equivalence relations","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EquivalenceClassRelation","type" : "GAP_Operation","filters" : [[["IsEquivalenceClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "EquivalenceClassRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(EquivalenceClassRelation)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EquivalenceClassRelation)","type" : "GAP_Operation","filters" : [[["IsEquivalenceClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EquivalenceClassRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EquivalenceClassRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EquivalenceClassRelation)","type" : "GAP_Operation","filters" : [[["IsEquivalenceClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EquivalenceClasses","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "EquivalenceClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(EquivalenceClasses)"]]},{"rank" : 26,"comment" : "EquivalenceClasses: for magma congruences","filters" : [["IsMagmaCongruence"]]},{"rank" : 23,"comment" : "EquivalenceClasses: for a Green's J-relation","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensJRelation"]]},{"rank" : 23,"comment" : "EquivalenceClasses: for a Green's D-relation","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensDRelation"]]},{"rank" : 23,"comment" : "EquivalenceClasses: for a Green's H-relation","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensHRelation"]]},{"rank" : 23,"comment" : "EquivalenceClasses: for a Green's L-relation","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensLRelation"]]},{"rank" : 23,"comment" : "EquivalenceClasses: for a Green's R-relation","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRRelation"]]},{"rank" : 21,"comment" : "EquivalenceClasses: wraparound to call 2-argument version","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]},{"rank" : 0,"comment" : "EquivalenceClasses: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [{"rank" : 23,"comment" : "EquivalenceClasses: for a generic equivalence relation","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EquivalenceClasses)","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EquivalenceClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EquivalenceClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EquivalenceClasses)","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EquivalenceClassOfElement","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "EquivalenceClassOfElement: for magma congruence with checking","filters" : [["IsMagmaCongruence"],[]]},{"rank" : 22,"comment" : "EquivalenceClassOfElement: for right magma congruence with checking","filters" : [["IsRightMagmaCongruence"],[]]},{"rank" : 22,"comment" : "EquivalenceClassOfElement: for left magma congruence with checking","filters" : [["IsLeftMagmaCongruence"],[]]},{"rank" : 21,"comment" : "EquivalenceClassOfElement: with checking","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EquivalenceClassOfElementNC","type" : "GAP_Operation","filters" : [[["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "EquivalenceClassOfElementNC: for magma congruence with no check","filters" : [["IsMagmaCongruence"],[]]},{"rank" : 22,"comment" : "EquivalenceClassOfElementNC: for a Green's relation and object","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation"],[]]},{"rank" : 22,"comment" : "EquivalenceClassOfElementNC: for magma congruence with no check","filters" : [["IsRightMagmaCongruence"],[]]},{"rank" : 22,"comment" : "EquivalenceClassOfElementNC: for magma congruence with no check","filters" : [["IsLeftMagmaCongruence"],[]]},{"rank" : 21,"comment" : "EquivalenceClassOfElementNC: no check","filters" : [["IsEquivalenceRelation","Tester(IsEquivalenceRelation)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "MagmaByGenerators: for collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 3,"comment" : "MagmaByGenerators: for family and list","filters" : [["IsFamily"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaWithOneByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "MagmaWithOneByGenerators: for collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 3,"comment" : "MagmaWithOneByGenerators: for family and list","filters" : [["IsFamily"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaWithInversesByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "MagmaWithInversesByGenerators: for collection","filters" : [["IsCollection","IsFinite","Tester(IsFinite)"]]}],"2args" : [{"rank" : 8,"comment" : "MagmaWithInversesByGenerators: for family and list","filters" : [["IsFamily"],["IsList","IsFinite","Tester(IsFinite)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsMagma","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "AsMagma: system getter","filters" : [["IsAttributeStoringRep","Tester(AsMagma)"]]},{"rank" : 111,"comment" : "AsMagma: for a magma (return the argument)","filters" : [["IsMagma"]]},{"rank" : 2,"comment" : "AsMagma: generic method for collections","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsMagma)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsMagma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsMagma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsMagma)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubmagma","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "AsSubmagma: generic method for a domain and a collection","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfMagma","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "GeneratorsOfMagma: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfMagma)"]]},{"rank" : 30,"comment" : "GeneratorsOfMagma","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 21,"comment" : "GeneratorsOfMagma","filters" : [["IsAttributeStoringRep","IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "GeneratorsOfMagma","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 18,"comment" : "GeneratorsOfMagma: for a magma-with-inv. with gens., all elms. of finite order","filters" : [["CategoryCollections(IsFiniteOrderElement)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 18,"comment" : "GeneratorsOfMagma: for a magma-with-one with generators, all elms. of finite order","filters" : [["CategoryCollections(IsFiniteOrderElement)","IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 17,"comment" : "GeneratorsOfMagma: for a magma-with-inverses with known generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 15,"comment" : "GeneratorsOfMagma: for a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 15,"comment" : "GeneratorsOfMagma: for a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 14,"comment" : "GeneratorsOfMagma: for a magma-with-one with known generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 11,"comment" : "GeneratorsOfMagma: generic method for a magma (take domain generators)","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfMagma)","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfMagma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfMagma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfMagma)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfMagmaWithOne","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GeneratorsOfMagmaWithOne: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 34,"comment" : "GeneratorsOfMagmaWithOne","filters" : [["CategoryCollections(IsPartialPerm)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","Tester(GeneratorsOfInverseMonoid)"]]},{"rank" : 18,"comment" : "GeneratorsOfMagmaWithOne: for a magma-with-inv. with gens., all elms. of finite order","filters" : [["CategoryCollections(IsFiniteOrderElement)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 17,"comment" : "GeneratorsOfMagmaWithOne: for a magma-with-inverses with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 14,"comment" : "GeneratorsOfMagmaWithOne: for a magma-with-one with known magma generators (take them)","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagma)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfMagmaWithOne)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfMagmaWithOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfMagmaWithOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfMagmaWithOne)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfMagmaWithInverses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20019,"comment" : "GeneratorsOfMagmaWithInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfMagmaWithInverses)"]]},{"rank" : 367,"comment" : "GeneratorsOfMagmaWithInverses","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 52,"comment" : "GeneratorsOfMagmaWithInverses: for a subgroup of a free group having a FreeGroupAutomaton","filters" : [["Tester(FreeGroupAutomaton)"]]},{"rank" : 49,"comment" : "GeneratorsOfMagmaWithInverses","filters" : [["Tester(FreeGeneratorsOfGroup)"]]},{"rank" : 36,"comment" : "GeneratorsOfMagmaWithInverses: for whole family f.p. group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 35,"comment" : "GeneratorsOfMagmaWithInverses: subgroup fp, via augmented coset table","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 34,"comment" : "GeneratorsOfMagmaWithInverses: Schreier generators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(ElementTestFunction)"]]},{"rank" : 17,"comment" : "GeneratorsOfMagmaWithInverses: for a magma-with-inverses with known magma-with-one gen.s (take them)","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithOne)"]]},{"rank" : 17,"comment" : "GeneratorsOfMagmaWithInverses: for a magma-with-inverses with known magma generators (take them)","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagma)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfMagmaWithInverses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfMagmaWithInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfMagmaWithInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfMagmaWithInverses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGeneratorsOfMagmaWithInverses","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsGeneratorsOfMagmaWithInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGeneratorsOfMagmaWithInverses)"]]},{"rank" : 10022,"comment" : "IsGeneratorsOfMagmaWithInverses: for a collection of cyclotomics (return false)","filters" : [["CategoryCollections(IsCyclotomic)"]]},{"rank" : 22,"comment" : "IsGeneratorsOfMagmaWithInverses: for a collection of FFEs","filters" : [["CategoryCollections(IsFFE)"]]},{"rank" : 16,"comment" : "IsGeneratorsOfMagmaWithInverses: for a list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))"]]},{"rank" : 16,"comment" : "IsGeneratorsOfMagmaWithInverses: for a collection of free magma ring elements","filters" : [["CategoryCollections(IsElementOfMagmaRingModuloRelations)"]]},{"rank" : 16,"comment" : "IsGeneratorsOfMagmaWithInverses: for list of direct product elements","filters" : [["CategoryCollections(IsDirectProductElement)"]]},{"rank" : 15,"comment" : "IsGeneratorsOfMagmaWithInverses: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 13,"comment" : "IsGeneratorsOfMagmaWithInverses: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 13,"comment" : "IsGeneratorsOfMagmaWithInverses: for a collection of general mappings","filters" : [["CategoryCollections(IsGeneralMapping)"]]},{"rank" : 11,"comment" : "IsGeneratorsOfMagmaWithInverses: cosets","filters" : [["CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"]]},{"rank" : 2,"comment" : "IsGeneratorsOfMagmaWithInverses: for a collection of magma by mult table elements","filters" : [["IsCollection"]]},{"rank" : 2,"comment" : "IsGeneratorsOfMagmaWithInverses: for an empty list","filters" : [["IsList"]]},{"rank" : 1,"comment" : "IsGeneratorsOfMagmaWithInverses: for a list or collection","filters" : [["IsListOrCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGeneratorsOfMagmaWithInverses)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGeneratorsOfMagmaWithInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGeneratorsOfMagmaWithInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGeneratorsOfMagmaWithInverses)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TrivialSubmagmaWithOne","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "TrivialSubmagmaWithOne: system getter","filters" : [["IsAttributeStoringRep","Tester(TrivialSubmagmaWithOne)"]]},{"rank" : 13,"comment" : "TrivialSubmagmaWithOne: for magma-with-one","filters" : [["IsMagmaWithOne"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TrivialSubmagmaWithOne)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TrivialSubmagmaWithOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TrivialSubmagmaWithOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TrivialSubmagmaWithOne)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAssociative","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "IsAssociative: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAssociative)"]]},{"rank" : 36,"comment" : "IsAssociative: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 34,"comment" : "IsAssociative: generic method for a (finite dimensional) FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 13,"comment" : "IsAssociative: for a magma of nonassoc. words","filters" : [["IsMagma","CategoryCollections(IsNonassocWord)"]]},{"rank" : 11,"comment" : "IsAssociative: for a magma","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAssociative)","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAssociative): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAssociative): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAssociative)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCommutative","type" : "GAP_Operation","filters" : [[["IsMagma"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "IsCommutative: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCommutative)"]]},{"rank" : 46,"comment" : "IsCommutative: finite fp grp","filters" : [["IsFinite","Tester(IsFinite)","Tester(Size)","IsSubgroupFpGroup"]]},{"rank" : 41,"comment" : "IsCommutative: for an associative FLMLOR-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 36,"comment" : "IsCommutative: for finitely presented groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 36,"comment" : "IsCommutative: for an associative FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 36,"comment" : "IsCommutative: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 34,"comment" : "IsCommutative: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 34,"comment" : "IsCommutative: generic method for a finite dimensional FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 33,"comment" : "IsCommutative: for an associative ring-with-one","filters" : [["IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 33,"comment" : "IsCommutative: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "IsCommutative","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 32,"comment" : "IsCommutative: for an associative magma with inverses","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 29,"comment" : "IsCommutative","filters" : [["Tester(Characteristic)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsAnticommutative","Tester(IsAnticommutative)"]]},{"rank" : 28,"comment" : "IsCommutative: for an associative ring","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 22,"comment" : "IsCommutative: for an ordinary character table","filters" : [["IsOrdinaryTable"]]},{"rank" : 18,"comment" : "IsCommutative: for associative magma-with-one","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 18,"comment" : "IsCommutative","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 17,"comment" : "IsCommutative: for an associative magma with one","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 14,"comment" : "IsCommutative","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "IsCommutative: for an associative magma","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 11,"comment" : "IsCommutative: for a magma","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCommutative)","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCommutative): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCommutative): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCommutative)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MultiplicativeNeutralElement","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "MultiplicativeNeutralElement: for a magma-with-one","filters" : [["IsMagmaWithOne","Tester(MultiplicativeNeutralElement)"]]},{"rank" : 20014,"comment" : "MultiplicativeNeutralElement: system getter","filters" : [["IsAttributeStoringRep","Tester(MultiplicativeNeutralElement)"]]},{"rank" : 36,"comment" : "MultiplicativeNeutralElement","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFiniteDimensional","Tester(IsFiniteDimensional)"]]},{"rank" : 11,"comment" : "MultiplicativeNeutralElement: for a magma","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MultiplicativeNeutralElement)","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 12,"comment" : "Setter(MultiplicativeNeutralElement): for a magma-with-one","filters" : [["IsMagma"],["IsBool"]]},{"rank" : 2,"comment" : "Setter(MultiplicativeNeutralElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MultiplicativeNeutralElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MultiplicativeNeutralElement)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Centre","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "Centre: system getter","filters" : [["IsAttributeStoringRep","Tester(Centre)"]]},{"rank" : 10015,"comment" : "Centre: for an associative and commutative magma","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"]]},{"rank" : 58,"comment" : "Centre: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "Centre: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "Centre: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 38,"comment" : "Centre: for a group ring","filters" : [["IsGroupRing","Tester(IsGroupRing)"]]},{"rank" : 34,"comment" : "Centre: for a finite dimensional FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 13,"comment" : "Centre: for an associative magma","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 11,"comment" : "Centre: generic method for a magma","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Centre)","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Centre): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Centre): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Centre)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Idempotents","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "Idempotents: system getter","filters" : [["IsAttributeStoringRep","Tester(Idempotents)"]]},{"rank" : 11,"comment" : "Idempotents: for finite magmas","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Idempotents)","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Idempotents): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Idempotents): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Idempotents)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCentral","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 82,"comment" : "IsCentral: for two associative FLMLORs-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 72,"comment" : "IsCentral: for two associative FLMLORs","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 68,"comment" : "IsCentral: for two FLMLORs","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 66,"comment" : "IsCentral: for two associative rings-with-one","filters" : [["IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 66,"comment" : "IsCentral: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 56,"comment" : "IsCentral: for two associative rings","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 34,"comment" : "IsCentral: for two magmas-with-inverses","filters" : [["IsMagmaWithInverses"],["IsMagmaWithInverses"]]},{"rank" : 28,"comment" : "IsCentral: for two magmas-with-one","filters" : [["IsMagmaWithOne"],["IsMagmaWithOne"]]},{"rank" : 22,"comment" : "IsCentral: for two magmas","filters" : [["IsMagma"],["IsMagma"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralizerOp","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 11,"comment" : "CentralizerOp","filters" : [["IsRationalClassGroupRep"]]},{"rank" : 11,"comment" : "CentralizerOp","filters" : [["IsRationalClassGroupRep"]]}],"2args" : [{"rank" : 10024,"comment" : "CentralizerOp: for two magmas, the first being commutative","filters" : [["IsMagma","IsCommutative","Tester(IsCommutative)"],["IsMagma"]]},{"rank" : 10016,"comment" : "CentralizerOp: for a commutative magma, and a mult. element","filters" : [["IsMagma","IsCommutative","Tester(IsCommutative)"],["IsMultiplicativeElement"]]},{"rank" : 858,"comment" : "CentralizerOp: TF method:subgroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingFreeLiftSetup)"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 736,"comment" : "CentralizerOp: handled by nice monomorphism: Subgroup CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 434,"comment" : "CentralizerOp: TF method:elm","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingFreeLiftSetup)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 368,"comment" : "CentralizerOp: handled by nice monomorphism: subgroup CollElm","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],[]]},{"rank" : 121,"comment" : "CentralizerOp: for full (associative) matrix FLMLOR, and FLMLOR","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)","IsGaussianSpace"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 116,"comment" : "CentralizerOp: perm group, perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 106,"comment" : "CentralizerOp: two AffineCrystGroupsOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "CentralizerOp: two AffineCrystGroupsOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 102,"comment" : "CentralizerOp: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNilpotentGroup","Tester(IsNilpotentGroup)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 100,"comment" : "CentralizerOp","filters" : [["IsNaturalGL","Tester(IsNaturalGL)","IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 99,"comment" : "CentralizerOp: for full (associative) matrix FLMLOR, and left module","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)","IsGaussianSpace"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 98,"comment" : "CentralizerOp: for associative Gaussian matrix FLMLOR-with-one, and FLMLOR","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsGaussianSpace"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 96,"comment" : "CentralizerOp: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 96,"comment" : "CentralizerOp: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 93,"comment" : "CentralizerOp: for associative Gaussian matrix FLMLOR, and FLMLOR","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsGaussianSpace"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 86,"comment" : "CentralizerOp: pcgs computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 86,"comment" : "CentralizerOp: for associative Gaussian matrix FLMLOR-with-one, and ordinary matrix","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsGaussianSpace"],["IsOrdinaryMatrix"]]},{"rank" : 84,"comment" : "CentralizerOp: for full (associative) matrix FLMLOR, and empty list","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 83,"comment" : "CentralizerOp: AffineCrystGroupOnLeft and element","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 83,"comment" : "CentralizerOp: AffineCrystGroupOnRight and element","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 82,"comment" : "CentralizerOp: for full (associative) matrix FLMLOR, and list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)","IsGaussianSpace"],["IsList","IsCollection"]]},{"rank" : 81,"comment" : "CentralizerOp: for associative Gaussian matrix FLMLOR, and ordinary matrix","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsGaussianSpace"],["IsOrdinaryMatrix"]]},{"rank" : 75,"comment" : "CentralizerOp: for a fin. dim. assoc. algebra and an algebra with parent","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["Tester(ParentAttr)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 74,"comment" : "CentralizerOp: for a fin. dim. assoc. algebra and an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 70,"comment" : "CentralizerOp: element in natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsPerm"]]},{"rank" : 70,"comment" : "CentralizerOp: element in natural alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["IsPerm"]]},{"rank" : 66,"comment" : "CentralizerOp: perm group,elm","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPerm"]]},{"rank" : 66,"comment" : "CentralizerOp: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 62,"comment" : "CentralizerOp: for a finite dimensional algebra and a vector space with parent","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["Tester(ParentAttr)","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 61,"comment" : "CentralizerOp: for a finite dimensional algebra and a vector space","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 60,"comment" : "CentralizerOp: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNilpotentGroup","Tester(IsNilpotentGroup)","CategoryCollections(IsPcpElement)"],["IsPcpElement"]]},{"rank" : 55,"comment" : "CentralizerOp: for an element in a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]},{"rank" : 54,"comment" : "CentralizerOp: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsPcpElement"]]},{"rank" : 48,"comment" : "CentralizerOp: pcgs computable group and element","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 36,"comment" : "CentralizerOp: for an algebra and an element","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]},{"rank" : 33,"comment" : "CentralizerOp: generic method for group and object","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]},{"rank" : 22,"comment" : "CentralizerOp: for two magmas","filters" : [["IsMagma"],["IsMagma"]]},{"rank" : 14,"comment" : "CentralizerOp: for a magma, and a mult. element","filters" : [["IsMagma"],["IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "CentralizerOp:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 11,"comment" : "CentralizerOp: dummy to ignore optional third argument","filters" : [["IsMagma"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralizerInParent","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "CentralizerInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(CentralizerInParent)"]]},{"rank" : 6,"comment" : "CentralizerInParent: method that calls the two-argument operation CentralizerOp","filters" : [["Tester(ParentAttr)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CentralizerInParent)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CentralizerInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CentralizerInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CentralizerInParent)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Centralizer","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 11,"comment" : "Centralizer","filters" : [["IsConjugacyClassGroupRep"]]}],"2args" : [{"rank" : 11,"comment" : "Centralizer: try to exploit the in-parent attribute CentralizerInParent","filters" : [["IsMagma"],[]]}],"3args" : [{"rank" : 124,"comment" : "Centralizer: with given subgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPerm"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SquareRoots","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 72,"comment" : "SquareRoots: for prime field and object in Z\/pZ","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsFFE","IsZmodnZObj","IsModulusRep"]]},{"rank" : 67,"comment" : "SquareRoots: for a field of FFEs, and a FFE","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFFE"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaGeneratorsOfFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MagmaGeneratorsOfFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(MagmaGeneratorsOfFamily)"]]},{"rank" : 4,"comment" : "MagmaGeneratorsOfFamily: for a family of assoc. words","filters" : [["CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 3,"comment" : "MagmaGeneratorsOfFamily: for a family of free monoid elements","filters" : [["CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]},{"rank" : 2,"comment" : "MagmaGeneratorsOfFamily: for a family of free semigroup elements","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))"]]},{"rank" : 2,"comment" : "MagmaGeneratorsOfFamily: for a family of free magma elements","filters" : [["CategoryFamily(IsNonassocWord)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MagmaGeneratorsOfFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MagmaGeneratorsOfFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MagmaGeneratorsOfFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MagmaGeneratorsOfFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsLeftMagmaIdeal","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "AsLeftMagmaIdeal: generic method for a domain and a collection","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftMagmaIdealByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 13,"comment" : "LeftMagmaIdealByGenerators: for a collection of magma elements","filters" : [["IsMagma"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsRightMagmaIdeal","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightMagmaIdealByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 13,"comment" : "RightMagmaIdealByGenerators: for a collection of magma elements","filters" : [["IsMagma"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsMagmaIdeal","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfMagmaIdeal","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "GeneratorsOfMagmaIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfMagmaIdeal)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfMagmaIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfMagmaIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfMagmaIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfMagmaIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaIdealByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 13,"comment" : "MagmaIdealByGenerators: for a collection of magma elements","filters" : [["IsMagma"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 45,"comment" : "NaturalHomomorphismByGenerators: for a free monoid and monoid","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "NaturalHomomorphismByGenerators: for an fp monoid and monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 34,"comment" : "NaturalHomomorphismByGenerators: for a free semigroup and semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "NaturalHomomorphismByGenerators: for an fp semigroup and semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MultiplicativeZeroOp","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithZero"]],[["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "MultiplicativeZeroOp: for a Rees matrix semigroup","filters" : [["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 7,"comment" : "MultiplicativeZeroOp: for an element of a magma with zero adjoined","filters" : [["IsMagmaWithZeroAdjoinedElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MultiplicativeZero","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithZero"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "MultiplicativeZero: system getter","filters" : [["IsAttributeStoringRep","Tester(MultiplicativeZero)"]]},{"rank" : 11,"comment" : "MultiplicativeZero: for a magma","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MultiplicativeZero)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithZero"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MultiplicativeZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MultiplicativeZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MultiplicativeZero)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithZero"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMultiplicativeZero","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 17,"comment" : "IsMultiplicativeZero: for a semigroup with generators and multiplicative element","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElement"]]},{"rank" : 17,"comment" : "IsMultiplicativeZero: for magma with multiplicative zero and multiplicative element","filters" : [["IsMagma","Tester(MultiplicativeZero)"],["IsMultiplicativeElement"]]},{"rank" : 14,"comment" : "IsMultiplicativeZero: for a magma and multiplicative element","filters" : [["IsMagma"],["IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InjectionZeroMagma","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "InjectionZeroMagma: system getter","filters" : [["IsAttributeStoringRep","Tester(InjectionZeroMagma)"]]},{"rank" : 11,"comment" : "InjectionZeroMagma: for a magma","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InjectionZeroMagma)","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InjectionZeroMagma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InjectionZeroMagma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InjectionZeroMagma)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaWithZeroAdjoined","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithZero","IsMagmaWithZeroAdjoinedElementRep"]],[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "MagmaWithZeroAdjoined: system getter","filters" : [["IsAttributeStoringRep","Tester(MagmaWithZeroAdjoined)"]]},{"rank" : 11,"comment" : "MagmaWithZeroAdjoined: for a magma","filters" : [["IsMagma"]]},{"rank" : 7,"comment" : "MagmaWithZeroAdjoined: for a magma with 0 adjoined element","filters" : [["IsMagmaWithZeroAdjoinedElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MagmaWithZeroAdjoined)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithZero","IsMagmaWithZeroAdjoinedElementRep"],[]],[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MagmaWithZeroAdjoined): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MagmaWithZeroAdjoined): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MagmaWithZeroAdjoined)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithZero","IsMagmaWithZeroAdjoinedElementRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingInjectionZeroMagma","type" : "GAP_Operation","filters" : [[["IsMagmaWithZeroAdjoined"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "UnderlyingInjectionZeroMagma: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingInjectionZeroMagma)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingInjectionZeroMagma)","type" : "GAP_Operation","filters" : [[["IsMagmaWithZeroAdjoined"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingInjectionZeroMagma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingInjectionZeroMagma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingInjectionZeroMagma)","type" : "GAP_Operation","filters" : [[["IsMagmaWithZeroAdjoined"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratingPairsOfLeftMagmaCongruence","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "GeneratingPairsOfLeftMagmaCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratingPairsOfLeftMagmaCongruence)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratingPairsOfLeftMagmaCongruence)","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratingPairsOfLeftMagmaCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratingPairsOfLeftMagmaCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratingPairsOfLeftMagmaCongruence)","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PartialClosureOfCongruence","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"]],[["IsRightMagmaCongruence"]],[["IsMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "PartialClosureOfCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(PartialClosureOfCongruence)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PartialClosureOfCongruence)","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"],[]],[["IsRightMagmaCongruence"],[]],[["IsMagmaCongruence"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PartialClosureOfCongruence): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PartialClosureOfCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PartialClosureOfCongruence)","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftMagmaCongruenceByGeneratingPairs","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "LeftMagmaCongruenceByGeneratingPairs: for a magma and an empty list","filters" : [["IsMagma"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 13,"comment" : "LeftMagmaCongruenceByGeneratingPairs: for a magma and a list of pairs of its elements","filters" : [["IsMagma"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratingPairsOfRightMagmaCongruence","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "GeneratingPairsOfRightMagmaCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratingPairsOfRightMagmaCongruence)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratingPairsOfRightMagmaCongruence)","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratingPairsOfRightMagmaCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratingPairsOfRightMagmaCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratingPairsOfRightMagmaCongruence)","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightMagmaCongruenceByGeneratingPairs","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "RightMagmaCongruenceByGeneratingPairs: for a magma and an empty list","filters" : [["IsMagma"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 13,"comment" : "RightMagmaCongruenceByGeneratingPairs: for a magma and a list of pairs of its elements","filters" : [["IsMagma"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaCongruenceByGeneratingPairs","type" : "GAP_Operation","filters" : [[["IsMagma"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "MagmaCongruenceByGeneratingPairs: for a magma and an empty list","filters" : [["IsMagma"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 13,"comment" : "MagmaCongruenceByGeneratingPairs: for a magma and a list of pairs of its elements","filters" : [["IsMagma"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratingPairsOfMagmaCongruence","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "GeneratingPairsOfMagmaCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratingPairsOfMagmaCongruence)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratingPairsOfMagmaCongruence)","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratingPairsOfMagmaCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratingPairsOfMagmaCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratingPairsOfMagmaCongruence)","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "JoinMagmaCongruences","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"],["IsMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "JoinMagmaCongruences: for magma congruences","filters" : [["IsMagmaCongruence"],["IsMagmaCongruence"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MeetMagmaCongruences","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"],["IsMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "MeetMagmaCongruences: for magma congruences","filters" : [["IsMagmaCongruence"],["IsMagmaCongruence"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemigroupCongruenceByGeneratingPairs","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "SemigroupCongruenceByGeneratingPairs: for a semigroup and an empty list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "SemigroupCongruenceByGeneratingPairs: for a semigroup and a list of pairs of its elements","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightSemigroupCongruenceByGeneratingPairs","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "RightSemigroupCongruenceByGeneratingPairs: for a Semigroup and an empty list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "RightSemigroupCongruenceByGeneratingPairs: for a Semigroup and a list of pairs of its elements","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftSemigroupCongruenceByGeneratingPairs","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "LeftSemigroupCongruenceByGeneratingPairs: for a Semigroup and an empty list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "LeftSemigroupCongruenceByGeneratingPairs: for a Semigroup  and a list of pairs of its elements","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftSemigroupCongruence","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsLeftSemigroupCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLeftSemigroupCongruence)"]]},{"rank" : 22,"comment" : "IsLeftSemigroupCongruence: test whether a left magma congruence is a semigroup a congruence","filters" : [["IsLeftMagmaCongruence"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLeftSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLeftSemigroupCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLeftSemigroupCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLeftSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsLeftMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRightSemigroupCongruence","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsRightSemigroupCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRightSemigroupCongruence)"]]},{"rank" : 22,"comment" : "IsRightSemigroupCongruence: test whether a right magma congruence is a semigroup a congruence","filters" : [["IsRightMagmaCongruence"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRightSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRightSemigroupCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRightSemigroupCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRightSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSemigroupCongruence","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsSemigroupCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSemigroupCongruence)"]]},{"rank" : 26,"comment" : "IsSemigroupCongruence: test whether a magma congruence is a semigroup a congruence","filters" : [["IsMagmaCongruence"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSemigroupCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSemigroupCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsReesCongruence","type" : "GAP_Operation","filters" : [[["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsReesCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(IsReesCongruence)"]]},{"rank" : 32,"comment" : "IsReesCongruence: for a semigroup congruence","filters" : [["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 0,"comment" : "IsReesCongruence: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsReesCongruence)","type" : "GAP_Operation","filters" : [[["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsReesCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsReesCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsReesCongruence)","type" : "GAP_Operation","filters" : [[["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InversesOfSemigroupElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 17,"comment" : "InversesOfSemigroupElement: for a semigroup and an element","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsAssociativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemigroupByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "SemigroupByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSemigroup","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "AsSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSemigroup)"]]},{"rank" : 113,"comment" : "AsSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 2,"comment" : "AsSemigroup: generic method for collections","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSemigroup)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSemigroup)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubsemigroup","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "AsSubsemigroup: generic method for a domain and a collection","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGeneratorsOfSemigroup","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsGeneratorsOfSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGeneratorsOfSemigroup)"]]},{"rank" : 17,"comment" : "IsGeneratorsOfSemigroup: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGeneratorsOfSemigroup)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGeneratorsOfSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGeneratorsOfSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGeneratorsOfSemigroup)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CayleyGraphSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "CayleyGraphSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(CayleyGraphSemigroup)"]]},{"rank" : 15,"comment" : "CayleyGraphSemigroup: for generic finite semigroups","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "CayleyGraphSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CayleyGraphSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CayleyGraphSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CayleyGraphSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CayleyGraphSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CayleyGraphDualSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "CayleyGraphDualSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(CayleyGraphDualSemigroup)"]]},{"rank" : 15,"comment" : "CayleyGraphDualSemigroup: for generic finite semigroups","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "CayleyGraphDualSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CayleyGraphDualSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CayleyGraphDualSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CayleyGraphDualSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CayleyGraphDualSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZeroGroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsZeroGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZeroGroup)"]]},{"rank" : 0,"comment" : "IsZeroGroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZeroGroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZeroGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZeroGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZeroGroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSimpleSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsSimpleSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSimpleSemigroup)"]]},{"rank" : 18,"comment" : "IsSimpleSemigroup: for a subsemigroup of a Rees matrix semigroup with an underlying semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)","Tester(UnderlyingSemigroup)"]]},{"rank" : 14,"comment" : "IsSimpleSemigroup: for a semigroup with a MultiplicativeNeutralElement","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)"]]},{"rank" : 14,"comment" : "IsSimpleSemigroup: for semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "IsSimpleSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsSimpleSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSimpleSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSimpleSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSimpleSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSimpleSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZeroSimpleSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsZeroSimpleSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZeroSimpleSemigroup)"]]},{"rank" : 33,"comment" : "IsZeroSimpleSemigroup: for a ZeroGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 28,"comment" : "IsZeroSimpleSemigroup: for a trivial semigroup","filters" : [["IsTrivial","Tester(IsTrivial)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "IsZeroSimpleSemigroup: for a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 14,"comment" : "IsZeroSimpleSemigroup: for a semigroup with a MultiplicativeNeutralElement","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)"]]},{"rank" : 14,"comment" : "IsZeroSimpleSemigroup: for a semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "IsZeroSimpleSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsZeroSimpleSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZeroSimpleSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZeroSimpleSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZeroSimpleSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZeroSimpleSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ANonReesCongruenceOfSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "ANonReesCongruenceOfSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(ANonReesCongruenceOfSemigroup)"]]},{"rank" : 15,"comment" : "ANonReesCongruenceOfSemigroup: for a semigroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ANonReesCongruenceOfSemigroup:  fallback method to test conditions","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ANonReesCongruenceOfSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ANonReesCongruenceOfSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ANonReesCongruenceOfSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ANonReesCongruenceOfSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ANonReesCongruenceOfSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsReesCongruenceSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsReesCongruenceSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsReesCongruenceSemigroup)"]]},{"rank" : 13,"comment" : "IsReesCongruenceSemigroup: for a (possibly infinite) semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsReesCongruenceSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsReesCongruenceSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsReesCongruenceSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsReesCongruenceSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsReesCongruenceSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HomomorphismFactorSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 56,"comment" : "HomomorphismFactorSemigroup: for an fp monoid and a congruence","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 52,"comment" : "HomomorphismFactorSemigroup: for a free monoid and a congruence","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsMagmaCongruence"]]},{"rank" : 52,"comment" : "HomomorphismFactorSemigroup: for a free semigroup and a congruence","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 51,"comment" : "HomomorphismFactorSemigroup: for an fp semigroup and a congruence","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]},{"rank" : 45,"comment" : "HomomorphismFactorSemigroup: for a semigroup and a congruence","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HomomorphismFactorSemigroupByClosure","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "HomomorphismFactorSemigroupByClosure: for a semigroup and empty list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "HomomorphismFactorSemigroupByClosure: for a semigroup and generating pairs of a congruence","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 45,"comment" : "FactorSemigroup: for a semigroup and a congruence","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorSemigroupByClosure","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "FactorSemigroupByClosure: for a semigroup and empty list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 15,"comment" : "FactorSemigroupByClosure: for a semigroup and generating pairs of a congruence","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRegularSemigroupElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "IsRegularSemigroupElement: for an inverse semigroup","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)"],["IsAssociativeElement"]]},{"rank" : 17,"comment" : "IsRegularSemigroupElement: for generic semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsAssociativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRegularSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsRegularSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRegularSemigroup)"]]},{"rank" : 15,"comment" : "IsRegularSemigroup: for a Rees 0-matrix semigroup","filters" : [["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 13,"comment" : "IsRegularSemigroup: for generic semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsRegularSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRegularSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRegularSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRegularSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRegularSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInverseSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsInverseSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsInverseSemigroup)"]]},{"rank" : 13,"comment" : "IsInverseSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsInverseSemigroup: for an object","filters" : [[]]},{"rank" : 0,"comment" : "IsInverseSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsInverseSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsInverseSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DisplaySemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "DisplaySemigroup: for finite semigroups","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NilpotencyDegree","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "NilpotencyDegree: system getter","filters" : [["IsAttributeStoringRep","Tester(NilpotencyDegree)"]]},{"rank" : 0,"comment" : "NilpotencyDegree: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NilpotencyDegree)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NilpotencyDegree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NilpotencyDegree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NilpotencyDegree)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubsemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 39,"comment" : "IsSubsemigroup: for an inverse semigroup and inverse semigroup with generators","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)"],["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 27,"comment" : "IsSubsemigroup: for semigroup and semigroup with generators","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 26,"comment" : "IsSubsemigroup: for a semigroup and semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsMagma","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBand","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsBand: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBand)"]]},{"rank" : 0,"comment" : "IsBand: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBand)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBand): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBand): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBand)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBrandtSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsBrandtSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBrandtSemigroup)"]]},{"rank" : 0,"comment" : "IsBrandtSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBrandtSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBrandtSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBrandtSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBrandtSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCliffordSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsCliffordSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCliffordSemigroup)"]]},{"rank" : 0,"comment" : "IsCliffordSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCliffordSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCliffordSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCliffordSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCliffordSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCommutativeSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsCommutativeSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCommutativeSemigroup)"]]},{"rank" : 0,"comment" : "IsCommutativeSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCommutativeSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCommutativeSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCommutativeSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCommutativeSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCompletelyRegularSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsCompletelyRegularSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCompletelyRegularSemigroup)"]]},{"rank" : 0,"comment" : "IsCompletelyRegularSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCompletelyRegularSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCompletelyRegularSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCompletelyRegularSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCompletelyRegularSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCompletelySimpleSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsCompletelySimpleSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCompletelySimpleSemigroup)"]]},{"rank" : 0,"comment" : "IsCompletelySimpleSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCompletelySimpleSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCompletelySimpleSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCompletelySimpleSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCompletelySimpleSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupAsSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsGroupAsSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupAsSemigroup)"]]},{"rank" : 0,"comment" : "IsGroupAsSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupAsSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupAsSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupAsSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupAsSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIdempotentGenerated","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsIdempotentGenerated: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIdempotentGenerated)"]]},{"rank" : 0,"comment" : "IsIdempotentGenerated: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIdempotentGenerated)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIdempotentGenerated): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIdempotentGenerated): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIdempotentGenerated)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftZeroSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsLeftZeroSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLeftZeroSemigroup)"]]},{"rank" : 0,"comment" : "IsLeftZeroSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLeftZeroSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLeftZeroSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLeftZeroSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLeftZeroSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonogenicSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsMonogenicSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMonogenicSemigroup)"]]},{"rank" : 0,"comment" : "IsMonogenicSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMonogenicSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMonogenicSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMonogenicSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMonogenicSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonoidAsSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsMonoidAsSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMonoidAsSemigroup)"]]},{"rank" : 0,"comment" : "IsMonoidAsSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMonoidAsSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMonoidAsSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMonoidAsSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMonoidAsSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotentSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsNilpotentSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNilpotentSemigroup)"]]},{"rank" : 0,"comment" : "IsNilpotentSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNilpotentSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNilpotentSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNilpotentSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNilpotentSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsOrthodoxSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsOrthodoxSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsOrthodoxSemigroup)"]]},{"rank" : 0,"comment" : "IsOrthodoxSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsOrthodoxSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsOrthodoxSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsOrthodoxSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsOrthodoxSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRectangularBand","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsRectangularBand: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRectangularBand)"]]},{"rank" : 0,"comment" : "IsRectangularBand: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRectangularBand)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRectangularBand): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRectangularBand): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRectangularBand)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRightZeroSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsRightZeroSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRightZeroSemigroup)"]]},{"rank" : 0,"comment" : "IsRightZeroSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRightZeroSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRightZeroSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRightZeroSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRightZeroSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSemiband","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsSemiband: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSemiband)"]]},{"rank" : 0,"comment" : "IsSemiband: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSemiband)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSemiband): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSemiband): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSemiband)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSemilattice","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsSemilattice: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSemilattice)"]]},{"rank" : 0,"comment" : "IsSemilattice: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSemilattice)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSemilattice): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSemilattice): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSemilattice)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZeroSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsZeroSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZeroSemigroup)"]]},{"rank" : 0,"comment" : "IsZeroSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZeroSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZeroSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZeroSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZeroSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemigroupViewStringPrefix","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "SemigroupViewStringPrefix: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 19,"comment" : "SemigroupViewStringPrefix: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "SemigroupViewStringPrefix: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemigroupViewStringSuffix","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "SemigroupViewStringSuffix: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 19,"comment" : "SemigroupViewStringSuffix: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "SemigroupViewStringSuffix: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftSemigroupIdeal","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsLeftSemigroupIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLeftSemigroupIdeal)"]]},{"rank" : 16,"comment" : "IsLeftSemigroupIdeal","filters" : [["IsAttributeStoringRep","IsLeftActedOnBySuperset","Tester(LeftActingDomain)","IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLeftSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsMagma"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLeftSemigroupIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLeftSemigroupIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLeftSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRightSemigroupIdeal","type" : "GAP_Operation","filters" : [[["IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsRightSemigroupIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRightSemigroupIdeal)"]]},{"rank" : 16,"comment" : "IsRightSemigroupIdeal","filters" : [["IsAttributeStoringRep","IsRightActedOnBySuperset","Tester(RightActingDomain)","IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRightSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsRightActedOnBySuperset","IsMagma"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRightSemigroupIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRightSemigroupIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRightSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSemigroupIdeal","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IsSemigroupIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSemigroupIdeal)"]]},{"rank" : 19,"comment" : "IsSemigroupIdeal","filters" : [["IsAttributeStoringRep","IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","Tester(ActingDomain)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSemigroupIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSemigroupIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReesCongruenceOfSemigroupIdeal","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "ReesCongruenceOfSemigroupIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(ReesCongruenceOfSemigroupIdeal)"]]},{"rank" : 17,"comment" : "ReesCongruenceOfSemigroupIdeal: for a two sided semigroup congruence","filters" : [["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma","IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ReesCongruenceOfSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ReesCongruenceOfSemigroupIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ReesCongruenceOfSemigroupIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ReesCongruenceOfSemigroupIdeal)","type" : "GAP_Operation","filters" : [[["IsLeftActedOnBySuperset","IsRightActedOnBySuperset","IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MonoidByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "MonoidByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 7,"comment" : "MonoidByGenerators: for empty collection and identity","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsMultiplicativeElementWithOne"]]},{"rank" : 6,"comment" : "MonoidByGenerators: for collection and identity","filters" : [["IsCollection"],["IsMultiplicativeElementWithOne"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsMonoid","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "AsMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(AsMonoid)"]]},{"rank" : 118,"comment" : "AsMonoid: for a monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "AsMonoid: for transformation semigroup with generators","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 14,"comment" : "AsMonoid: for a semigroup with known generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 2,"comment" : "AsMonoid: generic method for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsMonoid)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsMonoid)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubmonoid","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "AsSubmonoid: generic method for a domain and a collection","filters" : [["IsCollection","IsGeneralizedDomain"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupString","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "GroupString: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NameIsomorphismClass","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NameIsomorphismClass: system getter","filters" : [["IsAttributeStoringRep","Tester(NameIsomorphismClass)"]]},{"rank" : 0,"comment" : "NameIsomorphismClass: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NameIsomorphismClass)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NameIsomorphismClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NameIsomorphismClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NameIsomorphismClass)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCyclic","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsCyclic: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCyclic)"]]},{"rank" : 368,"comment" : "IsCyclic: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 51,"comment" : "IsCyclic: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 34,"comment" : "IsCyclic","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "IsCyclic: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsCyclic: for an ordinary character table","filters" : [["IsOrdinaryTable"]]},{"rank" : 0,"comment" : "IsCyclic: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCyclic)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCyclic): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCyclic): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCyclic)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsElementaryAbelian","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsElementaryAbelian: system getter","filters" : [["IsAttributeStoringRep","Tester(IsElementaryAbelian)"]]},{"rank" : 48,"comment" : "IsElementaryAbelian: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 33,"comment" : "IsElementaryAbelian: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsElementaryAbelian: for an ordinary character table","filters" : [["IsOrdinaryTable"]]},{"rank" : 0,"comment" : "IsElementaryAbelian: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsElementaryAbelian)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsElementaryAbelian): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsElementaryAbelian): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsElementaryAbelian)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFinitelyGeneratedGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsFinitelyGeneratedGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFinitelyGeneratedGroup)"]]},{"rank" : 35,"comment" : "IsFinitelyGeneratedGroup: subgroups of fp group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 34,"comment" : "IsFinitelyGeneratedGroup","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsFinitelyGeneratedGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFinitelyGeneratedGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFinitelyGeneratedGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFinitelyGeneratedGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFinitelyGeneratedGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubsetLocallyFiniteGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSubsetLocallyFiniteGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSubsetLocallyFiniteGroup)"]]},{"rank" : 0,"comment" : "IsSubsetLocallyFiniteGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSubsetLocallyFiniteGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSubsetLocallyFiniteGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSubsetLocallyFiniteGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSubsetLocallyFiniteGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanComputeIndex","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 106,"comment" : "CanComputeIndex","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "CanComputeIndex","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 92,"comment" : "CanComputeIndex","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 69,"comment" : "CanComputeIndex: subgroup of full fp groups","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(CosetTableInWholeGroup)"]]},{"rank" : 69,"comment" : "CanComputeIndex: subgroup of full fp groups","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(IndexInWholeGroup)"]]},{"rank" : 68,"comment" : "CanComputeIndex: subgroups fp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(IndexInWholeGroup)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(IndexInWholeGroup)"]]},{"rank" : 68,"comment" : "CanComputeIndex: if sizes can be computed","filters" : [["CanComputeSize","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CanComputeSize","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "CanComputeIndex: by default impossible unless identical","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KnowsHowToDecompose","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "KnowsHowToDecompose: system getter","filters" : [["IsAttributeStoringRep","Tester(KnowsHowToDecompose)"]]},{"rank" : 33,"comment" : "KnowsHowToDecompose: group: use GeneratorsOfGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "KnowsHowToDecompose: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 60,"comment" : "KnowsHowToDecompose: perm group and generators: always true","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : 50,"comment" : "KnowsHowToDecompose: pcp group and generators: always true","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsList"]]},{"rank" : 45,"comment" : "KnowsHowToDecompose: matrix groups","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : 45,"comment" : "KnowsHowToDecompose: pc group and generators: always true","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsList"]]},{"rank" : 37,"comment" : "KnowsHowToDecompose: fp groups: Say yes if finite index","filters" : [["IsSubgroupFpGroup"],["IsList"]]},{"rank" : 36,"comment" : "KnowsHowToDecompose: trivial group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 35,"comment" : "KnowsHowToDecompose: generic: just groups of order < 1000","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KnowsHowToDecompose)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KnowsHowToDecompose): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KnowsHowToDecompose): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KnowsHowToDecompose)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsPGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPGroup)"]]},{"rank" : 39,"comment" : "IsPGroup: for nilpotent groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNilpotentGroup","Tester(IsNilpotentGroup)"]]},{"rank" : 34,"comment" : "IsPGroup: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 33,"comment" : "IsPGroup: generic method (check order of the group or of generators if nilpotent)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsPGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimePGroup","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "PrimePGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimePGroup)"]]},{"rank" : 42,"comment" : "PrimePGroup: for direct products","filters" : [["IsPGroup","Tester(IsPGroup)","Tester(DirectProductInfo)"]]},{"rank" : 42,"comment" : "PrimePGroup: generic method, check the order of a nontrivial generator","filters" : [["Tester(GeneratorsOfMagmaWithInverses)","IsPGroup","Tester(IsPGroup)"]]},{"rank" : 41,"comment" : "PrimePGroup: generic method, check the group order","filters" : [["IsPGroup","Tester(IsPGroup)"]]},{"rank" : 0,"comment" : "PrimePGroup:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "PrimePGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimePGroup)","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimePGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimePGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimePGroup)","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PClassPGroup","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "PClassPGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(PClassPGroup)"]]},{"rank" : 64,"comment" : "PClassPGroup: for groups with special pcgs","filters" : [["IsPGroup","Tester(IsPGroup)","Tester(SpecialPcgs)"]]},{"rank" : 41,"comment" : "PClassPGroup: generic method for group","filters" : [["IsPGroup","Tester(IsPGroup)"]]},{"rank" : 0,"comment" : "PClassPGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PClassPGroup)","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PClassPGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PClassPGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PClassPGroup)","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankPGroup","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "RankPGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RankPGroup)"]]},{"rank" : 64,"comment" : "RankPGroup: for groups with special pcgs","filters" : [["IsPGroup","Tester(IsPGroup)","Tester(SpecialPcgs)"]]},{"rank" : 41,"comment" : "RankPGroup: generic method for group","filters" : [["IsPGroup","Tester(IsPGroup)"]]},{"rank" : 0,"comment" : "RankPGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RankPGroup)","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RankPGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RankPGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RankPGroup)","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotentGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsNilpotentGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNilpotentGroup)"]]},{"rank" : 368,"comment" : "IsNilpotentGroup: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 64,"comment" : "IsNilpotentGroup: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 59,"comment" : "IsNilpotentGroup: if group size can be computed and is a prime power","filters" : [["CanComputeSize","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "IsNilpotentGroup: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 52,"comment" : "IsNilpotentGroup: for pcgs computable group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 49,"comment" : "IsNilpotentGroup: for a pcp group with known lower central series","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(LowerCentralSeriesOfGroup)","CategoryCollections(IsPcpElement)"]]},{"rank" : 48,"comment" : "IsNilpotentGroup: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 38,"comment" : "IsNilpotentGroup: method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 33,"comment" : "IsNilpotentGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsNilpotentGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNilpotentGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNilpotentGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNilpotentGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNilpotentGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPerfectGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsPerfectGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPerfectGroup)"]]},{"rank" : 368,"comment" : "IsPerfectGroup: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 42,"comment" : "IsPerfectGroup: method for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 37,"comment" : "IsPerfectGroup","filters" : [["Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 35,"comment" : "IsPerfectGroup: for a (subgroup of a) finitely presented group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 33,"comment" : "IsPerfectGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsPerfectGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPerfectGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPerfectGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPerfectGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPerfectGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSporadicSimpleGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSporadicSimpleGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSporadicSimpleGroup)"]]},{"rank" : 33,"comment" : "IsSporadicSimpleGroup: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsSporadicSimpleGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSporadicSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSporadicSimpleGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSporadicSimpleGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSporadicSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSimpleGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSimpleGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSimpleGroup)"]]},{"rank" : 368,"comment" : "IsSimpleGroup: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 58,"comment" : "IsSimpleGroup: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 56,"comment" : "IsSimpleGroup: for solvable groups","filters" : [["IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 33,"comment" : "IsSimpleGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsSimpleGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSimpleGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSimpleGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAlmostSimpleGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsAlmostSimpleGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAlmostSimpleGroup)"]]},{"rank" : 33,"comment" : "IsAlmostSimpleGroup: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsAlmostSimpleGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAlmostSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAlmostSimpleGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAlmostSimpleGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAlmostSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSupersolvableGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSupersolvableGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSupersolvableGroup)"]]},{"rank" : 368,"comment" : "IsSupersolvableGroup: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 38,"comment" : "IsSupersolvableGroup: method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 33,"comment" : "IsSupersolvableGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsSupersolvableGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSupersolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSupersolvableGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSupersolvableGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSupersolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonomialGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsMonomialGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMonomialGroup)"]]},{"rank" : 368,"comment" : "IsMonomialGroup: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "IsMonomialGroup: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsMonomialGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMonomialGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMonomialGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMonomialGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMonomialGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSolvableGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSolvableGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSolvableGroup)"]]},{"rank" : 368,"comment" : "IsSolvableGroup: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 58,"comment" : "IsSolvableGroup: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 51,"comment" : "IsSolvableGroup: for AffineCrystGroup, via PointGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 48,"comment" : "IsSolvableGroup: for rational matrix groups (Polenta)","filters" : [["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)"]]},{"rank" : 46,"comment" : "IsSolvableGroup: for matrix groups over a finte field (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "IsSolvableGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 35,"comment" : "IsSolvableGroup","filters" : [["Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 34,"comment" : "IsSolvableGroup: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 33,"comment" : "IsSolvableGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsSolvableGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSolvableGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSolvableGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPolycyclicGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsPolycyclicGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPolycyclicGroup)"]]},{"rank" : 50,"comment" : "IsPolycyclicGroup: for integer matrix groups (Polenta)","filters" : [["IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"]]},{"rank" : 48,"comment" : "IsPolycyclicGroup: for rational matrix groups (Polenta)","filters" : [["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)"]]},{"rank" : 46,"comment" : "IsPolycyclicGroup: for matrix groups over a finite field (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "IsPolycyclicGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "IsPolycyclicGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsPolycyclicGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPolycyclicGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPolycyclicGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPolycyclicGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPolycyclicGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbelianInvariants","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "AbelianInvariants: system getter","filters" : [["IsAttributeStoringRep","Tester(AbelianInvariants)"]]},{"rank" : 395,"comment" : "AbelianInvariants: for groups of FFE","filters" : [["CategoryCollections(IsFFE)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 368,"comment" : "AbelianInvariants: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 56,"comment" : "AbelianInvariants: for an abelian pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 48,"comment" : "AbelianInvariants: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 36,"comment" : "AbelianInvariants: for a finitely presented group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 35,"comment" : "AbelianInvariants: for a subgroup of a finitely presented group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 34,"comment" : "AbelianInvariants: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 33,"comment" : "AbelianInvariants: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "AbelianInvariants: for an ordinary character table","filters" : [["IsOrdinaryTable"]]},{"rank" : 0,"comment" : "AbelianInvariants: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AbelianInvariants)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AbelianInvariants): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AbelianInvariants): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AbelianInvariants)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInfiniteAbelianizationGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsInfiniteAbelianizationGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsInfiniteAbelianizationGroup)"]]},{"rank" : 36,"comment" : "IsInfiniteAbelianizationGroup: for a finitely presented group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 35,"comment" : "IsInfiniteAbelianizationGroup: for a subgroup of a finitely presented group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 33,"comment" : "IsInfiniteAbelianizationGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsInfiniteAbelianizationGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsInfiniteAbelianizationGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsInfiniteAbelianizationGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsInfiniteAbelianizationGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsInfiniteAbelianizationGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsGroup","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "AsGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AsGroup)"]]},{"rank" : 133,"comment" : "AsGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "AsGroup: for a simple inverse Automaton","filters" : [["IsSimpleInvAutomatonRep"]]},{"rank" : 2,"comment" : "AsGroup: generic method for collections","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsGroup)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsGroup)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ChiefSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ChiefSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(ChiefSeries)"]]},{"rank" : 368,"comment" : "ChiefSeries: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 39,"comment" : "ChiefSeries: for pcgs computable group refining PcgsElementaryAbelianSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 33,"comment" : "ChiefSeries: generic method for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "ChiefSeries: method for a group (delegate to `ChiefSeriesUnderAction')","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ChiefSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ChiefSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ChiefSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ChiefSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ChiefSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ChiefSeriesUnderAction","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "ChiefSeriesUnderAction: method for a pcgs computable group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 66,"comment" : "ChiefSeriesUnderAction: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ChiefSeriesThrough","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "ChiefSeriesThrough: generic method for a group and a list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [{"rank" : 68,"comment" : "ChiefSeriesThrough: generic method for two groups and a list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CommutatorFactorGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CommutatorFactorGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(CommutatorFactorGroup)"]]},{"rank" : 368,"comment" : "CommutatorFactorGroup: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "CommutatorFactorGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "CommutatorFactorGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CommutatorFactorGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CommutatorFactorGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CommutatorFactorGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CommutatorFactorGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CompositionSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CompositionSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(CompositionSeries)"]]},{"rank" : 368,"comment" : "CompositionSeries: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 135,"comment" : "CompositionSeries: for simple group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSimpleGroup","Tester(IsSimpleGroup)"]]},{"rank" : 58,"comment" : "CompositionSeries: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "CompositionSeries: pcgs computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "CompositionSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 42,"comment" : "CompositionSeries: using DerivedSubgroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "CompositionSeries:  fallback method to test conditions","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "CompositionSeries:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "CompositionSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CompositionSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CompositionSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CompositionSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CompositionSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugacyClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ConjugacyClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(ConjugacyClasses)"]]},{"rank" : 20032,"comment" : "ConjugacyClasses: test options","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 444,"comment" : "ConjugacyClasses: perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 429,"comment" : "ConjugacyClasses: TF Method","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingFreeLiftSetup)"]]},{"rank" : 397,"comment" : "ConjugacyClasses: for natural sl","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalSL","Tester(IsNaturalSL)"]]},{"rank" : 395,"comment" : "ConjugacyClasses: for natural gl","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalGL","Tester(IsNaturalGL)"]]},{"rank" : 391,"comment" : "ConjugacyClasses: matrix groups: test naturality","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 368,"comment" : "ConjugacyClasses: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 62,"comment" : "ConjugacyClasses: symmetric","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 62,"comment" : "ConjugacyClasses: alternating","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 33,"comment" : "ConjugacyClasses: try solvable method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "ConjugacyClasses: for groups: try random search","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ConjugacyClasses:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ConjugacyClasses: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConjugacyClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConjugacyClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugacyClassesMaximalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ConjugacyClassesMaximalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ConjugacyClassesMaximalSubgroups)"]]},{"rank" : 33,"comment" : "ConjugacyClassesMaximalSubgroups: use MaximalSubgroupClassReps","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ConjugacyClassesMaximalSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 52,"comment" : "ConjugacyClassesMaximalSubgroups: forAffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConjugacyClassesMaximalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConjugacyClassesMaximalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConjugacyClassesMaximalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConjugacyClassesMaximalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "MaximalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalSubgroups)"]]},{"rank" : 51,"comment" : "MaximalSubgroups: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FamilyPcgs)"]]},{"rank" : 33,"comment" : "MaximalSubgroups: expand list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MaximalSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalSubgroupClassReps","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "MaximalSubgroupClassReps: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalSubgroupClassReps)"]]},{"rank" : 429,"comment" : "MaximalSubgroupClassReps: TF method","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingFreeLiftSetup)"]]},{"rank" : 368,"comment" : "MaximalSubgroupClassReps: handled by nice monomorphism: subgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 62,"comment" : "MaximalSubgroupClassReps: alternating","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 62,"comment" : "MaximalSubgroupClassReps: symmetric","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 58,"comment" : "MaximalSubgroupClassReps: perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 56,"comment" : "MaximalSubgroupClassReps: solvable perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 50,"comment" : "MaximalSubgroupClassReps: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 46,"comment" : "MaximalSubgroupClassReps: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 33,"comment" : "MaximalSubgroupClassReps: using lattice","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MaximalSubgroupClassReps: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 54,"comment" : "MaximalSubgroupClassReps: for AffineCrystGroupOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsRecord"]]},{"rank" : 54,"comment" : "MaximalSubgroupClassReps: for AffineCrystGroupOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalSubgroupClassReps)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalSubgroupClassReps): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalSubgroupClassReps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalSubgroupClassReps)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PerfectResiduum","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PerfectResiduum: system getter","filters" : [["IsAttributeStoringRep","Tester(PerfectResiduum)"]]},{"rank" : 35,"comment" : "PerfectResiduum: for solvable groups","filters" : [["IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 35,"comment" : "PerfectResiduum: for perfect groups","filters" : [["IsPerfectGroup","Tester(IsPerfectGroup)"]]},{"rank" : 33,"comment" : "PerfectResiduum: for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "PerfectResiduum: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PerfectResiduum)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PerfectResiduum): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PerfectResiduum): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PerfectResiduum)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativesPerfectSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "RepresentativesPerfectSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(RepresentativesPerfectSubgroups)"]]},{"rank" : 62,"comment" : "RepresentativesPerfectSubgroups: symmetric","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 62,"comment" : "RepresentativesPerfectSubgroups: alternating","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 35,"comment" : "RepresentativesPerfectSubgroups: solvable","filters" : [["IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 33,"comment" : "RepresentativesPerfectSubgroups: using Holt\/Plesken library","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RepresentativesPerfectSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RepresentativesPerfectSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RepresentativesPerfectSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RepresentativesPerfectSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RepresentativesPerfectSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativesSimpleSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "RepresentativesSimpleSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(RepresentativesSimpleSubgroups)"]]},{"rank" : 34,"comment" : "RepresentativesSimpleSubgroups: if perfect subs are known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(RepresentativesPerfectSubgroups)"]]},{"rank" : 33,"comment" : "RepresentativesSimpleSubgroups: using Holt\/Plesken library","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RepresentativesSimpleSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RepresentativesSimpleSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RepresentativesSimpleSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RepresentativesSimpleSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RepresentativesSimpleSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugacyClassesPerfectSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ConjugacyClassesPerfectSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ConjugacyClassesPerfectSubgroups)"]]},{"rank" : 33,"comment" : "ConjugacyClassesPerfectSubgroups: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ConjugacyClassesPerfectSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConjugacyClassesPerfectSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConjugacyClassesPerfectSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConjugacyClassesPerfectSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConjugacyClassesPerfectSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugacyClassesSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ConjugacyClassesSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ConjugacyClassesSubgroups)"]]},{"rank" : 33,"comment" : "ConjugacyClassesSubgroups: group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 3,"comment" : "ConjugacyClassesSubgroups: lattice","filters" : [["IsLatticeSubgroupsRep"]]},{"rank" : 0,"comment" : "ConjugacyClassesSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConjugacyClassesSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConjugacyClassesSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConjugacyClassesSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConjugacyClassesSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LatticeSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "LatticeSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(LatticeSubgroups)"]]},{"rank" : 44,"comment" : "LatticeSubgroups: for a group with table of marks","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(TableOfMarks)"]]},{"rank" : 43,"comment" : "LatticeSubgroups: for a cyclic group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCyclic","Tester(IsCyclic)"]]},{"rank" : 34,"comment" : "LatticeSubgroups: elementary abelian extension","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "LatticeSubgroups: via radical","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "LatticeSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LatticeSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LatticeSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LatticeSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LatticeSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DerivedLength","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DerivedLength: system getter","filters" : [["IsAttributeStoringRep","Tester(DerivedLength)"]]},{"rank" : 368,"comment" : "DerivedLength: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "DerivedLength: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DerivedLength: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DerivedLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DerivedLength): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DerivedLength): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DerivedLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HirschLength","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "HirschLength: system getter","filters" : [["IsAttributeStoringRep","Tester(HirschLength)"]]},{"rank" : 51,"comment" : "HirschLength","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 48,"comment" : "HirschLength","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 42,"comment" : "HirschLength: generic method for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "HirschLength: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(HirschLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(HirschLength): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(HirschLength): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(HirschLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DerivedSeriesOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DerivedSeriesOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DerivedSeriesOfGroup)"]]},{"rank" : 368,"comment" : "DerivedSeriesOfGroup: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "DerivedSeriesOfGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DerivedSeriesOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DerivedSeriesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DerivedSeriesOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DerivedSeriesOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DerivedSeriesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DerivedSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DerivedSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DerivedSubgroup)"]]},{"rank" : 10041,"comment" : "DerivedSubgroup: for a group that knows it is abelian","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"]]},{"rank" : 10035,"comment" : "DerivedSubgroup: for a group that knows it is perfect","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsPerfectGroup","Tester(IsPerfectGroup)"]]},{"rank" : 368,"comment" : "DerivedSubgroup: handled by nice monomorphism: Subgroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 62,"comment" : "DerivedSubgroup","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 58,"comment" : "DerivedSubgroup: permgrps","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "DerivedSubgroup: pcgs computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "DerivedSubgroup: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 36,"comment" : "DerivedSubgroup: for a finitely presented group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 35,"comment" : "DerivedSubgroup: subgroup of a finitely presented group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 33,"comment" : "DerivedSubgroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DerivedSubgroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DerivedSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DerivedSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DerivedSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DerivedSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalAbelianQuotient","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "MaximalAbelianQuotient: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalAbelianQuotient)"]]},{"rank" : 38,"comment" : "MaximalAbelianQuotient: whole fp group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"]]},{"rank" : 35,"comment" : "MaximalAbelianQuotient: for subgroups of finitely presented groups","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 33,"comment" : "MaximalAbelianQuotient: not fp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MaximalAbelianQuotient: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalAbelianQuotient)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalAbelianQuotient): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalAbelianQuotient): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalAbelianQuotient)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CommutatorLength","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CommutatorLength: system getter","filters" : [["IsAttributeStoringRep","Tester(CommutatorLength)"]]},{"rank" : 33,"comment" : "CommutatorLength: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 21,"comment" : "CommutatorLength: for a character table","filters" : [["IsCharacterTable"]]},{"rank" : 0,"comment" : "CommutatorLength: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CommutatorLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CommutatorLength): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CommutatorLength): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CommutatorLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DimensionsLoewyFactors","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DimensionsLoewyFactors: system getter","filters" : [["IsAttributeStoringRep","Tester(DimensionsLoewyFactors)"]]},{"rank" : 33,"comment" : "DimensionsLoewyFactors: for a group (that must be a finite p-group)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DimensionsLoewyFactors: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DimensionsLoewyFactors)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DimensionsLoewyFactors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DimensionsLoewyFactors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DimensionsLoewyFactors)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementaryAbelianSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ElementaryAbelianSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(ElementaryAbelianSeries)"]]},{"rank" : 368,"comment" : "ElementaryAbelianSeries: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 63,"comment" : "ElementaryAbelianSeries: perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "ElementaryAbelianSeries: pcgs computable groups using `PcgsElementaryAbelianSeries'","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 42,"comment" : "ElementaryAbelianSeries: generic method for groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 8,"comment" : "ElementaryAbelianSeries: list of pcgs computable groups","filters" : [["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 7,"comment" : "ElementaryAbelianSeries: method for lists","filters" : [["IsList","IsFinite","Tester(IsFinite)"]]},{"rank" : 0,"comment" : "ElementaryAbelianSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ElementaryAbelianSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ElementaryAbelianSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementaryAbelianSeriesLargeSteps","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ElementaryAbelianSeriesLargeSteps: system getter","filters" : [["IsAttributeStoringRep","Tester(ElementaryAbelianSeriesLargeSteps)"]]},{"rank" : 368,"comment" : "ElementaryAbelianSeriesLargeSteps: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "ElementaryAbelianSeriesLargeSteps: remove spurious factors","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 2,"comment" : "ElementaryAbelianSeriesLargeSteps: remove spurious factors","filters" : [["IsList"]]},{"rank" : 0,"comment" : "ElementaryAbelianSeriesLargeSteps: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ElementaryAbelianSeriesLargeSteps)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ElementaryAbelianSeriesLargeSteps): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ElementaryAbelianSeriesLargeSteps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ElementaryAbelianSeriesLargeSteps)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Exponent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Exponent: system getter","filters" : [["IsAttributeStoringRep","Tester(Exponent)"]]},{"rank" : 368,"comment" : "Exponent: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 42,"comment" : "Exponent: method for abelian groups with generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"]]},{"rank" : 35,"comment" : "Exponent: solvable group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 33,"comment" : "Exponent: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "Exponent: for an ordinary character table","filters" : [["IsOrdinaryTable"]]},{"rank" : 0,"comment" : "Exponent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Exponent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Exponent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Exponent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Exponent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FittingSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "FittingSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FittingSubgroup)"]]},{"rank" : 10039,"comment" : "FittingSubgroup: for nilpotent group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNilpotentGroup","Tester(IsNilpotentGroup)"]]},{"rank" : 368,"comment" : "FittingSubgroup: handled by nice monomorphism: Subgroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 54,"comment" : "FittingSubgroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNilpotentGroup","Tester(IsNilpotentGroup)","CategoryCollections(IsPcpElement)"]]},{"rank" : 49,"comment" : "FittingSubgroup: for ac pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)","Tester(AlmostCrystallographicInfo)"]]},{"rank" : 48,"comment" : "FittingSubgroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 42,"comment" : "FittingSubgroup: generic method for groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "FittingSubgroup:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "FittingSubgroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FittingSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FittingSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FittingSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FittingSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrefrattiniSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PrefrattiniSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(PrefrattiniSubgroup)"]]},{"rank" : 50,"comment" : "PrefrattiniSubgroup: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 0,"comment" : "PrefrattiniSubgroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrefrattiniSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrefrattiniSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrefrattiniSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrefrattiniSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FrattiniSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "FrattiniSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FrattiniSubgroup)"]]},{"rank" : 368,"comment" : "FrattiniSubgroup: handled by nice monomorphism: Subgroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 58,"comment" : "FrattiniSubgroup: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "FrattiniSubgroup: pcgs computable groups using prefrattini and core","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "FrattiniSubgroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 33,"comment" : "FrattiniSubgroup: Using radical","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "FrattiniSubgroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "FrattiniSubgroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FrattiniSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FrattiniSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FrattiniSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FrattiniSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InvariantForm","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "InvariantForm: system getter","filters" : [["IsAttributeStoringRep","Tester(InvariantForm)"]]},{"rank" : 0,"comment" : "InvariantForm: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InvariantForm)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InvariantForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InvariantForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InvariantForm)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "JenningsSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "JenningsSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(JenningsSeries)"]]},{"rank" : 368,"comment" : "JenningsSeries: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "JenningsSeries: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "JenningsSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(JenningsSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(JenningsSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(JenningsSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(JenningsSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LowerCentralSeriesOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "LowerCentralSeriesOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(LowerCentralSeriesOfGroup)"]]},{"rank" : 368,"comment" : "LowerCentralSeriesOfGroup: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 58,"comment" : "LowerCentralSeriesOfGroup: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 48,"comment" : "LowerCentralSeriesOfGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 35,"comment" : "LowerCentralSeriesOfGroup: fp group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 33,"comment" : "LowerCentralSeriesOfGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "LowerCentralSeriesOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LowerCentralSeriesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LowerCentralSeriesOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LowerCentralSeriesOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LowerCentralSeriesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NilpotencyClassOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NilpotencyClassOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NilpotencyClassOfGroup)"]]},{"rank" : 33,"comment" : "NilpotencyClassOfGroup: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NilpotencyClassOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NilpotencyClassOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NilpotencyClassOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NilpotencyClassOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NilpotencyClassOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "MaximalNormalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalNormalSubgroups)"]]},{"rank" : 33,"comment" : "MaximalNormalSubgroups: generic search","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MaximalNormalSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalNormalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalNormalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalMaximalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NormalMaximalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalMaximalSubgroups)"]]},{"rank" : 50,"comment" : "NormalMaximalSubgroups: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "NormalMaximalSubgroups: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "NormalMaximalSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalMaximalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalMaximalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalMaximalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalMaximalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "MinimalNormalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimalNormalSubgroups)"]]},{"rank" : 376,"comment" : "MinimalNormalSubgroups: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 48,"comment" : "MinimalNormalSubgroups: for solvable groups: use AbelianMinimalNormalSubgroups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 43,"comment" : "MinimalNormalSubgroups: generic search in NormalSubgroups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(NormalSubgroups)"]]},{"rank" : 42,"comment" : "MinimalNormalSubgroups: compute from conjugacy classes","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MinimalNormalSubgroups:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MinimalNormalSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimalNormalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimalNormalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NormalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalSubgroups)"]]},{"rank" : 379,"comment" : "NormalSubgroups: via nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 368,"comment" : "NormalSubgroups: handled by nice monomorphism: subgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 66,"comment" : "NormalSubgroups:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 65,"comment" : "NormalSubgroups: normal complement method for solvable perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 58,"comment" : "NormalSubgroups: homomorphism principle perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 48,"comment" : "NormalSubgroups: via IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 47,"comment" : "NormalSubgroups: normal complement method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 46,"comment" : "NormalSubgroups: homomorphism principle pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 39,"comment" : "NormalSubgroups: normal complement method for pcgs computable groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 33,"comment" : "NormalSubgroups: generic class union","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NormalSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrConjugacyClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NrConjugacyClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(NrConjugacyClasses)"]]},{"rank" : 397,"comment" : "NrConjugacyClasses: for natural SL","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalSL","Tester(IsNaturalSL)"]]},{"rank" : 395,"comment" : "NrConjugacyClasses: for natural SU","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSubgroupSL","Tester(IsSubgroupSL)","IsFullSubgroupGLorSLRespectingSesquilinearForm","Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]]},{"rank" : 395,"comment" : "NrConjugacyClasses: for natural GL","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalGL","Tester(IsNaturalGL)"]]},{"rank" : 393,"comment" : "NrConjugacyClasses: for GU(n,q)","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFullSubgroupGLorSLRespectingSesquilinearForm","Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]]},{"rank" : 368,"comment" : "NrConjugacyClasses: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 36,"comment" : "NrConjugacyClasses","filters" : [["IsAttributeStoringRep","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(ConjugacyClasses)"]]},{"rank" : 34,"comment" : "NrConjugacyClasses: for a group with known ordinary character table","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(OrdinaryCharacterTable)"]]},{"rank" : 33,"comment" : "NrConjugacyClasses: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "NrConjugacyClasses: for an ordinary character table with underlying group","filters" : [["IsOrdinaryTable","Tester(UnderlyingGroup)"]]},{"rank" : 22,"comment" : "NrConjugacyClasses: for a Brauer character table","filters" : [["IsBrauerTable"]]},{"rank" : 21,"comment" : "NrConjugacyClasses: for a character table with known class lengths","filters" : [["IsNearlyCharacterTable","Tester(SizesConjugacyClasses)"]]},{"rank" : 21,"comment" : "NrConjugacyClasses: for a character table with known centralizer orders","filters" : [["IsNearlyCharacterTable","Tester(SizesCentralizers)"]]},{"rank" : 0,"comment" : "NrConjugacyClasses: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrConjugacyClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrConjugacyClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Omega","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsFunction"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsFunction"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "Omega","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 38,"comment" : "Omega","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 71,"comment" : "Omega","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 56,"comment" : "Omega","filters" : [["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 39,"comment" : "Omega","filters" : [["IsFunction"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [{"rank" : 57,"comment" : "Omega","filters" : [["IsFunction"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "OmegaOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 71,"comment" : "OmegaOp: for p groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedOmegas","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedOmegas: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedOmegas)"]]},{"rank" : 33,"comment" : "ComputedOmegas","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedOmegas: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedOmegas)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedOmegas): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedOmegas): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedOmegas)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AgemoOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 79,"comment" : "AgemoOp: PGroups","filters" : [["IsPGroup","Tester(IsPGroup)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedAgemos","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedAgemos: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedAgemos)"]]},{"rank" : 33,"comment" : "ComputedAgemos","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedAgemos: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedAgemos)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedAgemos): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedAgemos): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedAgemos)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RadicalGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "RadicalGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RadicalGroup)"]]},{"rank" : 429,"comment" : "RadicalGroup: TF method, use tree","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingFreeLiftSetup)"]]},{"rank" : 368,"comment" : "RadicalGroup: handled by nice monomorphism: Subgroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 135,"comment" : "RadicalGroup: solvable group is its own radical","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 58,"comment" : "RadicalGroup:  for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 42,"comment" : "RadicalGroup: factor out Fitting subgroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RadicalGroup:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RadicalGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RadicalGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RadicalGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RadicalGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RadicalGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RationalClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "RationalClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(RationalClasses)"]]},{"rank" : 368,"comment" : "RationalClasses: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "RationalClasses: use classes","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "RationalClasses: trial","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RationalClasses: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RationalClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RationalClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RationalClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RationalClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsSmallest","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "GeneratorsSmallest: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsSmallest)"]]},{"rank" : 388,"comment" : "GeneratorsSmallest: matrix group via niceo","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "GeneratorsSmallest: perm group via minimal stab chain","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 44,"comment" : "GeneratorsSmallest: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 39,"comment" : "GeneratorsSmallest: group of pc words which is full family","filters" : [["Tester(FamilyPcgs)"]]},{"rank" : 33,"comment" : "GeneratorsSmallest: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 26,"comment" : "GeneratorsSmallest: for a free monoid","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"]]},{"rank" : 20,"comment" : "GeneratorsSmallest: for a free semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsSmallest)","type" : "GAP_Operation","filters" : [[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsSmallest): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsSmallest): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsSmallest)","type" : "GAP_Operation","filters" : [[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LargestElementGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "LargestElementGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(LargestElementGroup)"]]},{"rank" : 388,"comment" : "LargestElementGroup: matrix group via niceo","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "LargestElementGroup: perm group via minimal stab chain","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "LargestElementGroup: use `EnumeratorSorted'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "LargestElementGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LargestElementGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LargestElementGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LargestElementGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LargestElementGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalGeneratingSet","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "MinimalGeneratingSet: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimalGeneratingSet)"]]},{"rank" : 367,"comment" : "MinimalGeneratingSet","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 114,"comment" : "MinimalGeneratingSet: cyclic groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCyclic","Tester(IsCyclic)"]]},{"rank" : 91,"comment" : "MinimalGeneratingSet: compute via Smith normal form","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CanEasilyComputePcgs"]]},{"rank" : 62,"comment" : "MinimalGeneratingSet: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 50,"comment" : "MinimalGeneratingSet: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 48,"comment" : "MinimalGeneratingSet: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 33,"comment" : "MinimalGeneratingSet: solvable group via pc","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MinimalGeneratingSet: fallback method to inform user","filters" : [[]]},{"rank" : 0,"comment" : "MinimalGeneratingSet: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimalGeneratingSet)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimalGeneratingSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimalGeneratingSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimalGeneratingSet)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SmallGeneratingSet","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SmallGeneratingSet: system getter","filters" : [["IsAttributeStoringRep","Tester(SmallGeneratingSet)"]]},{"rank" : 367,"comment" : "SmallGeneratingSet","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 62,"comment" : "SmallGeneratingSet: using minimal generating set","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 58,"comment" : "SmallGeneratingSet: random and generators subset, randsims","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "SmallGeneratingSet: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 48,"comment" : "SmallGeneratingSet: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 34,"comment" : "SmallGeneratingSet: generators subset","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SmallGeneratingSet: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SmallGeneratingSet)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SmallGeneratingSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SmallGeneratingSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SmallGeneratingSet)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SupersolvableResiduum","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SupersolvableResiduum: system getter","filters" : [["IsAttributeStoringRep","Tester(SupersolvableResiduum)"]]},{"rank" : 42,"comment" : "SupersolvableResiduum: method for finite groups (call `SupersolvableResiduumDefault')","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SupersolvableResiduum: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SupersolvableResiduum)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SupersolvableResiduum): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SupersolvableResiduum): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SupersolvableResiduum)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComplementSystem","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComplementSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(ComplementSystem)"]]},{"rank" : 42,"comment" : "ComplementSystem: generic method for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComplementSystem: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComplementSystem)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComplementSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComplementSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComplementSystem)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SylowSystem","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SylowSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(SylowSystem)"]]},{"rank" : 42,"comment" : "SylowSystem: generic method for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SylowSystem: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SylowSystem)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SylowSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SylowSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SylowSystem)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HallSystem","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "HallSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(HallSystem)"]]},{"rank" : 42,"comment" : "HallSystem: test whether finite group is solvable","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "HallSystem: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(HallSystem)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(HallSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(HallSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(HallSystem)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Socle","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Socle: system getter","filters" : [["IsAttributeStoringRep","Tester(Socle)"]]},{"rank" : 62,"comment" : "Socle","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 62,"comment" : "Socle","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 58,"comment" : "Socle: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 53,"comment" : "Socle: for finite nilpotent groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 48,"comment" : "Socle: for finite soluble group, via SolvableSocle","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 41,"comment" : "Socle: for p-groups","filters" : [["IsPGroup","Tester(IsPGroup)"]]},{"rank" : 33,"comment" : "Socle: from normal subgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "Socle:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "Socle: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Socle)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Socle): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Socle): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Socle)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UpperCentralSeriesOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "UpperCentralSeriesOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(UpperCentralSeriesOfGroup)"]]},{"rank" : 368,"comment" : "UpperCentralSeriesOfGroup: handled by nice monomorphism: GroupSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 48,"comment" : "UpperCentralSeriesOfGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 33,"comment" : "UpperCentralSeriesOfGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "UpperCentralSeriesOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UpperCentralSeriesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UpperCentralSeriesOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UpperCentralSeriesOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UpperCentralSeriesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EulerianFunction","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "EulerianFunction: for a group with table of marks","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(TableOfMarks)"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "EulerianFunction: pcgs computable groups using special pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsInt","IsPosRat"]]},{"rank" : 1,"comment" : "EulerianFunction:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "EulerianFunction: for a group, compute table of marks","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 116,"comment" : "AsSubgroup: perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "AsSubgroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassMultiplicationCoefficient","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection"],["IsCollection"],["IsCollection"]],[["IsOrdinaryTable"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 89,"comment" : "ClassMultiplicationCoefficient: for an ord. table, and three pos. integers","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "ClosureGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10068,"comment" : "ClosureGroup: for two groups, the bigger conatining the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 10040,"comment" : "ClosureGroup: method for group that contains the whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 736,"comment" : "ClosureGroup: handled by nice monomorphism:group CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 373,"comment" : "ClosureGroup: by niceo","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 119,"comment" : "ClosureGroup: permgroup, elements","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsPerm)"]]},{"rank" : 96,"comment" : "ClosureGroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 75,"comment" : "ClosureGroup: empty list","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 71,"comment" : "ClosureGroup: for subgroup of fp group, and subgroup","filters" : [["Tester(ParentAttr)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 68,"comment" : "ClosureGroup: groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 66,"comment" : "ClosureGroup: permgroup, element","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPerm"]]},{"rank" : 66,"comment" : "ClosureGroup: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "ClosureGroup: AffineCrystGroupOnLeft method for group and element","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 58,"comment" : "ClosureGroup: AffineCrystGroupOnRight method for group and element","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 50,"comment" : "ClosureGroup: for group and empty element list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 43,"comment" : "ClosureGroup: subgrp fp: Has coset table","filters" : [["Tester(ParentAttr)","IsSubgroupFpGroup","Tester(CosetTableInWholeGroup)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 42,"comment" : "ClosureGroup: subgrp fp: by quotient subgroup","filters" : [["Tester(ParentAttr)","IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 39,"comment" : "ClosureGroup: groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 39,"comment" : "ClosureGroup: groups with cheap membership test","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyTestMembership"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 38,"comment" : "ClosureGroup: generic method for group and element","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 35,"comment" : "ClosureGroup: for group and element list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection"]]},{"rank" : 0,"comment" : "ClosureGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 120,"comment" : "ClosureGroup: permgroup, elements, options","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsPerm)"],["IsRecord"]]},{"rank" : 117,"comment" : "ClosureGroup: permgroup, permgroup, options","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]},{"rank" : 76,"comment" : "ClosureGroup: empty list and options","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsRecord"]]},{"rank" : 67,"comment" : "ClosureGroup: permgroup, element, options","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPerm"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CommutatorSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "CommutatorSubgroup: handled by nice monomorphism:group CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 116,"comment" : "CommutatorSubgroup: permgroups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 96,"comment" : "CommutatorSubgroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 73,"comment" : "CommutatorSubgroup: normal subgroup with whole fp group","filters" : [["IsSubgroupFpGroup"],["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"]]},{"rank" : 73,"comment" : "CommutatorSubgroup: whole fp group with normal subgroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 70,"comment" : "CommutatorSubgroup: normal subgroup with whole fp group","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 68,"comment" : "CommutatorSubgroup: groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 66,"comment" : "CommutatorSubgroup: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugateGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 374,"comment" : "ConjugateGroup: handled by nice monomorphism: group CollElm","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 66,"comment" : "ConjugateGroup: <P>, <g>","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPerm"]]},{"rank" : 58,"comment" : "ConjugateGroup: method for AffineCrystGroupOnLeft and element","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 58,"comment" : "ConjugateGroup: method for AffineCrystGroupOnRight and element","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 42,"comment" : "ConjugateGroup: subgroups of fp group with coset table","filters" : [["IsSubgroupFpGroup","Tester(CosetTableInWholeGroup)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 41,"comment" : "ConjugateGroup: subgroups of fp group by quotient","filters" : [["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 39,"comment" : "ConjugateGroup: groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 38,"comment" : "ConjugateGroup: <G>, <g>","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugateSubgroup","type" : "GAP_Operation","filters" : [[["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 39,"comment" : "ConjugateSubgroup: for group with parent, and group element","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 38,"comment" : "ConjugateSubgroup: for group without parent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugateSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 68,"comment" : "ConjugateSubgroups: groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 66,"comment" : "ConjugateSubgroups: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoreOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "CoreOp: handled by nice monomorphism:group CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 71,"comment" : "CoreOp: subgroups of fp group by quotient","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 70,"comment" : "CoreOp: subgroups of fp group: use quotient rep","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 67,"comment" : "CoreOp: pcgs computable groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "CoreOp: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoreInParent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CoreInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(CoreInParent)"]]},{"rank" : 33,"comment" : "CoreInParent: method that calls the two-argument operation CoreOp","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "CoreInParent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoreInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoreInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoreInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoreInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Core","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "Core: try to exploit the in-parent attribute CoreInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CosetTable","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "CosetTable: for finitely presented groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CosetTableNormalClosure","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "CosetTableNormalClosure: for finitely presented groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorGroupNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 96,"comment" : "FactorGroupNC","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 66,"comment" : "FactorGroupNC: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphism","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "NaturalHomomorphism: for a group with natural homomorphism stored","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 96,"comment" : "NaturalHomomorphism: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndexOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "IndexOp: handled by nice monomorphism: attribute CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 106,"comment" : "IndexOp: AffineCrystGroupOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "IndexOp: AffineCrystGroupOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 100,"comment" : "IndexOp: for free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 96,"comment" : "IndexOp: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 73,"comment" : "IndexOp: for finitely presented group in whole group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 66,"comment" : "IndexOp: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 40,"comment" : "IndexOp: for two character tables","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]},{"rank" : 0,"comment" : "IndexOp:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [{"rank" : 101,"comment" : "IndexOp: for free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndexInParent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IndexInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(IndexInParent)"]]},{"rank" : 33,"comment" : "IndexInParent: method that calls the two-argument operation IndexOp","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IndexInParent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndexInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndexInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndexInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndexInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Index","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "Index: try to exploit the in-parent attribute IndexInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 40,"comment" : "Index: for two character tables","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndexNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 747,"comment" : "IndexNC: for two groups with known Size value","filters" : [["Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFinite","Tester(IsFinite)","Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 736,"comment" : "IndexNC: handled by nice monomorphism: attribute CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 106,"comment" : "IndexNC: AffineCrystGroupOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "IndexNC: AffineCrystGroupOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 100,"comment" : "IndexNC: for free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 96,"comment" : "IndexNC: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 70,"comment" : "IndexNC: for finitely presented groups","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 66,"comment" : "IndexNC: generic method for two groups (the second one being finite)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 40,"comment" : "IndexNC: for two character tables","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]},{"rank" : 0,"comment" : "IndexNC:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndexInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IndexInWholeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IndexInWholeGroup)"]]},{"rank" : 50,"comment" : "IndexInWholeGroup: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 38,"comment" : "IndexInWholeGroup: for full fp group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"]]},{"rank" : 36,"comment" : "IndexInWholeGroup: subgroup fp by quotient","filters" : [["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 35,"comment" : "IndexInWholeGroup: subgroup fp","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "IndexInWholeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndexInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndexInWholeGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndexInWholeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndexInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndependentGeneratorsOfAbelianGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20043,"comment" : "IndependentGeneratorsOfAbelianGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IndependentGeneratorsOfAbelianGroup)"]]},{"rank" : 396,"comment" : "IndependentGeneratorsOfAbelianGroup: for groups of FFE","filters" : [["CategoryCollections(IsFFE)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 72,"comment" : "IndependentGeneratorsOfAbelianGroup: for perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"]]},{"rank" : 57,"comment" : "IndependentGeneratorsOfAbelianGroup: for an abelian pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 45,"comment" : "IndependentGeneratorsOfAbelianGroup: Use Pcgs and NormalFormIntMat to find the independent generators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CanEasilyComputePcgs"]]},{"rank" : 44,"comment" : "IndependentGeneratorsOfAbelianGroup: For abelian fpgroup, use Smith normal form","filters" : [["IsCommutative","Tester(IsCommutative)","IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 42,"comment" : "IndependentGeneratorsOfAbelianGroup: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(DirectProductInfo)"]]},{"rank" : 41,"comment" : "IndependentGeneratorsOfAbelianGroup: finite abelian group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"]]},{"rank" : 0,"comment" : "IndependentGeneratorsOfAbelianGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndependentGeneratorsOfAbelianGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndependentGeneratorsOfAbelianGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndependentGeneratorsOfAbelianGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndependentGeneratorsOfAbelianGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndependentGeneratorExponents","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 411,"comment" : "IndependentGeneratorExponents: for groups of FFE","filters" : [["CategoryCollections(IsFFE)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFFE"]]},{"rank" : 63,"comment" : "IndependentGeneratorExponents: for an abelian pcp group and an element","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CategoryCollections(IsPcpElement)"],["IsPcpElement"]]},{"rank" : 57,"comment" : "IndependentGeneratorExponents: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(DirectProductInfo)"],["IsMultiplicativeElementWithInverse","IsDirectProductElement"]]},{"rank" : 46,"comment" : "IndependentGeneratorExponents","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsConjugate","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 144,"comment" : "IsConjugate: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 99,"comment" : "IsConjugate: subgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 60,"comment" : "IsConjugate: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsPcpElement"],["IsPcpElement"]]},{"rank" : 43,"comment" : "IsConjugate: group elements","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormalOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "IsNormalOp: handled by nice monomorphism: attribute CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 92,"comment" : "IsNormalOp: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 74,"comment" : "IsNormalOp: subgroups of fp group by quot. rep in full fp grp.","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 66,"comment" : "IsNormalOp: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormalInParent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsNormalInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNormalInParent)"]]},{"rank" : 33,"comment" : "IsNormalInParent: method that calls the two-argument operation IsNormalOp","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsNormalInParent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNormalInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNormalInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNormalInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNormalInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormal","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "IsNormal: try to exploit the in-parent attribute IsNormalInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCharacteristicSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "IsCharacteristicSubgroup: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPNilpotentOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 70,"comment" : "IsPNilpotentOp: for a group with special pcgs: test for normal Hall subgroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SpecialPcgs)"],["IsInt","IsPosRat"]]},{"rank" : 61,"comment" : "IsPNilpotentOp: check if p divides order of hypocentre","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "IsPNilpotentOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedIsPNilpotents","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedIsPNilpotents: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedIsPNilpotents)"]]},{"rank" : 32,"comment" : "ComputedIsPNilpotents: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedIsPNilpotents: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedIsPNilpotents)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedIsPNilpotents): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedIsPNilpotents): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedIsPNilpotents)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPNilpotent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "IsPNilpotent: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasIsPNilpotent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "HasIsPNilpotent: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetIsPNilpotent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "SetIsPNilpotent: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPSolvableOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10065,"comment" : "IsPSolvableOp: for solvable groups: return true","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsInt","IsPosRat"]]},{"rank" : 61,"comment" : "IsPSolvableOp: generic method: build descending series with abelian or p'-factors","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "IsPSolvableOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedIsPSolvables","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedIsPSolvables: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedIsPSolvables)"]]},{"rank" : 32,"comment" : "ComputedIsPSolvables: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedIsPSolvables: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedIsPSolvables)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedIsPSolvables): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedIsPSolvables): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedIsPSolvables)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPSolvable","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "IsPSolvable: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasIsPSolvable","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "HasIsPSolvable: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetIsPSolvable","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "SetIsPSolvable: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubnormal","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "IsSubnormal: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalClosureOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "NormalClosureOp: handled by nice monomorphism:group CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 116,"comment" : "NormalClosureOp: subgroup of perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 96,"comment" : "NormalClosureOp: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 73,"comment" : "NormalClosureOp: whole fp group with normal subgroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 68,"comment" : "NormalClosureOp: groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 66,"comment" : "NormalClosureOp: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NormalClosureOp:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalClosureInParent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NormalClosureInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalClosureInParent)"]]},{"rank" : 33,"comment" : "NormalClosureInParent: method that calls the two-argument operation NormalClosureOp","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NormalClosureInParent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalClosureInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalClosureInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalClosureInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalClosureInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalClosure","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "NormalClosure: try to exploit the in-parent attribute NormalClosureInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalIntersection","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "NormalIntersection: handled by nice monomorphism:group CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 96,"comment" : "NormalIntersection: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 68,"comment" : "NormalIntersection: method for two groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 66,"comment" : "NormalIntersection: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 11,"comment" : "NormalizerOp","filters" : [["IsConjugacyClassSubgroupsRep"]]}],"2args" : [{"rank" : 736,"comment" : "NormalizerOp: handled by nice monomorphism: Subgroup CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 120,"comment" : "NormalizerOp: subgp of natural alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 120,"comment" : "NormalizerOp: subgp of natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 116,"comment" : "NormalizerOp: perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 106,"comment" : "NormalizerOp: two AffineCrystGroupsOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "NormalizerOp: two AffineCrystGroupsOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 100,"comment" : "NormalizerOp: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 100,"comment" : "NormalizerOp","filters" : [["IsNaturalGL","Tester(IsNaturalGL)","IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 96,"comment" : "NormalizerOp: for a pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 74,"comment" : "NormalizerOp: in whole group by quot. rep","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 72,"comment" : "NormalizerOp: subgroups of fp group by quot. rep","filters" : [["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 70,"comment" : "NormalizerOp: subgroups of fp group: find stabilizing cosets","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 69,"comment" : "NormalizerOp: for groups with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 68,"comment" : "NormalizerOp: slightly better orbit algorithm for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 66,"comment" : "NormalizerOp: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 55,"comment" : "NormalizerOp: for an element in a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]},{"rank" : 38,"comment" : "NormalizerOp: generic method for group and Element","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 0,"comment" : "NormalizerOp:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerInParent","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "NormalizerInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizerInParent)"]]},{"rank" : 6,"comment" : "NormalizerInParent: method that calls the two-argument operation NormalizerOp","filters" : [["Tester(ParentAttr)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizerInParent)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizerInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizerInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizerInParent)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Normalizer","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "Normalizer: try to exploit the in-parent attribute NormalizerInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 174,"comment" : "Normalizer: perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralizerModulo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 101,"comment" : "CentralizerModulo: group centralizer via generators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 73,"comment" : "CentralizerModulo: pcgs computable groups, for elm","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 0,"comment" : "CentralizerModulo:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PCentralSeriesOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 387,"comment" : "PCentralSeriesOp: handled by nice monomorphism: GroupSeries CollOther","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsInt","IsPosRat"]]},{"rank" : 81,"comment" : "PCentralSeriesOp: method for pc groups and prime","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt","IsPosRat"]]},{"rank" : 77,"comment" : "PCentralSeriesOp: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 67,"comment" : "PCentralSeriesOp","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : 52,"comment" : "PCentralSeriesOp: generic method for group and prime","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedPCentralSeriess","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedPCentralSeriess: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedPCentralSeriess)"]]},{"rank" : 32,"comment" : "ComputedPCentralSeriess: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedPCentralSeriess: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedPCentralSeriess)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedPCentralSeriess): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedPCentralSeriess): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedPCentralSeriess)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PCentralSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "PCentralSeries: pGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 51,"comment" : "PCentralSeries: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasPCentralSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "HasPCentralSeries: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPCentralSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "SetPCentralSeries: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PRumpOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "PRumpOp: for a pcp group and a prime","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : 52,"comment" : "PRumpOp: generic method for group and prime","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedPRumps","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedPRumps: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedPRumps)"]]},{"rank" : 32,"comment" : "ComputedPRumps: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedPRumps: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedPRumps)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedPRumps): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedPRumps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedPRumps)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PRump","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "PRump: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasPRump","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "HasPRump: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPRump","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "SetPRump: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PCoreOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 387,"comment" : "PCoreOp: handled by nice monomorphism: subgroup CollOther","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsInt","IsPosRat"]]},{"rank" : 77,"comment" : "PCoreOp: for a permutation group, and a positive integer","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 52,"comment" : "PCoreOp: generic method for group and prime","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedPCores","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedPCores: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedPCores)"]]},{"rank" : 32,"comment" : "ComputedPCores: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedPCores: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedPCores)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedPCores): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedPCores): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedPCores)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PCore","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "PCore: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasPCore","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "HasPCore: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPCore","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "SetPCore: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubnormalSeriesOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "SubnormalSeriesOp: handled by nice monomorphism: GroupSeries CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 66,"comment" : "SubnormalSeriesOp: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubnormalSeriesInParent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SubnormalSeriesInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(SubnormalSeriesInParent)"]]},{"rank" : 33,"comment" : "SubnormalSeriesInParent: method that calls the two-argument operation SubnormalSeriesOp","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SubnormalSeriesInParent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SubnormalSeriesInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SubnormalSeriesInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SubnormalSeriesInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SubnormalSeriesInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubnormalSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "SubnormalSeries: try to exploit the in-parent attribute SubnormalSeriesInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SylowSubgroupOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 414,"comment" : "SylowSubgroupOp: Direct construction for natural GL","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNaturalGL","Tester(IsNaturalGL)"],["IsInt","IsPosRat"]]},{"rank" : 387,"comment" : "SylowSubgroupOp: handled by nice monomorphism: subgroup CollOther","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsInt","IsPosRat"]]},{"rank" : 169,"comment" : "SylowSubgroupOp: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsInt","IsPosRat"]]},{"rank" : 81,"comment" : "SylowSubgroupOp: symmetric","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsInt","IsPosRat"]]},{"rank" : 81,"comment" : "SylowSubgroupOp: alternating","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["IsInt","IsPosRat"]]},{"rank" : 77,"comment" : "SylowSubgroupOp: permutation groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 67,"comment" : "SylowSubgroupOp","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : 58,"comment" : "SylowSubgroupOp: method for a nilpotent group, and a prime","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNilpotentGroup","Tester(IsNilpotentGroup)"],["IsInt","IsPosRat"]]},{"rank" : 52,"comment" : "SylowSubgroupOp: generic method for group and prime","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "SylowSubgroupOp:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedSylowSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedSylowSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedSylowSubgroups)"]]},{"rank" : 32,"comment" : "ComputedSylowSubgroups: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedSylowSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedSylowSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedSylowSubgroups): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedSylowSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedSylowSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SylowSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "SylowSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasSylowSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "HasSylowSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetSylowSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "SetSylowSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SylowComplementOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10063,"comment" : "SylowComplementOp: test trivial case","filters" : [["IsFinite","Tester(IsFinite)","Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 149,"comment" : "SylowComplementOp: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsInt","IsPosRat"]]},{"rank" : 65,"comment" : "SylowComplementOp: via IsomoprhismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsInt","IsPosRat"]]},{"rank" : 1,"comment" : "SylowComplementOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 1,"comment" : "SylowComplementOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "SylowComplementOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedSylowComplements","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedSylowComplements: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedSylowComplements)"]]},{"rank" : 32,"comment" : "ComputedSylowComplements: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedSylowComplements: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedSylowComplements)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedSylowComplements): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedSylowComplements): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedSylowComplements)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SylowComplement","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "SylowComplement: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasSylowComplement","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "HasSylowComplement: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetSylowComplement","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "SetSylowComplement: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HallSubgroupOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10046,"comment" : "HallSubgroupOp: test trivial cases","filters" : [["IsFinite","Tester(IsFinite)","Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : 370,"comment" : "HallSubgroupOp: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsList"]]},{"rank" : 52,"comment" : "HallSubgroupOp: pcgs computable groups using special pcgs","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsList"]]},{"rank" : 48,"comment" : "HallSubgroupOp: via IsomoprhismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsList"]]},{"rank" : 45,"comment" : "HallSubgroupOp: fitting free","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanComputeFittingFree"],["IsList"]]},{"rank" : 1,"comment" : "HallSubgroupOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : 1,"comment" : "HallSubgroupOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : 0,"comment" : "HallSubgroupOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedHallSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedHallSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedHallSubgroups)"]]},{"rank" : 32,"comment" : "ComputedHallSubgroups: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedHallSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedHallSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedHallSubgroups): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedHallSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedHallSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HallSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "HallSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasHallSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "HasHallSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetHallSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 34,"comment" : "SetHallSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrConjugacyClassesInSupergroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 736,"comment" : "NrConjugacyClassesInSupergroup: handled by nice monomorphism: attribute CollColl","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 66,"comment" : "NrConjugacyClassesInSupergroup: generic method for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Factorization","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "Factorization: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GrowthFunctionOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "GrowthFunctionOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(GrowthFunctionOfGroup)"]]},{"rank" : 43,"comment" : "GrowthFunctionOfGroup: finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GrowthFunctionOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 53,"comment" : "GrowthFunctionOfGroup: groups and orders","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GrowthFunctionOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GrowthFunctionOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GrowthFunctionOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GrowthFunctionOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]],[["IsCollection"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "GroupByGenerators: delegate to `GroupWithGenerators'","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 22,"comment" : "GroupByGenerators: delegate to `GroupWithGenerators'","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 7,"comment" : "GroupByGenerators: delegate to `GroupWithGenerators'","filters" : [["IsCollection"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupWithGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]],[["IsCollection"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 25,"comment" : "GroupWithGenerators: method for pc elements collection","filters" : [["IsCollection","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 19,"comment" : "GroupWithGenerators: list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]]},{"rank" : 4,"comment" : "GroupWithGenerators: for a homogeneous list (of class functions)","filters" : [["IsHomogeneousList"]]},{"rank" : 2,"comment" : "GroupWithGenerators: generic method for collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 48,"comment" : "GroupWithGenerators: for empty list and trivial character","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsClassFunction"]]},{"rank" : 47,"comment" : "GroupWithGenerators: list of matrices with identity","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"],["IsMultiplicativeElementWithInverse","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 35,"comment" : "GroupWithGenerators: for list (of class functions) and class function","filters" : [["IsHomogeneousList"],["IsClassFunction"]]},{"rank" : 35,"comment" : "GroupWithGenerators: method for empty pc collection and identity element","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsMultiplicativeElementWithInverseByPolycyclicCollector"]]},{"rank" : 23,"comment" : "GroupWithGenerators: method for pc collection and identity element","filters" : [["IsCollection","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMultiplicativeElementWithInverseByPolycyclicCollector"]]},{"rank" : 22,"comment" : "GroupWithGenerators: method for empty list and element","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 7,"comment" : "GroupWithGenerators: generic method for collection and identity element","filters" : [["IsCollection"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementTestFunction","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ElementTestFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(ElementTestFunction)"]]},{"rank" : 0,"comment" : "ElementTestFunction: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ElementTestFunction)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ElementTestFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ElementTestFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ElementTestFunction)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightTransversalOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 202,"comment" : "RightTransversalOp: for trivial subgroup, call `EnumeratorSorted' for the big group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsTrivial","Tester(IsTrivial)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 116,"comment" : "RightTransversalOp: for two perm. groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 79,"comment" : "RightTransversalOp: pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 72,"comment" : "RightTransversalOp: pc groups","filters" : [["Tester(Pcgs)","CanEasilyComputePcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 70,"comment" : "RightTransversalOp: via coset table","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 66,"comment" : "RightTransversalOp: generic, use RightCosets","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightTransversalInParent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "RightTransversalInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(RightTransversalInParent)"]]},{"rank" : 33,"comment" : "RightTransversalInParent: method that calls the two-argument operation RightTransversalOp","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RightTransversalInParent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RightTransversalInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RightTransversalInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RightTransversalInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RightTransversalInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightTransversal","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "RightTransversal: try to exploit the in-parent attribute RightTransversalInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntermediateSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 70,"comment" : "IntermediateSubgroups: fp group via quotient subgroups","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 67,"comment" : "IntermediateSubgroups: normal case","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "IntermediateSubgroups: blocks for coset operation","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismTypeInfoFiniteSimpleGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsInt","IsPosRat"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsomorphismTypeInfoFiniteSimpleGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismTypeInfoFiniteSimpleGroup)"]]},{"rank" : 33,"comment" : "IsomorphismTypeInfoFiniteSimpleGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsomorphismTypeInfoFiniteSimpleGroup: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]},{"rank" : 19,"comment" : "IsomorphismTypeInfoFiniteSimpleGroup","filters" : [["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "IsomorphismTypeInfoFiniteSimpleGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismTypeInfoFiniteSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsInt","IsPosRat"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismTypeInfoFiniteSimpleGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismTypeInfoFiniteSimpleGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismTypeInfoFiniteSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismPcGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsomorphismPcGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismPcGroup)"]]},{"rank" : 377,"comment" : "IsomorphismPcGroup: via niceomorphisms","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 55,"comment" : "IsomorphismPcGroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 48,"comment" : "IsomorphismPcGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 46,"comment" : "IsomorphismPcGroup: for finitely presented groups that know their size","filters" : [["IsFinite","Tester(IsFinite)","Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSubgroupFpGroup"]]},{"rank" : 46,"comment" : "IsomorphismPcGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 42,"comment" : "IsomorphismPcGroup: via permutation representation","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismPcGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismPcGroup:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismPcGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismPcGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismPcGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismSpecialPcGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsomorphismSpecialPcGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismSpecialPcGroup)"]]},{"rank" : 43,"comment" : "IsomorphismSpecialPcGroup: method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 33,"comment" : "IsomorphismSpecialPcGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismSpecialPcGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismSpecialPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismSpecialPcGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismSpecialPcGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismSpecialPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismPermGroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]],[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismPermGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismPermGroup)"]]},{"rank" : 389,"comment" : "IsomorphismPermGroup: imf matrix groups","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsImfMatrixGroup"]]},{"rank" : 134,"comment" : "IsomorphismPermGroup: perfect library groups","filters" : [["IsPerfectLibraryGroup"]]},{"rank" : 78,"comment" : "IsomorphismPermGroup: for full finitely presented groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 77,"comment" : "IsomorphismPermGroup: for subgroups of finitely presented groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSubgroupFpGroup"]]},{"rank" : 56,"comment" : "IsomorphismPermGroup: cyclotomic matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 55,"comment" : "IsomorphismPermGroup: perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 55,"comment" : "IsomorphismPermGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CanEasilyComputeWithIndependentGensAbelianGroup"]]},{"rank" : 54,"comment" : "IsomorphismPermGroup: for finite nilpotent groups","filters" : [["IsFinite","Tester(IsFinite)","KnowsHowToDecompose","Tester(KnowsHowToDecompose)","IsNilpotentGroup","Tester(IsNilpotentGroup)"]]},{"rank" : 53,"comment" : "IsomorphismPermGroup: matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 49,"comment" : "IsomorphismPermGroup: via niceomorphisms","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 42,"comment" : "IsomorphismPermGroup: right regular operation","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 8,"comment" : "IsomorphismPermGroup: for a group H-class of a semigroup","filters" : [["IsGreensHClass"]]},{"rank" : 2,"comment" : "IsomorphismPermGroup: for family of fp words","filters" : [["CategoryFamily(IsElementOfFpGroup)"]]},{"rank" : 0,"comment" : "IsomorphismPermGroup:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismPermGroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismPermGroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]],[["IsGreensHClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismPermGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismPermGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismPermGroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsomorphismFpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismFpGroup)"]]},{"rank" : 134,"comment" : "IsomorphismFpGroup: perfect library groups","filters" : [["IsPerfectLibraryGroup"]]},{"rank" : 72,"comment" : "IsomorphismFpGroup: alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 62,"comment" : "IsomorphismFpGroup: symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 51,"comment" : "IsomorphismFpGroup: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 48,"comment" : "IsomorphismFpGroup: for PointGroup","filters" : [["IsPointGroup","Tester(IsPointGroup)"]]},{"rank" : 48,"comment" : "IsomorphismFpGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 38,"comment" : "IsomorphismFpGroup: for automorphism groups of free groups","filters" : [["IsAutomorphismGroupOfFreeGroup"]]},{"rank" : 33,"comment" : "IsomorphismFpGroup: supply name","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismFpGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 373,"comment" : "IsomorphismFpGroup: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsString"]]},{"rank" : 77,"comment" : "IsomorphismFpGroup: alternating group,name","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["IsString"]]},{"rank" : 70,"comment" : "IsomorphismFpGroup: for simple solvable permutation groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSimpleGroup","Tester(IsSimpleGroup)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsString"]]},{"rank" : 67,"comment" : "IsomorphismFpGroup: symmetric group,name","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsString"]]},{"rank" : 65,"comment" : "IsomorphismFpGroup: for simple permutation groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSimpleGroup","Tester(IsSimpleGroup)"],["IsString"]]},{"rank" : 63,"comment" : "IsomorphismFpGroup: for perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]},{"rank" : 43,"comment" : "IsomorphismFpGroup: pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsString"]]},{"rank" : 40,"comment" : "IsomorphismFpGroup: subgroups of fp group","filters" : [["IsSubgroupFpGroup"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismFpGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismFpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismFpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismFpGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpGroupByGeneratorsNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 375,"comment" : "IsomorphismFpGroupByGeneratorsNC: via niceomorphism\/w. gens","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsList"],["IsString"]]},{"rank" : 65,"comment" : "IsomorphismFpGroupByGeneratorsNC: for perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsString"]]},{"rank" : 59,"comment" : "IsomorphismFpGroupByGeneratorsNC: pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPcgs"],["IsString"]]},{"rank" : 52,"comment" : "IsomorphismFpGroupByGeneratorsNC: subgroups of fp group","filters" : [["IsSubgroupFpGroup"],["IsList","CategoryCollections(IsMultiplicativeElementWithInverse)"],["IsString"]]},{"rank" : 40,"comment" : "IsomorphismFpGroupByGeneratorsNC: via cokernel","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpGroupBySubnormalSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 60,"comment" : "IsomorphismFpGroupBySubnormalSeries: for groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [{"rank" : 65,"comment" : "IsomorphismFpGroupBySubnormalSeries: for groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpGroupByCompositionSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "IsomorphismFpGroupByCompositionSeries: supply name","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 63,"comment" : "IsomorphismFpGroupByCompositionSeries: for permutation groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]},{"rank" : 43,"comment" : "IsomorphismFpGroupByCompositionSeries: pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpGroupByChiefSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "IsomorphismFpGroupByChiefSeries: supply name","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 63,"comment" : "IsomorphismFpGroupByChiefSeries: permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimePowerComponents","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "PrimePowerComponents: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimePowerComponents)"]]},{"rank" : 4,"comment" : "PrimePowerComponents: method for a pc element","filters" : [["IsMultiplicativeElementWithOne"]]},{"rank" : 3,"comment" : "PrimePowerComponents: generic method","filters" : [["IsMultiplicativeElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimePowerComponents)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimePowerComponents): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimePowerComponents): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimePowerComponents)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimePowerComponent","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "PrimePowerComponent: generic method","filters" : [["IsMultiplicativeElement"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PowerMapOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 390,"comment" : "PowerMapOfGroup: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 77,"comment" : "PowerMapOfGroup: method for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 65,"comment" : "PowerMapOfGroup: method for a matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsHomogeneousList"]]},{"rank" : 55,"comment" : "PowerMapOfGroup: method for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInverseSubsemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "IsInverseSubsemigroup: for a semigroup and a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsMagma","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGeneratorsOfInverseSemigroup","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsGeneratorsOfInverseSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGeneratorsOfInverseSemigroup)"]]},{"rank" : 13,"comment" : "IsGeneratorsOfInverseSemigroup: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 13,"comment" : "IsGeneratorsOfInverseSemigroup: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGeneratorsOfInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGeneratorsOfInverseSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGeneratorsOfInverseSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGeneratorsOfInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfInverseMonoid","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "GeneratorsOfInverseMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfInverseMonoid)"]]},{"rank" : 34,"comment" : "GeneratorsOfInverseMonoid: for an inverse partial perm monoid with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 34,"comment" : "GeneratorsOfInverseMonoid: for a group with known generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GeneratorsOfInverseMonoid: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfInverseMonoid)","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfInverseMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfInverseMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfInverseMonoid)","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfInverseSemigroup","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "GeneratorsOfInverseSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfInverseSemigroup)"]]},{"rank" : 34,"comment" : "GeneratorsOfInverseSemigroup: for a group with known generators","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 30,"comment" : "GeneratorsOfInverseSemigroup: for an inverse partial perm semigroup with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 0,"comment" : "GeneratorsOfInverseSemigroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfInverseSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfInverseSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseMonoidByGenerators","type" : "GAP_Operation","filters" : [[["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10,"comment" : "InverseMonoidByGenerators","filters" : [["CategoryCollections(IsAssociativeElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseSemigroupByGenerators","type" : "GAP_Operation","filters" : [[["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10,"comment" : "InverseSemigroupByGenerators: for associative element with unique semigroup inverse collection","filters" : [["CategoryCollections(IsAssociativeElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseSubsemigroup","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"],["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "InverseSubsemigroup: for an inverse semigroup and element collection","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)"],["CategoryCollections(IsAssociativeElement)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseSubsemigroupNC","type" : "GAP_Operation","filters" : [[["IsInverseSemigroup","Tester(IsInverseSemigroup)"],["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "InverseSubsemigroupNC: for an inverse semigroup and element collection","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)"],["CategoryCollections(IsAssociativeElement)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseSubmonoid","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"],["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "InverseSubmonoid: for an inverse monoid and element collection","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"],["CategoryCollections(IsAssociativeElement)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseSubmonoidNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"],["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "InverseSubmonoidNC: for an inverse monoid and element collection","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"],["CategoryCollections(IsAssociativeElement)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsInverseSemigroup","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "AsInverseSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AsInverseSemigroup)"]]},{"rank" : 119,"comment" : "AsInverseSemigroup: for an inverse semigroup","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsInverseSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsInverseSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsInverseSemigroup)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsInverseMonoid","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "AsInverseMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(AsInverseMonoid)"]]},{"rank" : 124,"comment" : "AsInverseMonoid: for an inverse monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 124,"comment" : "AsInverseMonoid: for an inverse monoid","filters" : [["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 20,"comment" : "AsInverseMonoid: for an inverse semigroup with known generators","filters" : [["IsInverseSemigroup","Tester(IsInverseSemigroup)","Tester(GeneratorsOfInverseSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsInverseMonoid)","type" : "GAP_Operation","filters" : [[["IsCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsInverseMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsInverseMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsInverseMonoid)","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsInverseSubsemigroup","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsInverseSubmonoid","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReverseNaturalPartialOrder","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "ReverseNaturalPartialOrder: system getter","filters" : [["IsAttributeStoringRep","Tester(ReverseNaturalPartialOrder)"]]},{"rank" : 29,"comment" : "ReverseNaturalPartialOrder: for an inverse partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 0,"comment" : "ReverseNaturalPartialOrder: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ReverseNaturalPartialOrder)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ReverseNaturalPartialOrder): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ReverseNaturalPartialOrder): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ReverseNaturalPartialOrder)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalPartialOrder","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "NaturalPartialOrder: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalPartialOrder)"]]},{"rank" : 29,"comment" : "NaturalPartialOrder: for an inverse partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 0,"comment" : "NaturalPartialOrder: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalPartialOrder)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalPartialOrder): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalPartialOrder): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalPartialOrder)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAdditivelyCommutative","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "IsAdditivelyCommutative: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAdditivelyCommutative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAdditivelyCommutative)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAdditivelyCommutative): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAdditivelyCommutative): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAdditivelyCommutative)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NearAdditiveMagmaByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "NearAdditiveMagmaByGenerators: for collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 3,"comment" : "NearAdditiveMagmaByGenerators: for family and list","filters" : [["IsFamily"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NearAdditiveMagmaWithZeroByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "NearAdditiveMagmaWithZeroByGenerators: for collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 3,"comment" : "NearAdditiveMagmaWithZeroByGenerators: for family and list","filters" : [["IsFamily"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NearAdditiveGroupByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "NearAdditiveGroupByGenerators: for collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 3,"comment" : "NearAdditiveGroupByGenerators: for family and list","filters" : [["IsFamily"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfNearAdditiveMagma","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "GeneratorsOfNearAdditiveMagma: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfNearAdditiveMagma)"]]},{"rank" : 17,"comment" : "GeneratorsOfNearAdditiveMagma","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveGroup)"]]},{"rank" : 15,"comment" : "GeneratorsOfNearAdditiveMagma","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfNearAdditiveMagma)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfNearAdditiveMagma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfNearAdditiveMagma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfNearAdditiveMagma)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfNearAdditiveMagmaWithZero","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagmaWithZero"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "GeneratorsOfNearAdditiveMagmaWithZero: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]]},{"rank" : 17,"comment" : "GeneratorsOfNearAdditiveMagmaWithZero","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveGroup)"]]},{"rank" : 17,"comment" : "GeneratorsOfNearAdditiveMagmaWithZero","filters" : [["IsAttributeStoringRep","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagma)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfNearAdditiveMagmaWithZero)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagmaWithZero"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfNearAdditiveMagmaWithZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfNearAdditiveMagmaWithZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfNearAdditiveMagmaWithZero)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagmaWithZero"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfNearAdditiveGroup","type" : "GAP_Operation","filters" : [[["IsNearAdditiveGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GeneratorsOfNearAdditiveGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfNearAdditiveGroup)"]]},{"rank" : 19,"comment" : "GeneratorsOfNearAdditiveGroup","filters" : [["IsAttributeStoringRep","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfNearAdditiveGroup)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfNearAdditiveGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfNearAdditiveGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfNearAdditiveGroup)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TrivialSubnearAdditiveMagmaWithZero","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagmaWithZero"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "TrivialSubnearAdditiveMagmaWithZero: system getter","filters" : [["IsAttributeStoringRep","Tester(TrivialSubnearAdditiveMagmaWithZero)"]]},{"rank" : 34,"comment" : "TrivialSubnearAdditiveMagmaWithZero: for a FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 22,"comment" : "TrivialSubnearAdditiveMagmaWithZero: generic method for left modules","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 14,"comment" : "TrivialSubnearAdditiveMagmaWithZero: for add.-magma-with-zero","filters" : [["IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TrivialSubnearAdditiveMagmaWithZero)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagmaWithZero"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TrivialSubnearAdditiveMagmaWithZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TrivialSubnearAdditiveMagmaWithZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TrivialSubnearAdditiveMagmaWithZero)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagmaWithZero"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditiveNeutralElement","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "AdditiveNeutralElement: system getter","filters" : [["IsAttributeStoringRep","Tester(AdditiveNeutralElement)"]]},{"rank" : 12,"comment" : "AdditiveNeutralElement","filters" : [["IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdditiveNeutralElement)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdditiveNeutralElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdditiveNeutralElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdditiveNeutralElement)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClosureNearAdditiveGroup","type" : "GAP_Operation","filters" : [[["IsNearAdditiveGroup"],["IsNearAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "ClosureNearAdditiveGroup: for two add. groups","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 19,"comment" : "ClosureNearAdditiveGroup: for add. group and element","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsAdditiveElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdditiveCoset","type" : "GAP_Operation","filters" : [[["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 19,"comment" : "AdditiveCoset: for additive group and additive element","filters" : [["IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsAdditiveElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLDistributive","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsLDistributive: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLDistributive)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLDistributive)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLDistributive): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLDistributive): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLDistributive)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRDistributive","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsRDistributive: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRDistributive)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRDistributive)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRDistributive): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRDistributive): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRDistributive)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfSemiring","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20027,"comment" : "GeneratorsOfSemiring: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfSemiring)"]]},{"rank" : -5,"comment" : "GeneratorsOfSemiring: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfSemiring)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfSemiring): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfSemiring): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfSemiring)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfSemiringWithOne","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "GeneratorsOfSemiringWithOne: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfSemiringWithOne)"]]},{"rank" : -5,"comment" : "GeneratorsOfSemiringWithOne: default method requiring categories and checking properties","filters" : [["IsMagmaWithOne","IsNearAdditiveMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfSemiringWithOne)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfSemiringWithOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfSemiringWithOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfSemiringWithOne)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfSemiringWithZero","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20028,"comment" : "GeneratorsOfSemiringWithZero: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfSemiringWithZero)"]]},{"rank" : -14,"comment" : "GeneratorsOfSemiringWithZero: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfSemiringWithZero)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfSemiringWithZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfSemiringWithZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfSemiringWithZero)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfSemiringWithOneAndZero","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20030,"comment" : "GeneratorsOfSemiringWithOneAndZero: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfSemiringWithOneAndZero)"]]},{"rank" : -14,"comment" : "GeneratorsOfSemiringWithOneAndZero: default method requiring categories and checking properties","filters" : [["IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfSemiringWithOneAndZero)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfSemiringWithOneAndZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfSemiringWithOneAndZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfSemiringWithOneAndZero)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSemiring","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AsSemiring: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSemiring)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSemiring)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSemiring): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSemiring): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSemiring)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSemiringWithOne","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AsSemiringWithOne: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSemiringWithOne)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSemiringWithOne)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSemiringWithOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSemiringWithOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSemiringWithOne)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSemiringWithZero","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AsSemiringWithZero: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSemiringWithZero)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSemiringWithZero)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSemiringWithZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSemiringWithZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSemiringWithZero)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSemiringWithOneAndZero","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AsSemiringWithOneAndZero: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSemiringWithOneAndZero)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSemiringWithOneAndZero)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSemiringWithOneAndZero): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSemiringWithOneAndZero): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSemiringWithOneAndZero)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClosureSemiring","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiringByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiringWithOneByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiringWithZeroByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiringWithOneAndZeroByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralIdempotentsOfSemiring","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20027,"comment" : "CentralIdempotentsOfSemiring: system getter","filters" : [["IsAttributeStoringRep","Tester(CentralIdempotentsOfSemiring)"]]},{"rank" : 36,"comment" : "CentralIdempotentsOfSemiring: for an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -5,"comment" : "CentralIdempotentsOfSemiring: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CentralIdempotentsOfSemiring)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CentralIdempotentsOfSemiring): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CentralIdempotentsOfSemiring): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CentralIdempotentsOfSemiring)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsNearRing","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "AsNearRing: system getter","filters" : [["IsAttributeStoringRep","Tester(AsNearRing)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsNearRing)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsMultiplicativeElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsNearRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsNearRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsNearRing)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsRing","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AsRing: system getter","filters" : [["IsAttributeStoringRep","Tester(AsRing)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsRing)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsRing)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "GeneratorsOfRing: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfRing)"]]},{"rank" : 36,"comment" : "GeneratorsOfRing: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 30,"comment" : "GeneratorsOfRing: for a ring-with-one with generators","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRingWithOne)"]]},{"rank" : 29,"comment" : "GeneratorsOfRing","filters" : [["IsAttributeStoringRep","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(GeneratorsOfNearAdditiveGroup)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 29,"comment" : "GeneratorsOfRing","filters" : [["IsAttributeStoringRep","IsMagma","Tester(GeneratorsOfMagma)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 27,"comment" : "GeneratorsOfRing: generic method for a two-sided ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)"]]},{"rank" : 27,"comment" : "GeneratorsOfRing: generic method for a right ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)"]]},{"rank" : 27,"comment" : "GeneratorsOfRing: generic method for a left ideal with known generators","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)"]]},{"rank" : 26,"comment" : "GeneratorsOfRing: for a ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "GeneratorsOfRing: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfRingWithOne","type" : "GAP_Operation","filters" : [[["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20031,"comment" : "GeneratorsOfRingWithOne: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfRingWithOne)"]]},{"rank" : 39,"comment" : "GeneratorsOfRingWithOne: for a free magma ring-with-one","filters" : [["IsMagmaWithOne","IsFreeMagmaRing"]]},{"rank" : 32,"comment" : "GeneratorsOfRingWithOne","filters" : [["IsAttributeStoringRep","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]},{"rank" : 32,"comment" : "GeneratorsOfRingWithOne","filters" : [["IsAttributeStoringRep","IsMagma","IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -25,"comment" : "GeneratorsOfRingWithOne: default method requiring categories and checking properties","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfRingWithOne)","type" : "GAP_Operation","filters" : [[["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfRingWithOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfRingWithOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfRingWithOne)","type" : "GAP_Operation","filters" : [[["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RingByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10022,"comment" : "RingByGenerators: method that catches the cases of `Integers' and subrings of `Integers'","filters" : [["CategoryCollections(IsCyclotomic)"]]},{"rank" : 29,"comment" : "RingByGenerators: for a list of Lie matrices over a finite field","filters" : [["CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))","CategoryCollections(IsLieObject)"]]},{"rank" : 22,"comment" : "RingByGenerators: for a collection of FFE","filters" : [["CategoryCollections(IsFFE)"]]},{"rank" : 19,"comment" : "RingByGenerators: for a list of matrices over the Cyclotomics","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"]]},{"rank" : 19,"comment" : "RingByGenerators: for a list of matrices over a finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]]},{"rank" : 13,"comment" : "RingByGenerators: for a list of linear mappings of finite vector spaces","filters" : [["CategoryCollections(IsGeneralMapping)"]]},{"rank" : 2,"comment" : "RingByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefaultRingByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10022,"comment" : "DefaultRingByGenerators: method that catches the cases of `(Gaussian)Integers' and cycl. fields","filters" : [["CategoryCollections(IsCyclotomic)"]]},{"rank" : 29,"comment" : "DefaultRingByGenerators: for a collection of FFE","filters" : [["IsList","CategoryCollections(IsFFE)"]]},{"rank" : 29,"comment" : "DefaultRingByGenerators: for a list of Lie matrices","filters" : [["CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))","CategoryCollections(IsLieObject)"]]},{"rank" : 21,"comment" : "DefaultRingByGenerators: for a collection over a ring Z\/nZ","filters" : [["CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 21,"comment" : "DefaultRingByGenerators: for lists of n x n integer matrices","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"]]},{"rank" : 19,"comment" : "DefaultRingByGenerators: for a list of matrices over the Cyclotomics","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"]]},{"rank" : 19,"comment" : "DefaultRingByGenerators: for a list of matrices over a finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]]},{"rank" : 18,"comment" : "DefaultRingByGenerators","filters" : [["CategoryCollections(IsRationalFunction)"]]},{"rank" : 13,"comment" : "DefaultRingByGenerators: for a list of linear mappings of vector spaces","filters" : [["CategoryCollections(IsGeneralMapping)"]]},{"rank" : 2,"comment" : "DefaultRingByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RingWithOneByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10022,"comment" : "RingWithOneByGenerators: method that catches the cases of `Integers'","filters" : [["CategoryCollections(IsCyclotomic)"]]},{"rank" : 22,"comment" : "RingWithOneByGenerators: for a collection of FFE","filters" : [["CategoryCollections(IsFFE)"]]},{"rank" : 19,"comment" : "RingWithOneByGenerators: for a list of matrices over the Cyclotomics","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"]]},{"rank" : 19,"comment" : "RingWithOneByGenerators: for a list of matrices over a finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]]},{"rank" : 13,"comment" : "RingWithOneByGenerators: for a list of linear mappings of finite vector spaces","filters" : [["CategoryCollections(IsGeneralMapping)"]]},{"rank" : 2,"comment" : "RingWithOneByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClosureRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10036,"comment" : "ClosureRing: for a ring containing the whole family, and a ring element","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 10030,"comment" : "ClosureRing: for a ring cont. the whole family, and a collection","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]},{"rank" : 58,"comment" : "ClosureRing: for two rings-with-one","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 52,"comment" : "ClosureRing: for two rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 37,"comment" : "ClosureRing: for a ring-with-one and a ring element","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 34,"comment" : "ClosureRing: for a ring and a ring element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 28,"comment" : "ClosureRing: for ring and collection of elements","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAnticommutative","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsAnticommutative: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAnticommutative)"]]},{"rank" : 34,"comment" : "IsAnticommutative: generic method for a (finite dimensional) FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 29,"comment" : "IsAnticommutative","filters" : [["Tester(Characteristic)","IsMagma","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 26,"comment" : "IsAnticommutative: generic method for rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "IsAnticommutative: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAnticommutative)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAnticommutative): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAnticommutative): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAnticommutative)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIntegralRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsIntegralRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIntegralRing)"]]},{"rank" : 40,"comment" : "IsIntegralRing","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 26,"comment" : "IsIntegralRing: for a ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "IsIntegralRing: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIntegralRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIntegralRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIntegralRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIntegralRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsJacobianRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsJacobianRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsJacobianRing)"]]},{"rank" : 34,"comment" : "IsJacobianRing: for a (finite dimensional) FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : -14,"comment" : "IsJacobianRing: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsJacobianRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsJacobianRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsJacobianRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsJacobianRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZeroSquaredRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsZeroSquaredRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZeroSquaredRing)"]]},{"rank" : 34,"comment" : "IsZeroSquaredRing: for a finite dimensional FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 29,"comment" : "IsZeroSquaredRing","filters" : [["Tester(Characteristic)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsAnticommutative","Tester(IsAnticommutative)"]]},{"rank" : 26,"comment" : "IsZeroSquaredRing: for a ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "IsZeroSquaredRing: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZeroSquaredRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZeroSquaredRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZeroSquaredRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZeroSquaredRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZeroMultiplicationRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsZeroMultiplicationRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZeroMultiplicationRing)"]]},{"rank" : 30,"comment" : "IsZeroMultiplicationRing","filters" : [["Tester(IsTrivial)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "IsZeroMultiplicationRing: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZeroMultiplicationRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZeroMultiplicationRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZeroMultiplicationRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZeroMultiplicationRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Units","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "Units: system getter","filters" : [["IsAttributeStoringRep","Tester(Units)"]]},{"rank" : 73,"comment" : "Units: for a full matrix algebra (over a finite field)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 56,"comment" : "Units: for a finite field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 50,"comment" : "Units: for a division ring","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 44,"comment" : "Units: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 42,"comment" : "Units: for full ring Z\/nZ","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : 33,"comment" : "Units: zmodnze : for full ring Z\/nZ(m)","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZepsObj)"]]},{"rank" : 26,"comment" : "Units: for a (finite) ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "Units: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Units)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Units): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Units): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Units)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Factors","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "Factors","filters" : [["IsInt"]]},{"rank" : 8,"comment" : "Factors: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "Factors:  fallback method to test conditions","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]}],"2args" : [{"rank" : 59,"comment" : "Factors: for integers (FactInt)","filters" : [["IsIntegers"],["IsInt"]]},{"rank" : 58,"comment" : "Factors: for Gaussian integers","filters" : [["IsGaussianIntegers"],["IsCyc"]]},{"rank" : 58,"comment" : "Factors: for a division ring and a ring element","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 57,"comment" : "Factors: for integers","filters" : [["IsIntegers"],["IsInt"]]},{"rank" : 50,"comment" : "Factors: for Z_(pi) and an element thereof (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsRat"]]},{"rank" : 48,"comment" : "Factors: univariate rational polynomial","filters" : [["IsRationalsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 47,"comment" : "Factors: for a polynomial over a field of cyclotomics","filters" : [["IsAbelianNumberFieldPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 47,"comment" : "Factors: alg ext polynomial","filters" : [["IsAlgebraicExtensionPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 47,"comment" : "Factors: polynomial over a finite field","filters" : [["IsFiniteFieldPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 41,"comment" : "Factors: multivariate, reduce to univariate case","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 40,"comment" : "Factors: fallback error message","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "Factors:  fallback method to test conditions","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsPolynomial","Tester(IsPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAssociated","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "IsAssociated: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [{"rank" : 66,"comment" : "IsAssociated: for a division ring, and two ring elements","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 42,"comment" : "IsAssociated: for ring and two ring elements","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Associates","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "Associates: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 34,"comment" : "Associates: for a ring and a ring element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUnit","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 13,"comment" : "IsUnit: LAGUNA: for an element of modular group algebra","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]},{"rank" : 13,"comment" : "IsUnit: zmodnze : for element in Z\/nZ(m) (ZModnZepsRep) without given ring","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 11,"comment" : "IsUnit: for a Lie object (return `false')","filters" : [["IsLieObject"]]},{"rank" : 8,"comment" : "IsUnit: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 74,"comment" : "IsUnit: for matrix FLMLOR and matrix","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 58,"comment" : "IsUnit: for element in Z\/nZ (ModulusRep)","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"],["IsZmodnZObj","IsModulusRep"]]},{"rank" : 58,"comment" : "IsUnit: for a division ring, and a ring element","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 57,"comment" : "IsUnit: LAGUNA: for an element of modular group algebra","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]},{"rank" : 50,"comment" : "IsUnit: for Z_(pi) and an element thereof (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsRat"]]},{"rank" : 46,"comment" : "IsUnit: zmodnze : for element in Z\/nZ(m) (ZModnZepsRep) with given ring","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZepsObj)"],["IsZmodnZepsObj","IsZmodnZepsRep"]]},{"rank" : 36,"comment" : "IsUnit: for finite Rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 35,"comment" : "IsUnit: for a ring with known units and a ring element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(Units)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 34,"comment" : "IsUnit: for a ring and a ring element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InterpolatedPolynomial","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 26,"comment" : "InterpolatedPolynomial","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Quotient","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "Quotient: laurent","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 28,"comment" : "Quotient: multivar","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 16,"comment" : "Quotient: for two ring elements (delegate to three argument version","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "Quotient:  fallback method to test conditions","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"3args" : [{"rank" : 75,"comment" : "Quotient: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"]]},{"rank" : 74,"comment" : "Quotient: for Gaussian integers","filters" : [["IsGaussianIntegers"],["IsCyc"],["IsCyc"]]},{"rank" : 66,"comment" : "Quotient: for a division ring, and two ring elements","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 61,"comment" : "Quotient: laurent, ring","filters" : [["IsPolynomialRing"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 55,"comment" : "Quotient: multivar with ring","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 42,"comment" : "Quotient: for a ring and two ring elements","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StandardAssociate","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "StandardAssociate: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 10036,"comment" : "StandardAssociate: for a ring and its zero element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement","IsZero","Tester(IsZero)"]]},{"rank" : 88,"comment" : "StandardAssociate: HNF of n x n integer matrix (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFullMatrixModule","Tester(IsFullMatrixModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 60,"comment" : "StandardAssociate: for a division ring and a ring element","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 57,"comment" : "StandardAssociate: for integers","filters" : [["IsIntegers"],["IsInt"]]},{"rank" : 50,"comment" : "StandardAssociate: for Z_(pi) and an element thereof (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsRat"]]},{"rank" : 34,"comment" : "StandardAssociate: for a ring and a ring element (using StandardAssociateUnit)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StandardAssociateUnit","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "StandardAssociateUnit: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 10036,"comment" : "StandardAssociateUnit: for a ring and its zero element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement","IsZero","Tester(IsZero)"]]},{"rank" : 60,"comment" : "StandardAssociateUnit: for a division ring and a ring element","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 58,"comment" : "StandardAssociateUnit: for Gaussian integers","filters" : [["IsGaussianIntegers"],["IsCyc"]]},{"rank" : 57,"comment" : "StandardAssociateUnit: for integers","filters" : [["IsIntegers"],["IsInt"]]},{"rank" : 44,"comment" : "StandardAssociateUnit: laurent","filters" : [["IsPolynomialRing"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 41,"comment" : "StandardAssociateUnit: for a polynomial ring and a polynomial","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrime","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "IsPrime: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 60,"comment" : "IsPrime: for Gaussian integers and integer","filters" : [["IsGaussianIntegers"],["IsInt"]]},{"rank" : 60,"comment" : "IsPrime: for a division ring and a ring element","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 58,"comment" : "IsPrime: for Gaussian integers and cyclotomic","filters" : [["IsGaussianIntegers"],["IsCyc"]]},{"rank" : 57,"comment" : "IsPrime: for integers","filters" : [["IsIntegers"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIrreducibleRingElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "IsIrreducibleRingElement: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 60,"comment" : "IsIrreducibleRingElement: for a division ring and a ring element","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 57,"comment" : "IsIrreducibleRingElement: for integers","filters" : [["IsIntegers"],["IsInt"]]},{"rank" : 50,"comment" : "IsIrreducibleRingElement: for Z_(pi) and an element thereof (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsRat"]]},{"rank" : 47,"comment" : "IsIrreducibleRingElement: AlgPol","filters" : [["IsAlgebraicExtensionPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 41,"comment" : "IsIrreducibleRingElement: polynomial","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "IsIrreducibleRingElement:  fallback method to test conditions","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsPolynomial","Tester(IsPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EuclideanDegree","type" : "GAP_Operation","filters" : [[["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "EuclideanDegree: univariate","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 17,"comment" : "EuclideanDegree: laurent","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 8,"comment" : "EuclideanDegree: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 58,"comment" : "EuclideanDegree: for Gaussian integers","filters" : [["IsGaussianIntegers"],["IsCyc"]]},{"rank" : 58,"comment" : "EuclideanDegree: for a division ring and a ring element","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 57,"comment" : "EuclideanDegree: for integers","filters" : [["IsIntegers"],["IsInt"]]},{"rank" : 46,"comment" : "EuclideanDegree: univariate,ring","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 44,"comment" : "EuclideanDegree: laurent,ring","filters" : [["IsPolynomialRing"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EuclideanRemainder","type" : "GAP_Operation","filters" : [[["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "EuclideanRemainder: laurent","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 16,"comment" : "EuclideanRemainder: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "EuclideanRemainder:  fallback method to test conditions","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"3args" : [{"rank" : 75,"comment" : "EuclideanRemainder: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"]]},{"rank" : 74,"comment" : "EuclideanRemainder: for Gaussian integers","filters" : [["IsGaussianIntegers"],["IsCyc"],["IsCyc"]]},{"rank" : 65,"comment" : "EuclideanRemainder: laurent,ring","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 47,"comment" : "EuclideanRemainder: for a Euclidean ring and two ring elements","filters" : [["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "EuclideanRemainder:  fallback method to test conditions","filters" : [["IsPolynomialRing"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EuclideanQuotient","type" : "GAP_Operation","filters" : [[["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "EuclideanQuotient: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [{"rank" : 75,"comment" : "EuclideanQuotient: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"]]},{"rank" : 74,"comment" : "EuclideanQuotient: for Gaussian integers","filters" : [["IsGaussianIntegers"],["IsCyc"],["IsCyc"]]},{"rank" : 47,"comment" : "EuclideanQuotient: for a Euclidean ring and two ring elements","filters" : [["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuotientRemainder","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "QuotientRemainder: laurent","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 16,"comment" : "QuotientRemainder: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "QuotientRemainder:  fallback method to test conditions","filters" : [["IsRationalFunction"],["IsRationalFunction"]]}],"3args" : [{"rank" : 75,"comment" : "QuotientRemainder: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"]]},{"rank" : 74,"comment" : "QuotientRemainder: for Gaussian integers","filters" : [["IsGaussianIntegers"],["IsCyc"],["IsCyc"]]},{"rank" : 66,"comment" : "QuotientRemainder: for a division ring, and two ring elements","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 65,"comment" : "QuotientRemainder: laurent, ring","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "QuotientRemainder:  fallback method to test conditions","filters" : [["IsPolynomialRing"],["IsRationalFunction"],["IsRationalFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuotientMod","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 57,"comment" : "QuotientMod: laurent","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 24,"comment" : "QuotientMod: for three ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "QuotientMod:  fallback method to test conditions","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"4args" : [{"rank" : 93,"comment" : "QuotientMod: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"],["IsInt"]]},{"rank" : 83,"comment" : "QuotientMod: laurent,ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 55,"comment" : "QuotientMod: for a Euclidean ring and three ring elements","filters" : [["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "QuotientMod:  fallback method to test conditions","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"5args" : [],"6args" : []}},{"name" : "PowerMod","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsInt"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 56,"comment" : "PowerMod: laurent","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsInt"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 34,"comment" : "PowerMod: for ring element, integer, and ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsInt"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "PowerMod:  fallback method to test conditions","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsInt"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"4args" : [{"rank" : 93,"comment" : "PowerMod: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"],["IsInt"]]},{"rank" : 83,"comment" : "PowerMod: laurent,ring ","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsInt"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 65,"comment" : "PowerMod: for Euclidean ring, ring element, integer, and ring element","filters" : [["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsInt"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "PowerMod:  fallback method to test conditions","filters" : [["IsPolynomialRing"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsInt"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"5args" : [],"6args" : []}},{"name" : "GcdOp","type" : "GAP_Operation","filters" : [[["IsUniqueFactorizationRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "GcdOp: univariate polynomials","filters" : [["IsRationalFunction","IsPolynomial","Tester(IsPolynomial)"],["IsRationalFunction","IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 16,"comment" : "GcdOp: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "GcdOp:  fallback method to test conditions","filters" : [["IsRationalFunction"],["IsRationalFunction"]]}],"3args" : [{"rank" : 75,"comment" : "GcdOp: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"]]},{"rank" : 72,"comment" : "GcdOp: rational univariate polynomials","filters" : [["IsEuclideanRing","IsRationalsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 67,"comment" : "GcdOp: for Z_(pi) and two elements thereof (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsRat"],["IsRat"]]},{"rank" : 59,"comment" : "GcdOp: univariate polynomials, ring","filters" : [["IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 57,"comment" : "GcdOp: Gcd(Polyring, Pol,Pol)","filters" : [["IsEuclideanRing"],["IsRationalFunction"],["IsRationalFunction"]]},{"rank" : 55,"comment" : "GcdOp: multivariate Gcd based on Groebner bases","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 47,"comment" : "GcdOp: for a Euclidean ring and two ring elements","filters" : [["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "GcdOp:  fallback method to test conditions","filters" : [["IsEuclideanRing"],["IsRationalFunction"],["IsRationalFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GcdRepresentationOp","type" : "GAP_Operation","filters" : [[["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "GcdRepresentationOp: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [{"rank" : 47,"comment" : "GcdRepresentationOp: for a Euclidean ring and two ring elements","filters" : [["IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LcmOp","type" : "GAP_Operation","filters" : [[["IsUniqueFactorizationRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "LcmOp: for two ring elements","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [{"rank" : 118,"comment" : "LcmOp: lattice intersection in Z^n (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFullMatrixModule","Tester(IsFullMatrixModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 75,"comment" : "LcmOp: for integers","filters" : [["IsIntegers"],["IsInt"],["IsInt"]]},{"rank" : 67,"comment" : "LcmOp: for Z_(pi) and two elements thereof (ResClasses)","filters" : [["IsZ_pi","Tester(IsZ_pi)"],["IsRat"],["IsRat"]]},{"rank" : 55,"comment" : "LcmOp: multivariate Lcm based on Groebner bases","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 43,"comment" : "LcmOp: for a Euclidean ring and two ring elements","filters" : [["IsUniqueFactorizationRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PadicValuation","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "PadicValuation: for rationals","filters" : [["IsRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGeneralizedCartanMatrix","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "IsGeneralizedCartanMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGeneralizedCartanMatrix)"]]},{"rank" : 30,"comment" : "IsGeneralizedCartanMatrix: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGeneralizedCartanMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGeneralizedCartanMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGeneralizedCartanMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGeneralizedCartanMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsDiagonalMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "IsDiagonalMat: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 15,"comment" : "IsDiagonalMat: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 3,"comment" : "IsDiagonalMat","filters" : [["IsEmpty","Tester(IsEmpty)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUpperTriangularMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "IsUpperTriangularMat: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 15,"comment" : "IsUpperTriangularMat: for a plist matrix","filters" : [["IsPlistMatrixRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLowerTriangularMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "IsLowerTriangularMat: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 15,"comment" : "IsLowerTriangularMat: for a plist matrix","filters" : [["IsPlistMatrixRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "BaseMat: system getter","filters" : [["IsAttributeStoringRep","Tester(BaseMat)"]]},{"rank" : 30,"comment" : "BaseMat: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BaseMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BaseMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BaseMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BaseMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseMatDestructive","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "BaseMatDestructive: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseOrthogonalSpaceMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "BaseOrthogonalSpaceMat: system getter","filters" : [["IsAttributeStoringRep","Tester(BaseOrthogonalSpaceMat)"]]},{"rank" : 30,"comment" : "BaseOrthogonalSpaceMat: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BaseOrthogonalSpaceMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BaseOrthogonalSpaceMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BaseOrthogonalSpaceMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BaseOrthogonalSpaceMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefaultFieldOfMatrix","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "DefaultFieldOfMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(DefaultFieldOfMatrix)"]]},{"rank" : 55,"comment" : "DefaultFieldOfMatrix: method for a compressed matrix over GF(q)","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 55,"comment" : "DefaultFieldOfMatrix: method for a matrix over GF(2)","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsGF2MatrixRep"]]},{"rank" : 42,"comment" : "DefaultFieldOfMatrix: method for a matrix over the cyclotomics","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]},{"rank" : 42,"comment" : "DefaultFieldOfMatrix: method for a matrix over a finite field","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 30,"comment" : "DefaultFieldOfMatrix: default method for a matrix (return `fail')","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DefaultFieldOfMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DefaultFieldOfMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DefaultFieldOfMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DefaultFieldOfMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DepthOfUpperTriangularMatrix","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "DepthOfUpperTriangularMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(DepthOfUpperTriangularMatrix)"]]},{"rank" : 30,"comment" : "DepthOfUpperTriangularMatrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DepthOfUpperTriangularMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DepthOfUpperTriangularMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DepthOfUpperTriangularMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DepthOfUpperTriangularMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeterminantMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "DeterminantMat: system getter","filters" : [["IsAttributeStoringRep","Tester(DeterminantMat)"]]},{"rank" : 30,"comment" : "DeterminantMat: for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DeterminantMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DeterminantMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DeterminantMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DeterminantMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeterminantMatDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 66,"comment" : "DeterminantMatDestructive: kernel method for plain list of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 56,"comment" : "DeterminantMatDestructive: kernel method for plain list of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 47,"comment" : "DeterminantMatDestructive: non fraction free","filters" : [["IsMutable","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 46,"comment" : "DeterminantMatDestructive: nonprime residue rings","filters" : [["IsMutable","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]]},{"rank" : 34,"comment" : "DeterminantMatDestructive: fraction-free method","filters" : [["IsMutable","IsOrdinaryMatrix"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeterminantMatDivFree","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "DeterminantMatDivFree: Division-free method","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DimensionsMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "DimensionsMat: system getter","filters" : [["IsAttributeStoringRep","Tester(DimensionsMat)"]]},{"rank" : 134,"comment" : "DimensionsMat: for a matrix with memory","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsObjWithMemory"]]},{"rank" : 34,"comment" : "DimensionsMat: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 30,"comment" : "DimensionsMat","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 15,"comment" : "DimensionsMat: for a plist matrix","filters" : [["IsPlistMatrixRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DimensionsMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]],[["IsMatrixObj"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DimensionsMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DimensionsMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DimensionsMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementaryDivisorsMat","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "ElementaryDivisorsMat: compatibility method -- supply ring","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [{"rank" : 60,"comment" : "ElementaryDivisorsMat: generic method for euclidean rings","filters" : [["IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementaryDivisorsTransformationsMat","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "ElementaryDivisorsTransformationsMat: compatibility method -- supply ring","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [{"rank" : 71,"comment" : "ElementaryDivisorsTransformationsMat: over the integers","filters" : [["IsIntegers"],["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 60,"comment" : "ElementaryDivisorsTransformationsMat: generic method for euclidean rings","filters" : [["IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizedNullspaceMatNT","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 32,"comment" : "TriangulizedNullspaceMatNT: generic method","filters" : [["IsOrdinaryMatrix"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NullspaceMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "NullspaceMat: system getter","filters" : [["IsAttributeStoringRep","Tester(NullspaceMat)"]]},{"rank" : 32,"comment" : "NullspaceMat: generic method for ordinary matrices","filters" : [["IsOrdinaryMatrix"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NullspaceMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NullspaceMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NullspaceMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NullspaceMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizedNullspaceMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "TriangulizedNullspaceMat: system getter","filters" : [["IsAttributeStoringRep","Tester(TriangulizedNullspaceMat)"]]},{"rank" : 32,"comment" : "TriangulizedNullspaceMat: generic method for ordinary matrices","filters" : [["IsOrdinaryMatrix"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TriangulizedNullspaceMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TriangulizedNullspaceMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TriangulizedNullspaceMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TriangulizedNullspaceMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NullspaceMatDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 34,"comment" : "NullspaceMatDestructive: generic method for ordinary matrices","filters" : [["IsMutable","IsOrdinaryMatrix"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizedNullspaceMatDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 34,"comment" : "TriangulizedNullspaceMatDestructive: generic method for ordinary matrices","filters" : [["IsMutable","IsOrdinaryMatrix"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneralisedEigenvalues","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 81,"comment" : "GeneralisedEigenvalues: for a matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneralisedEigenspaces","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 81,"comment" : "GeneralisedEigenspaces: for a matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Eigenvalues","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 81,"comment" : "Eigenvalues: for a matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 50,"comment" : "Eigenvalues","filters" : [["IsClassFunction"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Eigenspaces","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 81,"comment" : "Eigenspaces: for a matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Eigenvectors","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 81,"comment" : "Eigenvectors: for a matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectiveOrder","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "ProjectiveOrder: system getter","filters" : [["IsAttributeStoringRep","Tester(ProjectiveOrder)"]]},{"rank" : 107,"comment" : "ProjectiveOrder: object with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 45,"comment" : "ProjectiveOrder: ordinary matrix of finite field elements","filters" : [["IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 19,"comment" : "ProjectiveOrder: divide and conquer for univariate polynomials","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "ProjectiveOrder:  fallback method to test conditions","filters" : [["IsRationalFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ProjectiveOrder)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ProjectiveOrder): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ProjectiveOrder): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ProjectiveOrder)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "RankMat: system getter","filters" : [["IsAttributeStoringRep","Tester(RankMat)"]]},{"rank" : 30,"comment" : "RankMat: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 15,"comment" : "RankMat: for a plist matrix","filters" : [["IsPlistMatrixRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RankMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]],[["IsMatrixObj"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RankMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RankMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RankMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankMatDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 66,"comment" : "RankMatDestructive: kernel method for plain list of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 56,"comment" : "RankMatDestructive: kernel method for plain list of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 32,"comment" : "RankMatDestructive: generic method for mutable matrices","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "SemiEchelonMat: system getter","filters" : [["IsAttributeStoringRep","Tester(SemiEchelonMat)"]]},{"rank" : 55,"comment" : "SemiEchelonMat: shortcut method for 8bit matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 55,"comment" : "SemiEchelonMat: shortcut method for GF2 matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsGF2MatrixRep"]]},{"rank" : 30,"comment" : "SemiEchelonMat: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemiEchelonMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemiEchelonMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemiEchelonMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemiEchelonMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonMatDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 66,"comment" : "SemiEchelonMatDestructive: kernel method for plain lists of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 56,"comment" : "SemiEchelonMatDestructive: kernel method for plain lists of 8bit vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 32,"comment" : "SemiEchelonMatDestructive: generic method for matrices","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonMatTransformation","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "SemiEchelonMatTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(SemiEchelonMatTransformation)"]]},{"rank" : 55,"comment" : "SemiEchelonMatTransformation: shortcut method for 8bit matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 55,"comment" : "SemiEchelonMatTransformation: kernel method for plain lists of GF2 vectors","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsGF2MatrixRep"]]},{"rank" : 30,"comment" : "SemiEchelonMatTransformation: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemiEchelonMatTransformation)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemiEchelonMatTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemiEchelonMatTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemiEchelonMatTransformation)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonMatTransformationDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 66,"comment" : "SemiEchelonMatTransformationDestructive: kernel method for plain lists of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 56,"comment" : "SemiEchelonMatTransformationDestructive:  kernel method for plain lists of 8 bit vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 32,"comment" : "SemiEchelonMatTransformationDestructive: generic method for matrices","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonMats","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "SemiEchelonMats: for list of matrices","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonMatsDestructive","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "SemiEchelonMatsDestructive: for list of matrices","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransposedMatImmutable","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "TransposedMatImmutable: system getter","filters" : [["IsAttributeStoringRep","Tester(TransposedMatImmutable)"]]},{"rank" : 55,"comment" : "TransposedMatImmutable: for a compressed 8 bit matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 44,"comment" : "TransposedMatImmutable: GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"]]},{"rank" : 34,"comment" : "TransposedMatImmutable: for an ordinary block matrix","filters" : [["IsOrdinaryMatrix","IsBlockMatrixRep"]]},{"rank" : 15,"comment" : "TransposedMatImmutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 2,"comment" : "TransposedMatImmutable: generic method for matrices and lists","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransposedMatImmutable)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]],[["IsMatrixObj"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransposedMatImmutable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransposedMatImmutable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransposedMatImmutable)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransposedMatMutable","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 55,"comment" : "TransposedMatMutable: for a compressed 8 bit matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 44,"comment" : "TransposedMatMutable: GF2 matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"]]},{"rank" : 32,"comment" : "TransposedMatMutable: generic method","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsRectangularTable","Tester(IsRectangularTable)"]]},{"rank" : 15,"comment" : "TransposedMatMutable: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 2,"comment" : "TransposedMatMutable: for arbitrary lists of lists","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MutableTransposedMatDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 32,"comment" : "MutableTransposedMatDestructive: generic method","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransposedMatDestructive","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "TransposedMatDestructive: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 2,"comment" : "TransposedMatDestructive: method for empty matrices","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonomialMatrix","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "IsMonomialMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMonomialMatrix)"]]},{"rank" : 30,"comment" : "IsMonomialMatrix: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMonomialMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMonomialMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMonomialMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMonomialMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseMatMod","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 49,"comment" : "InverseMatMod: method for a matrix, and an integer","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]},{"rank" : 48,"comment" : "InverseMatMod: generic method for matrix and integer","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KroneckerProduct","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsMatrixObj"],["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 89,"comment" : "KroneckerProduct: for two 8bit matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 88,"comment" : "KroneckerProduct: for two 8bit matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","Is8BitMatrixRep"]]},{"rank" : 88,"comment" : "KroneckerProduct: for two gf2 matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGF2MatrixRep"]]},{"rank" : 60,"comment" : "KroneckerProduct: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 24,"comment" : "KroneckerProduct: for two matrices","filters" : [["IsMatrixObj"],["IsMatrixObj"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SolutionMatNoCo","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SolutionMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "SolutionMat: generic method for ordinary matrix and vector","filters" : [["IsOrdinaryMatrix"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SolutionMatDestructive","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 48,"comment" : "SolutionMatDestructive: generic method","filters" : [["IsMutable","IsOrdinaryMatrix"],["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SumIntersectionMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 60,"comment" : "SumIntersectionMat","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 33,"comment" : "SumIntersectionMat","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 33,"comment" : "SumIntersectionMat","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 6,"comment" : "SumIntersectionMat","filters" : [["IsEmpty","Tester(IsEmpty)"],["IsEmpty","Tester(IsEmpty)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizedMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "TriangulizedMat: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizeMat","type" : "GAP_Operation","filters" : [[["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 66,"comment" : "TriangulizeMat: kernel method for plain list of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 56,"comment" : "TriangulizeMat: method for compressed matrices","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","Is8BitMatrixRep"]]},{"rank" : 56,"comment" : "TriangulizeMat: kernel method for plain list of GF2 vectors","filters" : [["IsMutable","IsTable","IsPlistRep","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 56,"comment" : "TriangulizeMat: for GF2 matrices","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsGF2MatrixRep"]]},{"rank" : 46,"comment" : "TriangulizeMat: for a mutable ordinary matrix over a ring Z\/nZ","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsOrdinaryMatrix","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]]},{"rank" : 32,"comment" : "TriangulizeMat: generic method for mutable matrices","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 17,"comment" : "TriangulizeMat: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UpperSubdiagonal","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 49,"comment" : "UpperSubdiagonal","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DiagonalizeMat","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "DiagonalizeMat: over the integers","filters" : [["IsIntegers"],["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 62,"comment" : "DiagonalizeMat: method for general Euclidean Ring","filters" : [["IsEuclideanRing"],["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MutableCopyMat","type" : "GAP_Operation","filters" : [[["IsList"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "MutableCopyMat: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "MutableCopyMat: for an 8bit matrix","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "MutableCopyMat: for a gf2 matrix","filters" : [["IsGF2MatrixRep"]]},{"rank" : 2,"comment" : "MutableCopyMat: generic method","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TraceMat","type" : "GAP_Operation","filters" : [[["IsList"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 12,"comment" : "TraceMat: generic method","filters" : [["IsMatrixObj"]]},{"rank" : 2,"comment" : "TraceMat: method for lists","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "JordanDecomposition","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "JordanDecomposition: system getter","filters" : [["IsAttributeStoringRep","Tester(JordanDecomposition)"]]},{"rank" : 30,"comment" : "JordanDecomposition: method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(JordanDecomposition)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(JordanDecomposition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(JordanDecomposition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(JordanDecomposition)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacteristicPolynomial","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]],[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]],[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "CharacteristicPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(CharacteristicPolynomial)"]]},{"rank" : 30,"comment" : "CharacteristicPolynomial: supply field and indeterminate 1","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [{"rank" : 82,"comment" : "CharacteristicPolynomial: supply indeterminate 1","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 49,"comment" : "CharacteristicPolynomial: supply field","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 132,"comment" : "CharacteristicPolynomial: supply indeterminate 1","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 114,"comment" : "CharacteristicPolynomial: call `TracePolynomial'","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 103,"comment" : "CharacteristicPolynomial: check default field, print error if ambiguous","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsOrdinaryMatrix"],["IsInt","IsPosRat"]]}],"4args" : [{"rank" : 153,"comment" : "CharacteristicPolynomial: spinning over field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsOrdinaryMatrix"],["IsInt","IsPosRat"]]},{"rank" : 133,"comment" : "CharacteristicPolynomial: call `TracePolynomial'","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "Setter(CharacteristicPolynomial)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CharacteristicPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CharacteristicPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CharacteristicPolynomial)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacteristicPolynomialMatrixNC","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsOrdinaryMatrix"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 102,"comment" : "CharacteristicPolynomialMatrixNC: spinning over field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsOrdinaryMatrix"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalPolynomialMatrixNC","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsOrdinaryMatrix"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 102,"comment" : "MinimalPolynomialMatrixNC: spinning over field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsOrdinaryMatrix"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FieldOfMatrixList","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "FieldOfMatrixList: finite field matrices","filters" : [["IsListOrCollection","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]]},{"rank" : 1,"comment" : "FieldOfMatrixList: generic: form field","filters" : [["IsListOrCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefaultScalarDomainOfMatrixList","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "DefaultScalarDomainOfMatrixList: finite field matrices","filters" : [["IsListOrCollection","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]]},{"rank" : 1,"comment" : "DefaultScalarDomainOfMatrixList: generic: form ring","filters" : [["IsListOrCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseField","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "BaseField: for a compressed 8bit matrix","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "BaseField: for a compressed gf2 matrix","filters" : [["IsGF2MatrixRep"]]},{"rank" : 11,"comment" : "BaseField: for a compressed 8bit vector","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "BaseField: for a compressed gf2 vector","filters" : [["IsGF2VectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizedIntegerMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "TriangulizedIntegerMat: dispatch","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "TriangulizedIntegerMat: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "TriangulizedIntegerMat: empty matrix","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizeIntegerMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 32,"comment" : "TriangulizeIntegerMat: dispatch","filters" : [["IsMutable","IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "TriangulizeIntegerMat: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TriangulizedIntegerMatTransform","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "TriangulizedIntegerMatTransform: dispatch","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "TriangulizedIntegerMatTransform: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "TriangulizedIntegerMatTransform: empty matrix","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HermiteNormalFormIntegerMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "HermiteNormalFormIntegerMat: dispatch","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "HermiteNormalFormIntegerMat: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "HermiteNormalFormIntegerMat: empty matrix","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HermiteNormalFormIntegerMatTransform","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "HermiteNormalFormIntegerMatTransform: dispatch","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "HermiteNormalFormIntegerMatTransform: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "HermiteNormalFormIntegerMatTransform: empty matrix","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SmithNormalFormIntegerMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "SmithNormalFormIntegerMat: dispatch","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "SmithNormalFormIntegerMat: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "SmithNormalFormIntegerMat: empty matrix","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SmithNormalFormIntegerMatTransforms","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "SmithNormalFormIntegerMatTransforms: dispatch","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 3,"comment" : "SmithNormalFormIntegerMatTransforms: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 2,"comment" : "SmithNormalFormIntegerMatTransforms: empty matrix","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseIntMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "BaseIntMat: system getter","filters" : [["IsAttributeStoringRep","Tester(BaseIntMat)"]]},{"rank" : 42,"comment" : "BaseIntMat: use HNF","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]},{"rank" : 3,"comment" : "BaseIntMat: empty","filters" : [["IsEmpty","Tester(IsEmpty)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BaseIntMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BaseIntMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BaseIntMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BaseIntMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseIntersectionIntMats","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 84,"comment" : "BaseIntersectionIntMats: use HNF","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]},{"rank" : 3,"comment" : "BaseIntersectionIntMats: emptyR","filters" : [[],["IsEmpty","Tester(IsEmpty)"]]},{"rank" : 3,"comment" : "BaseIntersectionIntMats: emptyL","filters" : [["IsEmpty","Tester(IsEmpty)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComplementIntMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 84,"comment" : "ComplementIntMat: use HNF and SNF","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]},{"rank" : 59,"comment" : "ComplementIntMat: empty submodule","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsList","IsEmpty","Tester(IsEmpty)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NullspaceIntMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "NullspaceIntMat: system getter","filters" : [["IsAttributeStoringRep","Tester(NullspaceIntMat)"]]},{"rank" : 42,"comment" : "NullspaceIntMat: use HNF","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NullspaceIntMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NullspaceIntMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NullspaceIntMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NullspaceIntMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SolutionIntMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsList","CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "SolutionIntMat: use HNF","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 3,"comment" : "SolutionIntMat: empty","filters" : [["IsEmpty","Tester(IsEmpty)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SolutionNullspaceIntMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsList","CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "SolutionNullspaceIntMat: use HNF","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"],["IsList","CategoryCollections(IsCyclotomic)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbelianInvariantsOfList","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "AbelianInvariantsOfList: system getter","filters" : [["IsAttributeStoringRep","Tester(AbelianInvariantsOfList)"]]},{"rank" : 22,"comment" : "AbelianInvariantsOfList","filters" : [["CategoryCollections(IsCyclotomic)"]]},{"rank" : 17,"comment" : "AbelianInvariantsOfList","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AbelianInvariantsOfList)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsCyclotomic)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AbelianInvariantsOfList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AbelianInvariantsOfList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AbelianInvariantsOfList)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MatrixByBlockMatrix","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "MatrixByBlockMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(MatrixByBlockMatrix)"]]},{"rank" : 30,"comment" : "MatrixByBlockMatrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MatrixByBlockMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MatrixByBlockMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MatrixByBlockMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MatrixByBlockMatrix)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTwoSidedIdealOp","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 59,"comment" : "IsTwoSidedIdealOp: for anti-commutative FLMLOR and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsAnticommutative","Tester(IsAnticommutative)","IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 59,"comment" : "IsTwoSidedIdealOp: for commutative FLMLOR and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 57,"comment" : "IsTwoSidedIdealOp: for FLMLOR and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 52,"comment" : "IsTwoSidedIdealOp: for rings and subrings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTwoSidedIdealInParent","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsTwoSidedIdealInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTwoSidedIdealInParent)"]]},{"rank" : 29,"comment" : "IsTwoSidedIdealInParent","filters" : [["Tester(ParentAttr)","IsRightIdealInParent","Tester(IsRightIdealInParent)"]]},{"rank" : 29,"comment" : "IsTwoSidedIdealInParent","filters" : [["Tester(ParentAttr)","IsLeftIdealInParent","Tester(IsLeftIdealInParent)"]]},{"rank" : 27,"comment" : "IsTwoSidedIdealInParent: method that calls the two-argument operation IsTwoSidedIdealOp","filters" : [["Tester(ParentAttr)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "IsTwoSidedIdealInParent: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTwoSidedIdealInParent)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTwoSidedIdealInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTwoSidedIdealInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTwoSidedIdealInParent)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTwoSidedIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "IsTwoSidedIdeal: try to exploit the in-parent attribute IsTwoSidedIdealInParent","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftIdealOp","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 70,"comment" : "IsLeftIdealOp: for associative FLMLOR and FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 64,"comment" : "IsLeftIdealOp: for associative FLMLOR-with-one and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 59,"comment" : "IsLeftIdealOp: for associative FLMLOR and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 58,"comment" : "IsLeftIdealOp: for SCRings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]},{"rank" : 57,"comment" : "IsLeftIdealOp: for FLMLOR and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftIdealInParent","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsLeftIdealInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLeftIdealInParent)"]]},{"rank" : 27,"comment" : "IsLeftIdealInParent: method that calls the two-argument operation IsLeftIdealOp","filters" : [["Tester(ParentAttr)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "IsLeftIdealInParent: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLeftIdealInParent)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLeftIdealInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLeftIdealInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLeftIdealInParent)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 79,"comment" : "IsLeftIdeal: left ideal in ring, naive","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)"]]},{"rank" : 52,"comment" : "IsLeftIdeal: try to exploit the in-parent attribute IsLeftIdealInParent","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRightIdealOp","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 70,"comment" : "IsRightIdealOp: for associative FLMLOR and FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 64,"comment" : "IsRightIdealOp: for associative FLMLOR-with-one and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 59,"comment" : "IsRightIdealOp: for associative FLMLOR and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]},{"rank" : 58,"comment" : "IsRightIdealOp: for SCRings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]},{"rank" : 57,"comment" : "IsRightIdealOp: for FLMLOR and free left module","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRightIdealInParent","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "IsRightIdealInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRightIdealInParent)"]]},{"rank" : 27,"comment" : "IsRightIdealInParent: method that calls the two-argument operation IsRightIdealOp","filters" : [["Tester(ParentAttr)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "IsRightIdealInParent: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRightIdealInParent)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRightIdealInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRightIdealInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRightIdealInParent)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRightIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "IsRightIdeal: try to exploit the in-parent attribute IsRightIdealInParent","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TwoSidedIdealByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 65,"comment" : "TwoSidedIdealByGenerators: for Lie algebra and collection of Lie objects","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList","CategoryCollections(IsLieObject)"]]},{"rank" : 61,"comment" : "TwoSidedIdealByGenerators: for matrix algebra and empty list","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 59,"comment" : "TwoSidedIdealByGenerators: for Lie algebra and empty list","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 54,"comment" : "TwoSidedIdealByGenerators: for Gaussian matrix algebra and list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"],["IsList","IsCollection"]]},{"rank" : 53,"comment" : "TwoSidedIdealByGenerators: for non-Gaussian matrix algebra and list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsNonGaussianMatrixSpace"],["IsList","IsCollection"]]},{"rank" : 51,"comment" : "TwoSidedIdealByGenerators: for FLMLOR and empty list","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 36,"comment" : "TwoSidedIdealByGenerators: for FLMLOR and collection","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsCollection"]]},{"rank" : 28,"comment" : "TwoSidedIdealByGenerators: for ring and collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftIdealByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 65,"comment" : "LeftIdealByGenerators: for Lie algebra and collection of Lie objects","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList","CategoryCollections(IsLieObject)"]]},{"rank" : 61,"comment" : "LeftIdealByGenerators: for matrix algebra and empty list","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 59,"comment" : "LeftIdealByGenerators: for Lie algebra and empty list","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 54,"comment" : "LeftIdealByGenerators: for Gaussian matrix algebra and list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"],["IsList","IsCollection"]]},{"rank" : 53,"comment" : "LeftIdealByGenerators: for non-Gaussian matrix algebra and list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsNonGaussianMatrixSpace"],["IsList","IsCollection"]]},{"rank" : 51,"comment" : "LeftIdealByGenerators: for FLMLOR and empty list","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 38,"comment" : "LeftIdealByGenerators: to construct ideals of commutative rings","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsCollection"]]},{"rank" : 36,"comment" : "LeftIdealByGenerators: for FLMLOR and collection","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsCollection"]]},{"rank" : 28,"comment" : "LeftIdealByGenerators: for ring and collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightIdealByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 65,"comment" : "RightIdealByGenerators: for Lie algebra and collection of Lie objects","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList","CategoryCollections(IsLieObject)"]]},{"rank" : 61,"comment" : "RightIdealByGenerators: for matrix algebra and empty list","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 59,"comment" : "RightIdealByGenerators: for Lie algebra and empty list","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 54,"comment" : "RightIdealByGenerators: for Gaussian matrix algebra and list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"],["IsList","IsCollection"]]},{"rank" : 53,"comment" : "RightIdealByGenerators: for non-Gaussian matrix algebra and list of matrices","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsNonGaussianMatrixSpace"],["IsList","IsCollection"]]},{"rank" : 51,"comment" : "RightIdealByGenerators: for FLMLOR and empty list","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 38,"comment" : "RightIdealByGenerators: to construct ideals of commutative rings","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsCollection"]]},{"rank" : 36,"comment" : "RightIdealByGenerators: for FLMLOR and collection","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsCollection"]]},{"rank" : 28,"comment" : "RightIdealByGenerators: for ring and collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfTwoSidedIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "GeneratorsOfTwoSidedIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfTwoSidedIdeal)"]]},{"rank" : 29,"comment" : "GeneratorsOfTwoSidedIdeal: for a two-sided ideal with known `GeneratorsOfRightIdeal'","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : 29,"comment" : "GeneratorsOfTwoSidedIdeal: for a two-sided ideal with known `GeneratorsOfLeftIdeal'","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : -14,"comment" : "GeneratorsOfTwoSidedIdeal: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfTwoSidedIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfTwoSidedIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfTwoSidedIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfTwoSidedIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfLeftIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "GeneratorsOfLeftIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfLeftIdeal)"]]},{"rank" : 29,"comment" : "GeneratorsOfLeftIdeal: for an ideal with known `GeneratorsOfTwoSidedIdeal'","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : -14,"comment" : "GeneratorsOfLeftIdeal: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfLeftIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfLeftIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfLeftIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfLeftIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfRightIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "GeneratorsOfRightIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfRightIdeal)"]]},{"rank" : 29,"comment" : "GeneratorsOfRightIdeal: for an ideal with known `GeneratorsOfTwoSidedIdeal'","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)"]]},{"rank" : -14,"comment" : "GeneratorsOfRightIdeal: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfRightIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfRightIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfRightIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfRightIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftActingRingOfIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "LeftActingRingOfIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(LeftActingRingOfIdeal)"]]},{"rank" : -14,"comment" : "LeftActingRingOfIdeal: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeftActingRingOfIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LeftActingRingOfIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeftActingRingOfIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeftActingRingOfIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightActingRingOfIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "RightActingRingOfIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(RightActingRingOfIdeal)"]]},{"rank" : -14,"comment" : "RightActingRingOfIdeal: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RightActingRingOfIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RightActingRingOfIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RightActingRingOfIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RightActingRingOfIdeal)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsLeftIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 68,"comment" : "AsLeftIdeal: for two FLMLORs","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 52,"comment" : "AsLeftIdeal: for two rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsRightIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "AsRightIdeal: for two FLMLORs","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 52,"comment" : "AsRightIdeal: for two rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsTwoSidedIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "AsTwoSidedIdeal: for two FLMLORs","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 52,"comment" : "AsTwoSidedIdeal: for two rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFiniteDimensional","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "IsFiniteDimensional: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFiniteDimensional)"]]},{"rank" : 43,"comment" : "IsFiniteDimensional: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 43,"comment" : "IsFiniteDimensional: for a f.p. Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsSubalgebraFpAlgebra"]]},{"rank" : 39,"comment" : "IsFiniteDimensional: for a left module of free magma ring elements","filters" : [["IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorRing)","CategoryCollections(IsElementOfFreeMagmaRing)"]]},{"rank" : 37,"comment" : "IsFiniteDimensional: for f.p. algebra","filters" : [["IsSubalgebraFpAlgebra"]]},{"rank" : 36,"comment" : "IsFiniteDimensional: for a magma ring modulo the span of ``zero''","filters" : [["IsMagmaRingModuloSpanOfZero"]]},{"rank" : 36,"comment" : "IsFiniteDimensional: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 35,"comment" : "IsFiniteDimensional: for an ideal in an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(RightActingRingOfIdeal)","IsFreeLeftModule"]]},{"rank" : 35,"comment" : "IsFiniteDimensional: for an ideal in an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","IsFreeLeftModule"]]},{"rank" : 28,"comment" : "IsFiniteDimensional: for a space of algebra module elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsAlgebraModuleElement)"]]},{"rank" : 24,"comment" : "IsFiniteDimensional: for a free left module with known dimension","filters" : [["IsFreeLeftModule","Tester(Dimension)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFiniteDimensional)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFiniteDimensional): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFiniteDimensional): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFiniteDimensional)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullRowModule","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "IsFullRowModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullRowModule)"]]},{"rank" : 30,"comment" : "IsFullRowModule: for Gaussian row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]},{"rank" : 29,"comment" : "IsFullRowModule: for non-Gaussian row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsNonGaussianRowSpace"]]},{"rank" : 23,"comment" : "IsFullRowModule: for free left (row) module","filters" : [["IsFreeLeftModule"]]},{"rank" : 22,"comment" : "IsFullRowModule: for arbitrary free left module","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullRowModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullRowModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullRowModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullRowModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullMatrixModule","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "IsFullMatrixModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullMatrixModule)"]]},{"rank" : 30,"comment" : "IsFullMatrixModule: for Gaussian matrix space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"]]},{"rank" : 29,"comment" : "IsFullMatrixModule: for non-Gaussian matrix space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsNonGaussianMatrixSpace"]]},{"rank" : 23,"comment" : "IsFullMatrixModule: for matrix module","filters" : [["IsFreeLeftModule"]]},{"rank" : 22,"comment" : "IsFullMatrixModule: for arbitrary free left module","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullMatrixModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullMatrixModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullMatrixModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullMatrixModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Dimension","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "Dimension: system getter","filters" : [["IsAttributeStoringRep","Tester(Dimension)"]]},{"rank" : 48,"comment" : "Dimension: for full matrix module","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "Dimension: for full row module","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 43,"comment" : "Dimension: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 43,"comment" : "Dimension: for a f.p. Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsSubalgebraFpAlgebra"]]},{"rank" : 36,"comment" : "Dimension: for a magma ring modulo the span of ``zero''","filters" : [["IsMagmaRingModuloSpanOfZero"]]},{"rank" : 36,"comment" : "Dimension: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 36,"comment" : "Dimension: for full hom space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 23,"comment" : "Dimension: for a free left module","filters" : [["IsFreeLeftModule"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Dimension)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Dimension): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Dimension): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Dimension)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfLeftOperatorAdditiveGroup","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20021,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 62,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for FLMLOR with known right ideal generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)","IsFreeLeftModule"]]},{"rank" : 62,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for FLMLOR with known left ideal generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)","IsFreeLeftModule"]]},{"rank" : 56,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for a finite field (return the vectors of the canonical basis)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 48,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for full matrix module","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for full row module","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 36,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for a magma ring modulo the span of ``zero''","filters" : [["IsMagmaRingModuloSpanOfZero"]]},{"rank" : 36,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 36,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for full hom space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 35,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for FLMLOR with known ideal generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)","IsFreeLeftModule"]]},{"rank" : 34,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for a FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 28,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: for a space of algebra module elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsAlgebraModuleElement)"]]},{"rank" : 26,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup","filters" : [["IsAttributeStoringRep","IsFreeLeftModule","Tester(Basis)"]]},{"rank" : -20,"comment" : "GeneratorsOfLeftOperatorAdditiveGroup: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfLeftOperatorAdditiveGroup)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 27,"comment" : "Setter(GeneratorsOfLeftOperatorAdditiveGroup): method that checks for `IsFiniteDimensional'","filters" : [["IsAttributeStoringRep","IsFreeLeftModule"],["IsList"]]},{"rank" : 2,"comment" : "Setter(GeneratorsOfLeftOperatorAdditiveGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfLeftOperatorAdditiveGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfLeftOperatorAdditiveGroup)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsDistributiveLOpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfRightOperatorAdditiveGroup","type" : "GAP_Operation","filters" : [[["IsExtRSet","IsDistributiveROpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20021,"comment" : "GeneratorsOfRightOperatorAdditiveGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfRightOperatorAdditiveGroup)"]]},{"rank" : -20,"comment" : "GeneratorsOfRightOperatorAdditiveGroup: default method requiring categories and checking properties","filters" : [["IsExtRSet","IsDistributiveROpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfRightOperatorAdditiveGroup)","type" : "GAP_Operation","filters" : [[["IsExtRSet","IsDistributiveROpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfRightOperatorAdditiveGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfRightOperatorAdditiveGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfRightOperatorAdditiveGroup)","type" : "GAP_Operation","filters" : [[["IsExtRSet","IsDistributiveROpDSum","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsLeftModule","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 100,"comment" : "AsLeftModule: for two division rings","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 80,"comment" : "AsLeftModule: for division ring and matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 75,"comment" : "AsLeftModule: method for a division ring and a vector space","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 48,"comment" : "AsLeftModule:  for a ring and a left module","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 28,"comment" : "AsLeftModule: generic method for a ring and a collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClosureLeftModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "ClosureLeftModule: for two left modules","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 33,"comment" : "ClosureLeftModule: method for a vector space with basis, and a vector","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","Tester(Basis)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 31,"comment" : "ClosureLeftModule: for free left module and vector","filters" : [["IsFreeLeftModule","Tester(Basis)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 29,"comment" : "ClosureLeftModule: for left module and vector","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftModuleByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]],[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsListOrCollection"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 80,"comment" : "LeftModuleByGenerators: for division ring and matrix over it","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 28,"comment" : "LeftModuleByGenerators: for ring and collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [{"rank" : 92,"comment" : "LeftModuleByGenerators: for division ring, matrix over it, and row vector","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 79,"comment" : "LeftModuleByGenerators: for division ring, empty list, and row vector","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 30,"comment" : "LeftModuleByGenerators: for ring, homogeneous list, and vector","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UseBasis","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 27,"comment" : "UseBasis: for a free left module and a homog. list","filters" : [["IsFreeLeftModule"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRowModule","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "IsRowModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRowModule)"]]},{"rank" : 23,"comment" : "IsRowModule: for a free left module","filters" : [["IsFreeLeftModule"]]},{"rank" : 0,"comment" : "IsRowModule: return `false' for objects which are not free left modules","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRowModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRowModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRowModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRowModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMatrixModule","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "IsMatrixModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMatrixModule)"]]},{"rank" : 24,"comment" : "IsMatrixModule: for a free left module","filters" : [["IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 23,"comment" : "IsMatrixModule: for a free left module without generators","filters" : [["IsFreeLeftModule"]]},{"rank" : 0,"comment" : "IsMatrixModule: return `false' for objects which are not free left modules","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMatrixModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMatrixModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMatrixModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMatrixModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DimensionOfVectors","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "DimensionOfVectors: system getter","filters" : [["IsAttributeStoringRep","Tester(DimensionOfVectors)"]]},{"rank" : 23,"comment" : "DimensionOfVectors: generic method for left modules","filters" : [["IsFreeLeftModule"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DimensionOfVectors)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DimensionOfVectors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DimensionOfVectors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DimensionOfVectors)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCanonicalBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsCanonicalBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCanonicalBasis)"]]},{"rank" : 13,"comment" : "IsCanonicalBasis: for a basis handled by a nice basis","filters" : [["IsBasisByNiceBasis"]]},{"rank" : 10,"comment" : "IsCanonicalBasis: for a basis with replaced left module, and a vector","filters" : [["IsBasis","IsBasisWithReplacedLeftModuleRep"]]},{"rank" : 7,"comment" : "IsCanonicalBasis: for a basis","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCanonicalBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCanonicalBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCanonicalBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCanonicalBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCanonicalBasisFullRowModule","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsCanonicalBasisFullRowModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCanonicalBasisFullRowModule)"]]},{"rank" : 7,"comment" : "IsCanonicalBasisFullRowModule: for a basis","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCanonicalBasisFullRowModule)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCanonicalBasisFullRowModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCanonicalBasisFullRowModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCanonicalBasisFullRowModule)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCanonicalBasisFullMatrixModule","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsCanonicalBasisFullMatrixModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCanonicalBasisFullMatrixModule)"]]},{"rank" : 7,"comment" : "IsCanonicalBasisFullMatrixModule: for a basis","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCanonicalBasisFullMatrixModule)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCanonicalBasisFullMatrixModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCanonicalBasisFullMatrixModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCanonicalBasisFullMatrixModule)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIntegralBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsIntegralBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIntegralBasis)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIntegralBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIntegralBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIntegralBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIntegralBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormalBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsNormalBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNormalBasis)"]]},{"rank" : 7,"comment" : "IsNormalBasis: for a basis of a field","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNormalBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNormalBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNormalBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNormalBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSemiEchelonized","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsSemiEchelonized: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSemiEchelonized)"]]},{"rank" : 7,"comment" : "IsSemiEchelonized: for basis (of a Gaussian matrix space)","filters" : [["IsBasis"]]},{"rank" : 7,"comment" : "IsSemiEchelonized: for basis of a Gaussian row space","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSemiEchelonized)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSemiEchelonized): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSemiEchelonized): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSemiEchelonized)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BasisVectors","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "BasisVectors: system getter","filters" : [["IsAttributeStoringRep","Tester(BasisVectors)"]]},{"rank" : 10018,"comment" : "BasisVectors: for empty basis","filters" : [["IsEmpty","Tester(IsEmpty)","IsBasis"]]},{"rank" : 16,"comment" : "BasisVectors: for canonical basis of a full matrix module","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullMatrixModule","Tester(IsCanonicalBasisFullMatrixModule)"]]},{"rank" : 16,"comment" : "BasisVectors: for canonical basis of a full row module","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullRowModule","Tester(IsCanonicalBasisFullRowModule)"]]},{"rank" : 15,"comment" : "BasisVectors: for semi-ech. basis of a Gaussian matrix space","filters" : [["IsBasis","IsSemiEchelonBasisOfGaussianMatrixSpaceRep"]]},{"rank" : 15,"comment" : "BasisVectors: for semi-ech. basis of a Gaussian row space","filters" : [["IsBasis","IsSemiEchelonBasisOfGaussianRowSpaceRep"]]},{"rank" : 13,"comment" : "BasisVectors: for canon. basis of cyclotomic field of cyclotomics","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisCyclotomicFieldRep"]]},{"rank" : 13,"comment" : "BasisVectors: for basis by nice basis","filters" : [["IsBasisByNiceBasis"]]},{"rank" : 12,"comment" : "BasisVectors: for canon. basis of an algebraic extension","filters" : [["IsCanonicalBasisAlgebraicExtension"]]},{"rank" : 11,"comment" : "BasisVectors: for canonical basis of full s. c. algebra","filters" : [["IsBasis","IsCanonicalBasisFullSCAlgebra","Tester(IsCanonicalBasisFullSCAlgebra)"]]},{"rank" : 10,"comment" : "BasisVectors: for a basis with replaced left module","filters" : [["IsBasis","IsBasisWithReplacedLeftModuleRep"]]},{"rank" : 9,"comment" : "BasisVectors: for pseudo canonical basis of a full hom module","filters" : [["IsBasis","IsPseudoCanonicalBasisFullHomModule","Tester(IsPseudoCanonicalBasisFullHomModule)"]]},{"rank" : 3,"comment" : "BasisVectors: for mutable basis with underlying mutable basis","filters" : [["IsMutableBasis","IsMutableBasisViaUnderlyingMutableBasisRep"]]},{"rank" : 3,"comment" : "BasisVectors: for a mutable basis of a Gaussian matrix space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianMatrixSpaceRep"]]},{"rank" : 3,"comment" : "BasisVectors: for a mutable basis of a Gaussian row space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianRowSpaceRep"]]},{"rank" : 3,"comment" : "BasisVectors: for mutable basis represented by a nice mutable basis","filters" : [["IsMutableBasis","IsMutableBasisViaNiceMutableBasisRep"]]},{"rank" : 3,"comment" : "BasisVectors: for mutable basis represented by an immutable basis","filters" : [["IsMutableBasis","IsMutableBasisByImmutableBasisRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BasisVectors)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BasisVectors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BasisVectors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BasisVectors)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EnumeratorByBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "EnumeratorByBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(EnumeratorByBasis)"]]},{"rank" : 16,"comment" : "EnumeratorByBasis: for enumerator via canonical basis of a full row module","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullRowModule","Tester(IsCanonicalBasisFullRowModule)"]]},{"rank" : 7,"comment" : "EnumeratorByBasis: for basis of a finite dimensional left module","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EnumeratorByBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EnumeratorByBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EnumeratorByBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EnumeratorByBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StructureConstantsTable","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "StructureConstantsTable: system getter","filters" : [["IsAttributeStoringRep","Tester(StructureConstantsTable)"]]},{"rank" : 11,"comment" : "StructureConstantsTable: LAGUNA: for a basis of a Lie algebra of a group algebra","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsBasisOfLieAlgebraOfGroupRing","Tester(IsBasisOfLieAlgebraOfGroupRing)"]]},{"rank" : 7,"comment" : "StructureConstantsTable: for a basis","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StructureConstantsTable)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StructureConstantsTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StructureConstantsTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StructureConstantsTable)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingLeftModule","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "UnderlyingLeftModule: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingLeftModule)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingLeftModule)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingLeftModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingLeftModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingLeftModule)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Coefficients","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10025,"comment" : "Coefficients: for empty basis and vector","filters" : [["IsEmpty","Tester(IsEmpty)","IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 10019,"comment" : "Coefficients: for basis of a monomial space, and a vector","filters" : [["IsBasis","IsBasisOfMonomialSpaceRep"],["IsMonomialElement","IsMonomialElementRep"]]},{"rank" : 10017,"comment" : "Coefficients: for basis of a sparse rowspace, and a vector","filters" : [["IsBasis","IsBasisOfSparseRowSpaceRep"],["IsSparseRowSpaceElement"]]},{"rank" : 46,"comment" : "Coefficients: for canonical basis of a full matrix module","filters" : [["IsBasis","IsCanonicalBasisFullMatrixModule","Tester(IsCanonicalBasisFullMatrixModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 45,"comment" : "Coefficients: for semi-ech. basis of a Gaussian matrix space, and a matrix","filters" : [["IsBasis","IsSemiEchelonBasisOfGaussianMatrixSpaceRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 36,"comment" : "Coefficients: for pseudo can. basis of full hom module, and lin. m.b.m.","filters" : [["IsBasis","IsPseudoCanonicalBasisFullHomModule","Tester(IsPseudoCanonicalBasisFullHomModule)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsLinearMappingByMatrixDefaultRep"]]},{"rank" : 32,"comment" : "Coefficients: for basis of matrix field","filters" : [["IsBasisOfMatrixField"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 32,"comment" : "Coefficients: For a FFE in Conway polynomial represntation wrt the canonical basis of its natural field","filters" : [["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsBasisFiniteFieldRep"],["IsFFE","IsCoeffsModConwayPolRep"]]},{"rank" : 29,"comment" : "Coefficients: for canonical basis of cyclotomic field, and cyclotomic","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisCyclotomicFieldRep"],["IsCyc"]]},{"rank" : 28,"comment" : "Coefficients: for canonical basis of abelian number field, and cyclotomic","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisAbelianNumberFieldRep"],["IsCyc"]]},{"rank" : 28,"comment" : "Coefficients: for canon. basis of Gaussian integers, and cyclotomic","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisGaussianIntegersRep"],["IsCyc"]]},{"rank" : 28,"comment" : "Coefficients: for canonical basis of a full row module","filters" : [["IsBasis","IsCanonicalBasisFullRowModule","Tester(IsCanonicalBasisFullRowModule)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 28,"comment" : "Coefficients: for the canonical basis of Integers","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisIntegersRep"],["IsCyc"]]},{"rank" : 27,"comment" : "Coefficients: for canon. basis of an algebraic extension, and alg. element","filters" : [["IsCanonicalBasisAlgebraicExtension"],["IsAlgebraicElement"]]},{"rank" : 27,"comment" : "Coefficients: for semi-ech. basis of a Gaussian row space, and a row vector","filters" : [["IsBasis","IsSemiEchelonBasisOfGaussianRowSpaceRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 24,"comment" : "Coefficients: for canon. basis of a free magma ring, and a vector","filters" : [["IsCanonicalBasisFreeMagmaRingRep"],["IsElementOfFreeMagmaRing"]]},{"rank" : 23,"comment" : "Coefficients: for a basis of a finite field, and a scalar","filters" : [["IsBasis","IsBasisFiniteFieldRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 22,"comment" : "Coefficients: for canon. basis of an algebraic extension, and scalar","filters" : [["IsCanonicalBasisAlgebraicExtension"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 22,"comment" : "Coefficients: for canonical basis of full s. c. algebra","filters" : [["IsBasis","IsCanonicalBasisFullSCAlgebra","Tester(IsCanonicalBasisFullSCAlgebra)"],["IsSCAlgebraObj"]]},{"rank" : 20,"comment" : "Coefficients: for basis handled by nice basis, and vector","filters" : [["IsBasisByNiceBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 20,"comment" : "Coefficients: for relative basis and vector","filters" : [["IsBasis","IsRelativeBasisDefaultRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 19,"comment" : "Coefficients: method for canonical basis of Rationals","filters" : [["IsBasis","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisRationals"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 18,"comment" : "Coefficients: for basis of weight rep elements, and algebra module element","filters" : [["IsBasisOfWeightRepElementSpace"],["IsPackedElementDefaultRep","IsWeightRepElement"]]},{"rank" : 18,"comment" : "Coefficients: for basis of a space of algebra module elements, and algebra module element","filters" : [["IsBasisOfAlgebraModuleElementSpace"],["IsPackedElementDefaultRep","IsAlgebraModuleElement"]]},{"rank" : 17,"comment" : "Coefficients: for a basis with replaced left module, and a vector","filters" : [["IsBasis","IsBasisWithReplacedLeftModuleRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 16,"comment" : "Coefficients: for pseudo canon. basis of a full hom module, and lin. mapping","filters" : [["IsBasis","IsPseudoCanonicalBasisFullHomModule","Tester(IsPseudoCanonicalBasisFullHomModule)"],["IsGeneralMapping"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LinearCombination","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10035,"comment" : "LinearCombination: for empty basis and empty list","filters" : [["IsEmpty","Tester(IsEmpty)","IsBasis"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 27,"comment" : "LinearCombination","filters" : [["IsBasis","IsSemiEchelonBasisOfGaussianRowSpaceRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 23,"comment" : "LinearCombination: for canonical basis of full s. c. algebra","filters" : [["IsBasis","IsCanonicalBasisFullSCAlgebra","Tester(IsCanonicalBasisFullSCAlgebra)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 17,"comment" : "LinearCombination: for a basis of a finite field, and a hom. list","filters" : [["IsBasis","IsBasisFiniteFieldRep"],["IsHomogeneousList"]]},{"rank" : 14,"comment" : "LinearCombination: for a basis with replaced left module, and a hom. list","filters" : [["IsBasis","IsBasisWithReplacedLeftModuleRep"],["IsHomogeneousList"]]},{"rank" : 11,"comment" : "LinearCombination: for a basis and a homogeneous list","filters" : [["IsBasis"],["IsHomogeneousList"]]},{"rank" : 4,"comment" : "LinearCombination: for two lists","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SiftedVector","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10025,"comment" : "SiftedVector: for empty basis and vector","filters" : [["IsEmpty","Tester(IsEmpty)","IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 45,"comment" : "SiftedVector: for semi-ech. basis of Gaussian matrix space, and matrix","filters" : [["IsBasis","IsSemiEchelonBasisOfGaussianMatrixSpaceRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 33,"comment" : "SiftedVector: for mutable basis of Gaussian matrix space, and matrix","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianMatrixSpaceRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 27,"comment" : "SiftedVector: for semi-ech. basis of Gaussian row space, and row vector","filters" : [["IsBasis","IsSemiEchelonBasisOfGaussianRowSpaceRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 15,"comment" : "SiftedVector: for mutable basis of Gaussian row space, and row vector","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianRowSpaceRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IteratorByBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 16,"comment" : "IteratorByBasis: for canonical basis of a full row module","filters" : [["IsBasis","IsCanonicalBasisFullRowModule","Tester(IsCanonicalBasisFullRowModule)"]]},{"rank" : 7,"comment" : "IteratorByBasis: for basis of a finite dimensional left module","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Basis","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]],[["IsFreeLeftModule"],["IsHomogeneousList"]],[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "Basis: system getter","filters" : [["IsAttributeStoringRep","Tester(Basis)"]]},{"rank" : 10028,"comment" : "Basis: for a free module of sparse row space elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsSparseRowSpaceElement)"]]},{"rank" : 10028,"comment" : "Basis: for a space of monomial elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsMonomialElement)"]]},{"rank" : 2065,"comment" : "Basis: for abelian number field of cyclotomics (delegate to `CanonicalBasis')","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 2056,"comment" : "Basis: for a finite field (delegate to `CanonicalBasis')","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 2053,"comment" : "Basis: for an algebraic extension (delegate to `CanonicalBasis')","filters" : [["IsAlgebraicExtension"]]},{"rank" : 2048,"comment" : "Basis: for full matrix module (delegate to `CanonicalBasis')","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 2048,"comment" : "Basis: for full row module (delegate to `CanonicalBasis')","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 2042,"comment" : "Basis: for Gaussian integers (delegate to `CanonicalBasis')","filters" : [["IsGaussianIntegers"]]},{"rank" : 2041,"comment" : "Basis: for full s. c. algebra (delegate to `CanonicalBasis')","filters" : [["IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)","IsFullSCAlgebra","Tester(IsFullSCAlgebra)"]]},{"rank" : 2039,"comment" : "Basis: for integers (delegate to `CanonicalBasis')","filters" : [["IsIntegers"]]},{"rank" : 2036,"comment" : "Basis: for a free magma ring (delegate to `CanonicalBasis')","filters" : [["IsFreeMagmaRing"]]},{"rank" : 125,"comment" : "Basis: for full hom space of linear mappings","filters" : [["IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 56,"comment" : "Basis: for matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 42,"comment" : "Basis: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : 41,"comment" : "Basis: for an associative FLMLOR-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 36,"comment" : "Basis: for an associative FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 34,"comment" : "Basis: for a FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 30,"comment" : "Basis: for Gaussian matrix space (construct a semi-echelonized basis)","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"]]},{"rank" : 30,"comment" : "Basis: for Gaussian row space (construct a semi-echelonized basis)","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]},{"rank" : 30,"comment" : "Basis: for trivial free left module","filters" : [["IsTrivial","Tester(IsTrivial)","IsFreeLeftModule"]]},{"rank" : 28,"comment" : "Basis: for a space of weight rep elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsWeightRepElement)"]]},{"rank" : 28,"comment" : "Basis: for a space of algebra module elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsAlgebraModuleElement)"]]},{"rank" : 26,"comment" : "Basis: for free module that is handled by a nice basis","filters" : [["IsFreeLeftModule","IsHandledByNiceBasis"]]},{"rank" : 26,"comment" : "Basis","filters" : [["IsAttributeStoringRep","IsFreeLeftModule","Tester(CanonicalBasis)"]]},{"rank" : 25,"comment" : "Basis: for an algebra module","filters" : [["IsFreeLeftModule","IsAlgebraModule","Tester(IsAlgebraModule)"]]},{"rank" : 4,"comment" : "Basis: for group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]}],"2args" : [{"rank" : 10048,"comment" : "Basis: for a space of monomial elements and a list of tensor elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsMonomialElement)"],["IsList","CategoryCollections(IsMonomialElement)"]]},{"rank" : 10032,"comment" : "Basis: for a free module of sparse row space elements, and list","filters" : [["IsFreeLeftModule","CategoryCollections(IsSparseRowSpaceElement)"],["IsHomogeneousList"]]},{"rank" : 85,"comment" : "Basis: for a finite field, and a hom. list","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","CategoryCollections(IsFFE)"]]},{"rank" : 60,"comment" : "Basis: for Gaussian row space and matrix (try semi-echelonized)","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 48,"comment" : "Basis: for a space of weight rep elements and a list of weight rep elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsWeightRepElement)"],["IsList","CategoryCollections(IsWeightRepElement)"]]},{"rank" : 48,"comment" : "Basis: for a space of algebra module elements and a collection of algebra module elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsAlgebraModuleElement)"],["IsList","CategoryCollections(IsAlgebraModuleElement)"]]},{"rank" : 40,"comment" : "Basis: for free left module and empty list","filters" : [["IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 34,"comment" : "Basis: for Gaussian matrix space and list of matrices (try semi-ech.)","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"],["IsHomogeneousList"]]},{"rank" : 30,"comment" : "Basis: for free module that is handled by a nice basis, and hom. list","filters" : [["IsFreeLeftModule","IsHandledByNiceBasis"],["IsHomogeneousList"]]},{"rank" : 27,"comment" : "Basis: method returning a relative basis","filters" : [["IsFreeLeftModule"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Basis)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],[]],[["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Basis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Basis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Basis)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BasisNC","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10048,"comment" : "BasisNC: for a space of monomial elements and a list of monomial elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsMonomialElement)"],["IsList","CategoryCollections(IsMonomialElement)"]]},{"rank" : 10032,"comment" : "BasisNC: for a free module of sparse row space elements, and list","filters" : [["IsFreeLeftModule","CategoryCollections(IsSparseRowSpaceElement)"],["IsHomogeneousList"]]},{"rank" : 70,"comment" : "BasisNC: for a finite field, and a hom. list","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsHomogeneousList"]]},{"rank" : 60,"comment" : "BasisNC: for Gaussian row space and matrix (try semi-echelonized)","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 48,"comment" : "BasisNC: for a space of weight rep elements and a list of weight rep elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsWeightRepElement)"],["IsList","CategoryCollections(IsWeightRepElement)"]]},{"rank" : 48,"comment" : "BasisNC: for a space of algebra module elements and a collection of algebra module elements","filters" : [["IsFreeLeftModule","CategoryCollections(IsAlgebraModuleElement)"],["IsList","CategoryCollections(IsAlgebraModuleElement)"]]},{"rank" : 40,"comment" : "BasisNC: for free left module and empty list","filters" : [["IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 34,"comment" : "BasisNC: for Gaussian matrix space and list of matrices (try semi-ech.)","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"],["IsHomogeneousList"]]},{"rank" : 30,"comment" : "BasisNC: for free module that is handled by a nice basis, and hom. list","filters" : [["IsFreeLeftModule","IsHandledByNiceBasis"],["IsHomogeneousList"]]},{"rank" : 27,"comment" : "BasisNC: method returning a relative basis","filters" : [["IsFreeLeftModule"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonBasis","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]],[["IsFreeLeftModule"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "SemiEchelonBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(SemiEchelonBasis)"]]},{"rank" : 33,"comment" : "SemiEchelonBasis","filters" : [["IsAttributeStoringRep","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace","Tester(CanonicalBasis)"]]},{"rank" : 33,"comment" : "SemiEchelonBasis","filters" : [["IsAttributeStoringRep","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace","Tester(CanonicalBasis)"]]},{"rank" : 30,"comment" : "SemiEchelonBasis: for Gaussian matrix space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"]]},{"rank" : 30,"comment" : "SemiEchelonBasis: for Gaussian row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]}],"2args" : [{"rank" : 60,"comment" : "SemiEchelonBasis: for Gaussian row space and matrix","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 40,"comment" : "SemiEchelonBasis: for free left module and empty list","filters" : [["IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 34,"comment" : "SemiEchelonBasis: for Gaussian matrix space and list of matrices","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemiEchelonBasis)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemiEchelonBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemiEchelonBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemiEchelonBasis)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiEchelonBasisNC","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 60,"comment" : "SemiEchelonBasisNC: for Gaussian row space and matrix","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 40,"comment" : "SemiEchelonBasisNC: for free left module and empty list","filters" : [["IsFreeLeftModule"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 34,"comment" : "SemiEchelonBasisNC: for Gaussian matrix space and list of matrices","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelativeBasis","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "RelativeBasis: for a basis and a homogeneous list","filters" : [["IsBasis"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelativeBasisNC","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "RelativeBasisNC: for a basis and a homogeneous list","filters" : [["IsBasis"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceBasis","type" : "GAP_Operation","filters" : [[["IsBasisByNiceBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "NiceBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceBasis)"]]},{"rank" : 13,"comment" : "NiceBasis: for basis by nice basis","filters" : [["IsBasisByNiceBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceBasis)","type" : "GAP_Operation","filters" : [[["IsBasisByNiceBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NiceBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceBasis)","type" : "GAP_Operation","filters" : [[["IsBasisByNiceBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceBasisNC","type" : "GAP_Operation","filters" : [[["IsBasisByNiceBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 14,"comment" : "NiceBasisNC: for basis by nice basis with precomputed basis","filters" : [["IsBasisByNiceBasis","Tester(NiceBasis)"]]},{"rank" : 13,"comment" : "NiceBasisNC: for basis by nice basis","filters" : [["IsBasisByNiceBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceFreeLeftModule","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "NiceFreeLeftModule: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceFreeLeftModule)"]]},{"rank" : 39,"comment" : "NiceFreeLeftModule: for commutative FLMLOR that is handled by a nice basis","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsHandledByNiceBasis"]]},{"rank" : 39,"comment" : "NiceFreeLeftModule: for anticommutative FLMLOR that is handled by a nice basis","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsAnticommutative","Tester(IsAnticommutative)","IsFreeLeftModule","IsHandledByNiceBasis"]]},{"rank" : 39,"comment" : "NiceFreeLeftModule: for associative FLMLOR that is handled by a nice basis","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsHandledByNiceBasis"]]},{"rank" : 37,"comment" : "NiceFreeLeftModule: for FLMLOR that is handled by a nice basis","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsHandledByNiceBasis"]]},{"rank" : 36,"comment" : "NiceFreeLeftModule: for full hom space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule","IsFullHomModule","Tester(IsFullHomModule)"]]},{"rank" : 27,"comment" : "NiceFreeLeftModule: for free module that is handled by a nice basis","filters" : [["IsFreeLeftModule","IsHandledByNiceBasis","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : 27,"comment" : "NiceFreeLeftModule: for generic finite space (use that this is a full row module)","filters" : [["IsFreeLeftModule","IsGenericFiniteSpace"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceFreeLeftModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NiceFreeLeftModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceFreeLeftModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceFreeLeftModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceFreeLeftModuleInfo","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule","IsHandledByNiceBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20027,"comment" : "NiceFreeLeftModuleInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceFreeLeftModuleInfo)"]]},{"rank" : 29,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsLinearMappingsModule'","filters" : [["IsFreeLeftModule","IsLinearMappingsModule"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsClassFunctionsSpace'","filters" : [["IsFreeLeftModule","IsClassFunctionsSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsFieldElementsSpace'","filters" : [["IsFreeLeftModule","IsFieldElementsSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsCochainsSpace'","filters" : [["IsFreeLeftModule","IsCochainsSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsDirectSumElementsSpace'","filters" : [["IsFreeLeftModule","IsDirectSumElementsSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsLieObjectsModule'","filters" : [["IsFreeLeftModule","IsLieObjectsModule"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsSCAlgebraObjSpace'","filters" : [["IsFreeLeftModule","IsSCAlgebraObjSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsSpaceOfUEAElements'","filters" : [["IsFreeLeftModule","IsSpaceOfUEAElements"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsFpAlgebraElementsSpace'","filters" : [["IsFreeLeftModule","IsFpAlgebraElementsSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsSpaceOfElementsOfMagmaRing'","filters" : [["IsFreeLeftModule","IsSpaceOfElementsOfMagmaRing"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsNonGaussianMatrixSpace'","filters" : [["IsFreeLeftModule","IsNonGaussianMatrixSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsNonGaussianRowSpace'","filters" : [["IsFreeLeftModule","IsNonGaussianRowSpace"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsSpaceOfRationalFunctions'","filters" : [["IsFreeLeftModule","IsSpaceOfRationalFunctions"]]},{"rank" : 27,"comment" : "NiceFreeLeftModuleInfo: for left module in `IsGenericFiniteSpace'","filters" : [["IsFreeLeftModule","IsGenericFiniteSpace"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceFreeLeftModuleInfo)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule","IsHandledByNiceBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NiceFreeLeftModuleInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceFreeLeftModuleInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceFreeLeftModuleInfo)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule","IsHandledByNiceBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceVector","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule","IsHandledByNiceBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "NiceVector: for left module in `IsLinearMappingsModule', and object","filters" : [["IsFreeLeftModule","IsLinearMappingsModule"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsClassFunctionsSpace', and object","filters" : [["IsFreeLeftModule","IsClassFunctionsSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsFieldElementsSpace', and object","filters" : [["IsFreeLeftModule","IsFieldElementsSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsCochainsSpace', and object","filters" : [["IsFreeLeftModule","IsCochainsSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsDirectSumElementsSpace', and object","filters" : [["IsFreeLeftModule","IsDirectSumElementsSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsLieObjectsModule', and object","filters" : [["IsFreeLeftModule","IsLieObjectsModule"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsSCAlgebraObjSpace', and object","filters" : [["IsFreeLeftModule","IsSCAlgebraObjSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsSpaceOfUEAElements', and object","filters" : [["IsFreeLeftModule","IsSpaceOfUEAElements"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsFpAlgebraElementsSpace', and object","filters" : [["IsFreeLeftModule","IsFpAlgebraElementsSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsSpaceOfElementsOfMagmaRing', and object","filters" : [["IsFreeLeftModule","IsSpaceOfElementsOfMagmaRing"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsNonGaussianMatrixSpace', and object","filters" : [["IsFreeLeftModule","IsNonGaussianMatrixSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsNonGaussianRowSpace', and object","filters" : [["IsFreeLeftModule","IsNonGaussianRowSpace"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsSpaceOfRationalFunctions', and object","filters" : [["IsFreeLeftModule","IsSpaceOfRationalFunctions"],[]]},{"rank" : 27,"comment" : "NiceVector: for left module in `IsGenericFiniteSpace', and object","filters" : [["IsFreeLeftModule","IsGenericFiniteSpace"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UglyVector","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule","IsHandledByNiceBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "UglyVector: for left module in `IsLinearMappingsModule', and object","filters" : [["IsFreeLeftModule","IsLinearMappingsModule"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsClassFunctionsSpace', and object","filters" : [["IsFreeLeftModule","IsClassFunctionsSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsFieldElementsSpace', and object","filters" : [["IsFreeLeftModule","IsFieldElementsSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsCochainsSpace', and object","filters" : [["IsFreeLeftModule","IsCochainsSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsDirectSumElementsSpace', and object","filters" : [["IsFreeLeftModule","IsDirectSumElementsSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsLieObjectsModule', and object","filters" : [["IsFreeLeftModule","IsLieObjectsModule"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsSCAlgebraObjSpace', and object","filters" : [["IsFreeLeftModule","IsSCAlgebraObjSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsSpaceOfUEAElements', and object","filters" : [["IsFreeLeftModule","IsSpaceOfUEAElements"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsFpAlgebraElementsSpace', and object","filters" : [["IsFreeLeftModule","IsFpAlgebraElementsSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsSpaceOfElementsOfMagmaRing', and object","filters" : [["IsFreeLeftModule","IsSpaceOfElementsOfMagmaRing"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsNonGaussianMatrixSpace', and object","filters" : [["IsFreeLeftModule","IsNonGaussianMatrixSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsNonGaussianRowSpace', and object","filters" : [["IsFreeLeftModule","IsNonGaussianRowSpace"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsSpaceOfRationalFunctions', and object","filters" : [["IsFreeLeftModule","IsSpaceOfRationalFunctions"],[]]},{"rank" : 27,"comment" : "UglyVector: for left module in `IsGenericFiniteSpace', and object","filters" : [["IsFreeLeftModule","IsGenericFiniteSpace"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MutableBasis","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "MutableBasis: to construct a mutable basis of a Lie matrix space","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["CategoryCollections(IsLieObject)"]]},{"rank" : 56,"comment" : "MutableBasis: method to construct mutable bases of row spaces","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 42,"comment" : "MutableBasis: for ring and collection of Lie elements","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsLieObject)"]]},{"rank" : 42,"comment" : "MutableBasis: for ring and collection of s. c. algebra elements","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsSCAlgebraObj)"]]},{"rank" : 39,"comment" : "MutableBasis: for ring and vectors","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsAlgebraModuleElement)"]]},{"rank" : 28,"comment" : "MutableBasis: to construct mutable bases of Gaussian matrix spaces","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]},{"rank" : 28,"comment" : "MutableBasis: generic method for ring and collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [{"rank" : 60,"comment" : "MutableBasis: to construct mutable bases of matrix spaces","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 40,"comment" : "MutableBasis: method to construct mutable bases of row spaces","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 39,"comment" : "MutableBasis: for ring, (possibly empty) list, and Lie zero","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"],["IsLieObject"]]},{"rank" : 39,"comment" : "MutableBasis: for ring, (possibly empty) list, and zero element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"],["IsSCAlgebraObj"]]},{"rank" : 36,"comment" : "MutableBasis: for ring, list and zero","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"],["IsAlgebraModuleElement"]]},{"rank" : 28,"comment" : "MutableBasis: generic method for ring, list, and object","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrBasisVectors","type" : "GAP_Operation","filters" : [[["IsMutableBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "NrBasisVectors: for mutable basis represented by a nice mutable basis","filters" : [["IsMutableBasis","IsMutableBasisViaNiceMutableBasisRep"]]},{"rank" : 1,"comment" : "NrBasisVectors: generic method for mutable basis","filters" : [["IsMutableBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImmutableBasis","type" : "GAP_Operation","filters" : [[["IsMutableBasis"]],[["IsMutableBasis"],["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "ImmutableBasis: for a mutable basis of a Gaussian matrix space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianMatrixSpaceRep"]]},{"rank" : 3,"comment" : "ImmutableBasis: for a mutable basis of a Gaussian row space","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianRowSpaceRep"]]},{"rank" : 3,"comment" : "ImmutableBasis: for mutable basis represented by a nice mutable basis","filters" : [["IsMutableBasis","IsMutableBasisViaNiceMutableBasisRep"]]},{"rank" : 3,"comment" : "ImmutableBasis: for mutable basis represented by an immutable basis","filters" : [["IsMutableBasis","IsMutableBasisByImmutableBasisRep"]]}],"2args" : [{"rank" : 24,"comment" : "ImmutableBasis: for mutable basis, and free left module","filters" : [["IsMutableBasis"],["IsFreeLeftModule"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CloseMutableBasis","type" : "GAP_Operation","filters" : [[["IsMutable","IsMutableBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "CloseMutableBasis: for a mut. basis of a Gaussian matrix space, and a matrix","filters" : [["IsMutable","IsMutableBasis","IsMutableBasisOfGaussianMatrixSpaceRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 17,"comment" : "CloseMutableBasis: for a mut. basis of a Gaussian row space, and a row vector","filters" : [["IsMutable","IsMutableBasis","IsMutableBasisOfGaussianRowSpaceRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 12,"comment" : "CloseMutableBasis: for mutable basis with underlying mutable basis, and vector","filters" : [["IsMutable","IsMutableBasis","IsMutableBasisViaUnderlyingMutableBasisRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 12,"comment" : "CloseMutableBasis: for mutable basis repres. by a nice mutable basis, and vector","filters" : [["IsMutable","IsMutableBasis","IsMutableBasisViaNiceMutableBasisRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 12,"comment" : "CloseMutableBasis: for mutable basis represented by an immutable basis, and vector","filters" : [["IsMutable","IsMutableBasis","IsMutableBasisByImmutableBasisRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsContainedInSpan","type" : "GAP_Operation","filters" : [[["IsMutableBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "IsContainedInSpan: for a mut. basis of a Gaussian matrix space, and a matrix","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianMatrixSpaceRep"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 15,"comment" : "IsContainedInSpan: for a mut. basis of a Gaussian row space, and a row vector","filters" : [["IsMutableBasis","IsMutableBasisOfGaussianRowSpaceRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 12,"comment" : "IsContainedInSpan: for mutable basis with underlying mutable basis, and vector","filters" : [["IsMutable","IsMutableBasis","IsMutableBasisViaUnderlyingMutableBasisRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 10,"comment" : "IsContainedInSpan: for mutable basis repres. by a nice mutable basis, and vector","filters" : [["IsMutableBasis","IsMutableBasisViaNiceMutableBasisRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]},{"rank" : 10,"comment" : "IsContainedInSpan: for mutable basis represented by an immutable basis, and vector","filters" : [["IsMutableBasis","IsMutableBasisByImmutableBasisRep"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalBasis","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "CanonicalBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalBasis)"]]},{"rank" : 69,"comment" : "CanonicalBasis: for Rationals","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 67,"comment" : "CanonicalBasis: for cyclotomic field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"]]},{"rank" : 65,"comment" : "CanonicalBasis: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 56,"comment" : "CanonicalBasis: for matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 56,"comment" : "CanonicalBasis: for a finite field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 53,"comment" : "CanonicalBasis: for an algebraic extension","filters" : [["IsAlgebraicExtension"]]},{"rank" : 51,"comment" : "CanonicalBasis: for a full row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 48,"comment" : "CanonicalBasis: for full matrix space","filters" : [["IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "CanonicalBasis","filters" : [["IsFreeLeftModule","IsFullMatrixModule","Tester(IsFullMatrixModule)"]]},{"rank" : 48,"comment" : "CanonicalBasis: for a full row module","filters" : [["IsFreeLeftModule","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 45,"comment" : "CanonicalBasis: LAGUNA: for a Lie algebra of a group algebra","filters" : [["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 43,"comment" : "CanonicalBasis: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 42,"comment" : "CanonicalBasis: for Gaussian integers","filters" : [["IsGaussianIntegers"]]},{"rank" : 41,"comment" : "CanonicalBasis: for full s. c. algebras","filters" : [["IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)","IsFullSCAlgebra","Tester(IsFullSCAlgebra)"]]},{"rank" : 39,"comment" : "CanonicalBasis: for Integers","filters" : [["IsIntegers"]]},{"rank" : 36,"comment" : "CanonicalBasis: for a free magma ring","filters" : [["IsFreeMagmaRing"]]},{"rank" : 31,"comment" : "CanonicalBasis: for Gaussian row space with known semi-ech. basis","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","Tester(SemiEchelonBasis)","IsGaussianSpace"]]},{"rank" : 30,"comment" : "CanonicalBasis: for algebra module","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","CategoryCollections(IsAlgebraModuleElement)"]]},{"rank" : 30,"comment" : "CanonicalBasis: for Gaussian matrix space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"]]},{"rank" : 30,"comment" : "CanonicalBasis: for Gaussian row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]},{"rank" : 26,"comment" : "CanonicalBasis: for free module that is handled by a nice basis","filters" : [["IsFreeLeftModule","IsHandledByNiceBasis"]]},{"rank" : 23,"comment" : "CanonicalBasis: default method, return `fail'","filters" : [["IsFreeLeftModule"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalBasis)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalBasis)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormedRowVectors","type" : "GAP_Operation","filters" : [[["IsGaussianSpace"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "NormedRowVectors: system getter","filters" : [["IsAttributeStoringRep","Tester(NormedRowVectors)"]]},{"rank" : 30,"comment" : "NormedRowVectors: for Gaussian row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormedRowVectors)","type" : "GAP_Operation","filters" : [[["IsGaussianSpace"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormedRowVectors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormedRowVectors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormedRowVectors)","type" : "GAP_Operation","filters" : [[["IsGaussianSpace"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubspace","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 27,"comment" : "AsSubspace: for a vector space and a collection","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Subspaces","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]],[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "Subspaces: system getter","filters" : [["IsAttributeStoringRep","Tester(Subspaces)"]]},{"rank" : 51,"comment" : "Subspaces","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 25,"comment" : "Subspaces: for a vector space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : -44,"comment" : "Subspaces: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [{"rank" : 69,"comment" : "Subspaces: for (Gaussian) full row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFullRowModule","Tester(IsFullRowModule)"],["IsInt"]]},{"rank" : 56,"comment" : "Subspaces: for (Gaussian) full row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFullRowModule","Tester(IsFullRowModule)"],["IsString"]]},{"rank" : 43,"comment" : "Subspaces: for a vector space, and an integer","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Subspaces)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Subspaces): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Subspaces): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Subspaces)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrthogonalSpaceInFullRowSpace","type" : "GAP_Operation","filters" : [[["IsGaussianSpace"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "OrthogonalSpaceInFullRowSpace: system getter","filters" : [["IsAttributeStoringRep","Tester(OrthogonalSpaceInFullRowSpace)"]]},{"rank" : 30,"comment" : "OrthogonalSpaceInFullRowSpace: dual space for Gaussian row space","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsRowModule","Tester(IsRowModule)","IsGaussianSpace"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrthogonalSpaceInFullRowSpace)","type" : "GAP_Operation","filters" : [[["IsGaussianSpace"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrthogonalSpaceInFullRowSpace): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrthogonalSpaceInFullRowSpace): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrthogonalSpaceInFullRowSpace)","type" : "GAP_Operation","filters" : [[["IsGaussianSpace"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsVectorSpaceHomomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsVectorSpaceHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsVectorSpaceHomomorphism)"]]},{"rank" : 7,"comment" : "IsVectorSpaceHomomorphism","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsVectorSpaceHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsVectorSpaceHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsVectorSpaceHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsVectorSpaceHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftModuleGeneralMappingByImages","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 54,"comment" : "LeftModuleGeneralMappingByImages: for two free left modules and two homogeneous lists","filters" : [["IsFreeLeftModule"],["IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "LeftModuleHomomorphismByImagesNC","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 50,"comment" : "LeftModuleHomomorphismByImagesNC: for two left modules and two lists","filters" : [["IsFreeLeftModule"],["IsFreeLeftModule"],["IsList"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "AsLeftModuleGeneralMappingByImages","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "AsLeftModuleGeneralMappingByImages: system getter","filters" : [["IsAttributeStoringRep","Tester(AsLeftModuleGeneralMappingByImages)"]]},{"rank" : 25,"comment" : "AsLeftModuleGeneralMappingByImages: for an algebra general mapping by images","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsAlgebraGeneralMappingByImagesDefaultRep"]]},{"rank" : 23,"comment" : "AsLeftModuleGeneralMappingByImages: for a linear g.m.b.i.","filters" : [["IsGeneralMapping","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsLinearGeneralMappingByImagesDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsLeftModuleGeneralMappingByImages)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsLeftModuleGeneralMappingByImages): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsLeftModuleGeneralMappingByImages): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsLeftModuleGeneralMappingByImages)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftModuleHomomorphismByMatrix","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 44,"comment" : "LeftModuleHomomorphismByMatrix: for two bases of free left modules and a matrix","filters" : [["IsBasis"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsBasis"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismBySubspace","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10053,"comment" : "NaturalHomomorphismBySubspace: for left module and trivial left module","filters" : [["IsFreeLeftModule"],["IsTrivial","Tester(IsTrivial)","IsFreeLeftModule"]]},{"rank" : 46,"comment" : "NaturalHomomorphismBySubspace: for two finite dimensional free left modules","filters" : [["IsFreeLeftModule"],["IsFreeLeftModule"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullHomModule","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "IsFullHomModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullHomModule)"]]},{"rank" : 34,"comment" : "IsFullHomModule: for space of linear mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsFreeLeftModule"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullHomModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullHomModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullHomModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullHomModule)","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPseudoCanonicalBasisFullHomModule","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsPseudoCanonicalBasisFullHomModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPseudoCanonicalBasisFullHomModule)"]]},{"rank" : 7,"comment" : "IsPseudoCanonicalBasisFullHomModule: for a basis of a full hom module","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPseudoCanonicalBasisFullHomModule)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPseudoCanonicalBasisFullHomModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPseudoCanonicalBasisFullHomModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPseudoCanonicalBasisFullHomModule)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Hom","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 96,"comment" : "Hom: for division ring and two free left modules","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFreeLeftModule"],["IsFreeLeftModule"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "End","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 73,"comment" : "End: for division ring and space of linear mappings","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFreeLeftModule"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ScalarProduct","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]],[["IsFreeLeftModule"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]],[["IsRowVectorObj"],["IsRowVectorObj"]],[["IsCharacterTable"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 62,"comment" : "ScalarProduct: for two class functions","filters" : [["IsClassFunction"],["IsClassFunction"]]},{"rank" : 24,"comment" : "ScalarProduct: method for two row vectors","filters" : [["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 18,"comment" : "ScalarProduct: generic method","filters" : [["IsRowVectorObj"],["IsRowVectorObj"]]}],"3args" : [{"rank" : 85,"comment" : "ScalarProduct: for left module of class functions, and two class functions","filters" : [["IsFreeLeftModule"],["IsClassFunction"],["IsClassFunction"]]},{"rank" : 45,"comment" : "ScalarProduct: for character table and two homogeneous lists","filters" : [["IsCharacterTable"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 35,"comment" : "ScalarProduct: for module of class functions, and two values lists","filters" : [["IsFreeLeftModule","IsClassFunctionsSpace"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Decomposition","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 32,"comment" : "Decomposition: for a matrix of cyclotomics, a vector and a depth","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSimpleAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "IsSimpleAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSimpleAlgebra)"]]},{"rank" : 42,"comment" : "IsSimpleAlgebra: for a Lie algebra in characteristic zero","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : 36,"comment" : "IsSimpleAlgebra: for an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "IsSimpleAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSimpleAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSimpleAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSimpleAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSimpleAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfLeftOperatorRing","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20032,"comment" : "GeneratorsOfLeftOperatorRing: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfLeftOperatorRing)"]]},{"rank" : 62,"comment" : "GeneratorsOfLeftOperatorRing: for FLMLOR with known right ideal generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRightIdeal)","IsFreeLeftModule"]]},{"rank" : 62,"comment" : "GeneratorsOfLeftOperatorRing: for FLMLOR with known left ideal generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfLeftIdeal)","IsFreeLeftModule"]]},{"rank" : 43,"comment" : "GeneratorsOfLeftOperatorRing: LAGUNA: for a Lie algebra coming from an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 37,"comment" : "GeneratorsOfLeftOperatorRing: for a FLMLOR-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 35,"comment" : "GeneratorsOfLeftOperatorRing: for FLMLOR with known ideal generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfTwoSidedIdeal)","IsFreeLeftModule"]]},{"rank" : 35,"comment" : "GeneratorsOfLeftOperatorRing: for a FLMLOR with known left module generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : -31,"comment" : "GeneratorsOfLeftOperatorRing: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfLeftOperatorRing)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfLeftOperatorRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfLeftOperatorRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfLeftOperatorRing)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfLeftOperatorRingWithOne","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "GeneratorsOfLeftOperatorRingWithOne: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfLeftOperatorRingWithOne)"]]},{"rank" : 38,"comment" : "GeneratorsOfLeftOperatorRingWithOne: for a FLMLOR-with-one with known left module generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]]},{"rank" : -42,"comment" : "GeneratorsOfLeftOperatorRingWithOne: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfLeftOperatorRingWithOne)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfLeftOperatorRingWithOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfLeftOperatorRingWithOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfLeftOperatorRingWithOne)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PowerSubalgebraSeries","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "PowerSubalgebraSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(PowerSubalgebraSeries)"]]},{"rank" : 36,"comment" : "PowerSubalgebraSeries: for an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "PowerSubalgebraSeries: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PowerSubalgebraSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PowerSubalgebraSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PowerSubalgebraSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PowerSubalgebraSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdjointBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "AdjointBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(AdjointBasis)"]]},{"rank" : 7,"comment" : "AdjointBasis: for a basis of a Lie algebra","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdjointBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdjointBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdjointBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdjointBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicesOfAdjointBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IndicesOfAdjointBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(IndicesOfAdjointBasis)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndicesOfAdjointBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndicesOfAdjointBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndicesOfAdjointBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndicesOfAdjointBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RadicalOfAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "RadicalOfAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(RadicalOfAlgebra)"]]},{"rank" : 49,"comment" : "RadicalOfAlgebra: for associative Gaussian matrix algebra","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMatrixModule","Tester(IsMatrixModule)","IsGaussianSpace"]]},{"rank" : 46,"comment" : "RadicalOfAlgebra: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 36,"comment" : "RadicalOfAlgebra: for an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "RadicalOfAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RadicalOfAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RadicalOfAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RadicalOfAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RadicalOfAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectSumDecomposition","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "DirectSumDecomposition: system getter","filters" : [["IsAttributeStoringRep","Tester(DirectSumDecomposition)"]]},{"rank" : 42,"comment" : "DirectSumDecomposition: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : 38,"comment" : "DirectSumDecomposition: for semisimple associative algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "DirectSumDecomposition: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DirectSumDecomposition)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DirectSumDecomposition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DirectSumDecomposition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DirectSumDecomposition)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NullAlgebra","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "NullAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(NullAlgebra)"]]},{"rank" : 26,"comment" : "NullAlgebra: for a ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "NullAlgebra: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NullAlgebra)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NullAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NullAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NullAlgebra)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProductSpace","type" : "GAP_Operation","filters" : [[["IsFreeLeftModule"],["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 86,"comment" : "ProductSpace: for two ideals with same parent","filters" : [["Tester(ParentAttr)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsTwoSidedIdealInParent","Tester(IsTwoSidedIdealInParent)"],["Tester(ParentAttr)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsTwoSidedIdealInParent","Tester(IsTwoSidedIdealInParent)"]]},{"rank" : 72,"comment" : "ProductSpace: for two algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 46,"comment" : "ProductSpace: for two free left modules","filters" : [["IsFreeLeftModule"],["IsFreeLeftModule"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectSumOfAlgebras","type" : "GAP_Operation","filters" : [[["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "DirectSumOfAlgebras: for list of algebras","filters" : [["IsDenseList"]]}],"2args" : [{"rank" : 104,"comment" : "DirectSumOfAlgebras: for two matrix Lie FLMLORs","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsFreeLeftModule"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsFreeLeftModule"]]},{"rank" : 92,"comment" : "DirectSumOfAlgebras: for two associative matrix FLMLORs","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 72,"comment" : "DirectSumOfAlgebras: for two algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsFLMLOR","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 84,"comment" : "AsFLMLOR: for a division ring and an algebra","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 73,"comment" : "AsFLMLOR: for a division ring and a free left module","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFreeLeftModule"]]},{"rank" : 28,"comment" : "AsFLMLOR: for a ring and a collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsFLMLORWithOne","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 87,"comment" : "AsFLMLORWithOne: for a division ring and a algebra-with-one","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 84,"comment" : "AsFLMLORWithOne: for a division ring and an algebra","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 73,"comment" : "AsFLMLORWithOne: for a division ring and a free left module","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFreeLeftModule"]]},{"rank" : 28,"comment" : "AsFLMLORWithOne: for a ring and a collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubFLMLOR","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 75,"comment" : "AsSubFLMLOR: for an algebra and an algebra-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 72,"comment" : "AsSubFLMLOR: for two algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubFLMLORWithOne","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 75,"comment" : "AsSubFLMLORWithOne: for an algebra and a algebra-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 72,"comment" : "AsSubFLMLORWithOne: for two algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClosureLeftOperatorRing","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10044,"comment" : "ClosureLeftOperatorRing: for a FLMLOR containing the whole family, and a ring element","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 10033,"comment" : "ClosureLeftOperatorRing: for a left op. ring cont. the whole family, and a collection","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]},{"rank" : 64,"comment" : "ClosureLeftOperatorRing: for two left operator rings-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 58,"comment" : "ClosureLeftOperatorRing: for two left operator rings","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 46,"comment" : "ClosureLeftOperatorRing: for a FLMLOR-with-one with basis, and a ring element","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(Basis)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 45,"comment" : "ClosureLeftOperatorRing: for a FLMLOR-with-one and a ring element","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 43,"comment" : "ClosureLeftOperatorRing: for an FLMLOR with basis, and a ring element","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","Tester(Basis)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 42,"comment" : "ClosureLeftOperatorRing: for a FLMLOR and a ring element","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 31,"comment" : "ClosureLeftOperatorRing: for left operator ring and list of elements","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FLMLORByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 441,"comment" : "FLMLORByGenerators: for a field, and a collection of FFE","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["CategoryCollections(IsFFE)"]]},{"rank" : 73,"comment" : "FLMLORByGenerators: for division ring and list of Lie matrices over it","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","CategoryCollections(IsLieObject)"]]},{"rank" : 55,"comment" : "FLMLORByGenerators: for division ring and list of ordinary matrices over it","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsCollection"]]},{"rank" : 28,"comment" : "FLMLORByGenerators: for ring and collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [{"rank" : 107,"comment" : "FLMLORByGenerators: for division ring, list of Lie matrices over it, and Lie matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","CategoryCollections(IsLieObject)"],["IsLieMatrix","IsLieObject"]]},{"rank" : 101,"comment" : "FLMLORByGenerators: for division ring, empty list, and Lie matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsLieMatrix","IsLieObject"]]},{"rank" : 99,"comment" : "FLMLORByGenerators: for division ring, empty list, and square ordinary matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsOrdinaryMatrix"]]},{"rank" : 87,"comment" : "FLMLORByGenerators: for division ring, list of matrices over it, and ordinary matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsCollection"],["IsOrdinaryMatrix"]]},{"rank" : 38,"comment" : "FLMLORByGenerators: for ring, homogeneous list, and ring element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FLMLORWithOneByGenerators","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 441,"comment" : "FLMLORWithOneByGenerators: for a field, and a collection of FFE","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["CategoryCollections(IsFFE)"]]},{"rank" : 55,"comment" : "FLMLORWithOneByGenerators: for division ring and list of ordinary matrices over it","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsCollection"]]},{"rank" : 28,"comment" : "FLMLORWithOneByGenerators: for ring and collection","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsCollection"]]}],"3args" : [{"rank" : 99,"comment" : "FLMLORWithOneByGenerators: for division ring, empty list, and square ordinary matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsOrdinaryMatrix"]]},{"rank" : 87,"comment" : "FLMLORWithOneByGenerators: for division ring, list of matrices over it, and ordinary matrix","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsCollection"],["IsOrdinaryMatrix"]]},{"rank" : 38,"comment" : "FLMLORWithOneByGenerators: for ring, homogeneous list, and ring element","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieAlgebraByDomain","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "LieAlgebraByDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(LieAlgebraByDomain)"]]},{"rank" : 38,"comment" : "LieAlgebraByDomain: LAGUNA: for an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 36,"comment" : "LieAlgebraByDomain: for an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "LieAlgebraByDomain: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieAlgebraByDomain)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieAlgebraByDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieAlgebraByDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieAlgebraByDomain)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsLieAlgebra","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeviMalcevDecomposition","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "LeviMalcevDecomposition: system getter","filters" : [["IsAttributeStoringRep","Tester(LeviMalcevDecomposition)"]]},{"rank" : 36,"comment" : "LeviMalcevDecomposition: for an associative or a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "LeviMalcevDecomposition: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeviMalcevDecomposition)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LeviMalcevDecomposition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeviMalcevDecomposition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeviMalcevDecomposition)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotentElement","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "IsNilpotentElement: for an algebra, and an element","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Grading","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "Grading: system getter","filters" : [["IsAttributeStoringRep","Tester(Grading)"]]},{"rank" : -55,"comment" : "Grading: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Grading)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Grading): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Grading): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Grading)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsAndMagmaElements","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "CoefficientsAndMagmaElements: system getter","filters" : [["IsAttributeStoringRep","Tester(CoefficientsAndMagmaElements)"]]},{"rank" : 13,"comment" : "CoefficientsAndMagmaElements: for magma ring element in default repr.","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoefficientsAndMagmaElements)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoefficientsAndMagmaElements): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoefficientsAndMagmaElements): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoefficientsAndMagmaElements)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroCoefficient","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "ZeroCoefficient: system getter","filters" : [["IsAttributeStoringRep","Tester(ZeroCoefficient)"]]},{"rank" : 13,"comment" : "ZeroCoefficient: for magma ring element in default repr.","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ZeroCoefficient)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ZeroCoefficient): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ZeroCoefficient): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ZeroCoefficient)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizedElementOfMagmaRingModuloRelations","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfMagmaRingModuloRelations)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "NormalizedElementOfMagmaRingModuloRelations: for family of free Lie algebra elements, and list","filters" : [["IsFamilyElementOfFreeLieAlgebra"],["IsList"]]},{"rank" : 7,"comment" : "NormalizedElementOfMagmaRingModuloRelations: for family of magma rings modulo the span of ``zero'', and list","filters" : [["IsElementOfMagmaRingModuloSpanOfZeroFamily"],["IsList"]]},{"rank" : 7,"comment" : "NormalizedElementOfMagmaRingModuloRelations: for a family of elements in a *free* magma ring, and a list","filters" : [["CategoryFamily(IsElementOfFreeMagmaRing)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupRing","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "IsGroupRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupRing)"]]},{"rank" : 36,"comment" : "IsGroupRing: for free magma ring","filters" : [["IsFreeMagmaRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupRing)","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupRing)","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingMagma","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "UnderlyingMagma: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingMagma)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingMagma)","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingMagma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingMagma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingMagma)","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementOfMagmaRing","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 17,"comment" : "ElementOfMagmaRing: for family, ring element, and two homogeneous lists","filters" : [["IsFamily"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "AugmentationIdeal","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "AugmentationIdeal: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentationIdeal)"]]},{"rank" : 42,"comment" : "AugmentationIdeal: LAGUNA: for a modular group algebra of a finite group","filters" : [["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"]]},{"rank" : 36,"comment" : "AugmentationIdeal: for a free magma ring","filters" : [["IsFreeMagmaRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentationIdeal)","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentationIdeal): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentationIdeal): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentationIdeal)","type" : "GAP_Operation","filters" : [[["IsFreeMagmaRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullFpAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","CategoryCollections(IsElementOfFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "IsFullFpAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullFpAlgebra)"]]},{"rank" : 37,"comment" : "IsFullFpAlgebra: for f. p. algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsSubalgebraFpAlgebra"]]},{"rank" : -59,"comment" : "IsFullFpAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsFreeLeftModule","CategoryCollections(IsElementOfFpAlgebra)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","CategoryCollections(IsElementOfFpAlgebra)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullFpAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullFpAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","CategoryCollections(IsElementOfFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementOfFpAlgebra","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpAlgebra)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 13,"comment" : "ElementOfFpAlgebra: for fp. alg. elms. family with normal form, and ring element","filters" : [["CategoryFamily(IsElementOfFpAlgebra)","Tester(NiceNormalFormByExtRepFunction)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 12,"comment" : "ElementOfFpAlgebra: for family of fp. alg. elements and ring element","filters" : [["CategoryFamily(IsElementOfFpAlgebra)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MappedExpression","type" : "GAP_Operation","filters" : [[["IsElementOfFpAlgebra"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 17,"comment" : "MappedExpression: for element of f.p. algebra, and two lists of generators","filters" : [["IsElementOfFpAlgebra"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGeneratorsOfFpAlgebra","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20043,"comment" : "FreeGeneratorsOfFpAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGeneratorsOfFpAlgebra)"]]},{"rank" : 40,"comment" : "FreeGeneratorsOfFpAlgebra: for a full f.p. algebra","filters" : [["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]},{"rank" : 0,"comment" : "FreeGeneratorsOfFpAlgebra: default method requiring categories and checking properties","filters" : [["IsSubalgebraFpAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGeneratorsOfFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGeneratorsOfFpAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGeneratorsOfFpAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGeneratorsOfFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelatorsOfFpAlgebra","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20043,"comment" : "RelatorsOfFpAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(RelatorsOfFpAlgebra)"]]},{"rank" : 40,"comment" : "RelatorsOfFpAlgebra: for a full f.p. algebra","filters" : [["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]},{"rank" : 0,"comment" : "RelatorsOfFpAlgebra: default method requiring categories and checking properties","filters" : [["IsSubalgebraFpAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelatorsOfFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RelatorsOfFpAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelatorsOfFpAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelatorsOfFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeAlgebraOfFpAlgebra","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20043,"comment" : "FreeAlgebraOfFpAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeAlgebraOfFpAlgebra)"]]},{"rank" : 40,"comment" : "FreeAlgebraOfFpAlgebra: for a full f.p. algebra","filters" : [["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]},{"rank" : 0,"comment" : "FreeAlgebraOfFpAlgebra: default method requiring categories and checking properties","filters" : [["IsSubalgebraFpAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeAlgebraOfFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeAlgebraOfFpAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeAlgebraOfFpAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeAlgebraOfFpAlgebra)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormalForm","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsNormalForm: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNormalForm)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNormalForm)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNormalForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNormalForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNormalForm)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceNormalFormByExtRepFunction","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "NiceNormalFormByExtRepFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceNormalFormByExtRepFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceNormalFormByExtRepFunction)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NiceNormalFormByExtRepFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceNormalFormByExtRepFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceNormalFormByExtRepFunction)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceAlgebraMonomorphism","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20040,"comment" : "NiceAlgebraMonomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceAlgebraMonomorphism)"]]},{"rank" : 47,"comment" : "NiceAlgebraMonomorphism: for a full f.p. associative FLMLOR (call `IsomorphismMatrixFLMLOR')","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]},{"rank" : 43,"comment" : "NiceAlgebraMonomorphism: for a f.p. Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsSubalgebraFpAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceAlgebraMonomorphism)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NiceAlgebraMonomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceAlgebraMonomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceAlgebraMonomorphism)","type" : "GAP_Operation","filters" : [[["IsSubalgebraFpAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieAbelian","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsLieAbelian: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieAbelian)"]]},{"rank" : 43,"comment" : "IsLieAbelian: LAGUNA: for a Lie algebra of an associative algebra","filters" : [["IsLieAlgebraByAssociativeAlgebra"]]},{"rank" : 43,"comment" : "IsLieAbelian: for a Lie algebra with known basis","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","Tester(Basis)"]]},{"rank" : 42,"comment" : "IsLieAbelian: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "IsLieAbelian: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieAbelian)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieAbelian): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieAbelian): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieAbelian)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieNilpotent","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsLieNilpotent: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieNilpotent)"]]},{"rank" : 45,"comment" : "IsLieNilpotent: LAGUNA: for a Lie algebra of a group ring","filters" : [["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 42,"comment" : "IsLieNilpotent: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "IsLieNilpotent: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieNilpotent)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieNilpotent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieNilpotent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieNilpotent)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRestrictedLieAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsRestrictedLieAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRestrictedLieAlgebra)"]]},{"rank" : 42,"comment" : "IsRestrictedLieAlgebra: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "IsRestrictedLieAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRestrictedLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRestrictedLieAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRestrictedLieAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRestrictedLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieDerivedSubalgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieDerivedSubalgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(LieDerivedSubalgebra)"]]},{"rank" : 45,"comment" : "LieDerivedSubalgebra: LAGUNA: for a Lie algebra of a group ring","filters" : [["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 42,"comment" : "LieDerivedSubalgebra: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieDerivedSubalgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieDerivedSubalgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieDerivedSubalgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieDerivedSubalgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieDerivedSubalgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieDerivedSeries","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieDerivedSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(LieDerivedSeries)"]]},{"rank" : 42,"comment" : "LieDerivedSeries: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieDerivedSeries: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieDerivedSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieDerivedSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieDerivedSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieDerivedSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieSolvable","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsLieSolvable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieSolvable)"]]},{"rank" : 45,"comment" : "IsLieSolvable: LAGUNA: for a Lie algebra of a group ring","filters" : [["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 42,"comment" : "IsLieSolvable: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "IsLieSolvable: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieSolvable)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieSolvable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieSolvable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieSolvable)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieLowerCentralSeries","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieLowerCentralSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(LieLowerCentralSeries)"]]},{"rank" : 42,"comment" : "LieLowerCentralSeries: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieLowerCentralSeries: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieLowerCentralSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieLowerCentralSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieLowerCentralSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieLowerCentralSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieUpperCentralSeries","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieUpperCentralSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(LieUpperCentralSeries)"]]},{"rank" : 42,"comment" : "LieUpperCentralSeries: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieUpperCentralSeries: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieUpperCentralSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieUpperCentralSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieUpperCentralSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieUpperCentralSeries)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieCentre","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieCentre: system getter","filters" : [["IsAttributeStoringRep","Tester(LieCentre)"]]},{"rank" : 45,"comment" : "LieCentre: LAGUNA: for a Lie algebra of a group ring","filters" : [["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 42,"comment" : "LieCentre: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieCentre: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieCentre)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieCentre): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieCentre): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieCentre)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightDerivations","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RightDerivations: system getter","filters" : [["IsAttributeStoringRep","Tester(RightDerivations)"]]},{"rank" : 7,"comment" : "RightDerivations: method for a basis of an algebra","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RightDerivations)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RightDerivations): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RightDerivations): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RightDerivations)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftDerivations","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "LeftDerivations: system getter","filters" : [["IsAttributeStoringRep","Tester(LeftDerivations)"]]},{"rank" : 7,"comment" : "LeftDerivations: method for a basis of an algebra","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeftDerivations)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LeftDerivations): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeftDerivations): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeftDerivations)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KillingMatrix","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "KillingMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(KillingMatrix)"]]},{"rank" : 7,"comment" : "KillingMatrix: for a basis of a Lie algebra","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KillingMatrix)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KillingMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KillingMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KillingMatrix)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CartanSubalgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "CartanSubalgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(CartanSubalgebra)"]]},{"rank" : 42,"comment" : "CartanSubalgebra: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "CartanSubalgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CartanSubalgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CartanSubalgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CartanSubalgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CartanSubalgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PthPowerImages","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "PthPowerImages: system getter","filters" : [["IsAttributeStoringRep","Tester(PthPowerImages)"]]},{"rank" : 7,"comment" : "PthPowerImages: for a basis of a Lie algebra","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PthPowerImages)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PthPowerImages): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PthPowerImages): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PthPowerImages)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NonNilpotentElement","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "NonNilpotentElement: system getter","filters" : [["IsAttributeStoringRep","Tester(NonNilpotentElement)"]]},{"rank" : 42,"comment" : "NonNilpotentElement: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "NonNilpotentElement: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NonNilpotentElement)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NonNilpotentElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NonNilpotentElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NonNilpotentElement)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdjointAssociativeAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 84,"comment" : "AdjointAssociativeAlgebra: for a Lie algebra and a subalgebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieNilRadical","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieNilRadical: system getter","filters" : [["IsAttributeStoringRep","Tester(LieNilRadical)"]]},{"rank" : 42,"comment" : "LieNilRadical: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieNilRadical: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieNilRadical)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieNilRadical): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieNilRadical): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieNilRadical)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieSolvableRadical","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieSolvableRadical: system getter","filters" : [["IsAttributeStoringRep","Tester(LieSolvableRadical)"]]},{"rank" : 42,"comment" : "LieSolvableRadical: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieSolvableRadical: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieSolvableRadical)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieSolvableRadical): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieSolvableRadical): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieSolvableRadical)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiSimpleType","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "SemiSimpleType: system getter","filters" : [["IsAttributeStoringRep","Tester(SemiSimpleType)"]]},{"rank" : 42,"comment" : "SemiSimpleType: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "SemiSimpleType: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemiSimpleType)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemiSimpleType): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemiSimpleType): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemiSimpleType)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieCentralizer","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 73,"comment" : "LieCentralizer: for an abelian Lie algebra and a vector space","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsLieAbelian","Tester(IsLieAbelian)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]},{"rank" : 67,"comment" : "LieCentralizer: for a Lie algebra and a vector space","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieCentralizerInParent","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieCentralizerInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(LieCentralizerInParent)"]]},{"rank" : -55,"comment" : "LieCentralizerInParent: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieCentralizerInParent)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieCentralizerInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieCentralizerInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieCentralizerInParent)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieNormalizer","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "LieNormalizer: for a Lie algebra and a vector space","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieNormalizerInParent","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieNormalizerInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(LieNormalizerInParent)"]]},{"rank" : -55,"comment" : "LieNormalizerInParent: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieNormalizerInParent)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieNormalizerInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieNormalizerInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieNormalizerInParent)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdjointMatrix","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "AdjointMatrix: for a basis of a Lie algebra, and an element","filters" : [["IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KappaPerp","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "KappaPerp: for a Lie algebra and a vector space","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PowerS","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "PowerS: system getter","filters" : [["IsAttributeStoringRep","Tester(PowerS)"]]},{"rank" : 42,"comment" : "PowerS: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "PowerS: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PowerS)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PowerS): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PowerS): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PowerS)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PthPowerImage","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]],[["IsJacobianElement"]],[["IsJacobianElement"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 12,"comment" : "PthPowerImage: for restricted Lie object","filters" : [["IsRestrictedJacobianElement","IsLieObject"]]},{"rank" : 9,"comment" : "PthPowerImage: for an element of a restricted Lie algebra","filters" : [["IsJacobianElement"]]}],"2args" : [{"rank" : 30,"comment" : "PthPowerImage: for restricted Lie object and integer","filters" : [["IsRestrictedJacobianElement","IsLieObject"],["IsInt"]]},{"rank" : 27,"comment" : "PthPowerImage: for an element of a restricted Lie algebra and an integer","filters" : [["IsJacobianElement"],["IsInt"]]},{"rank" : 15,"comment" : "PthPowerImage: for a basis of an algebra, and a ring element","filters" : [["IsBasis"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PClosureSubalgebra","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsJacobianElement)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 43,"comment" : "PClosureSubalgebra: for a subalgebra of restricted jacobian elements","filters" : [["CategoryCollections(IsJacobianElement)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingLieAlgebra","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "UnderlyingLieAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingLieAlgebra)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingLieAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingLieAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RootSystem","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "RootSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(RootSystem)"]]},{"rank" : 42,"comment" : "RootSystem: for a (semisimple) Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "RootSystem: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RootSystem)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RootSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RootSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RootSystem)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositiveRoots","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "PositiveRoots: system getter","filters" : [["IsAttributeStoringRep","Tester(PositiveRoots)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PositiveRoots)","type" : "GAP_Operation","filters" : [[["IsRootSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PositiveRoots): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PositiveRoots): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PositiveRoots)","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NegativeRoots","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "NegativeRoots: system getter","filters" : [["IsAttributeStoringRep","Tester(NegativeRoots)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NegativeRoots)","type" : "GAP_Operation","filters" : [[["IsRootSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NegativeRoots): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NegativeRoots): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NegativeRoots)","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositiveRootVectors","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "PositiveRootVectors: system getter","filters" : [["IsAttributeStoringRep","Tester(PositiveRootVectors)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PositiveRootVectors)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PositiveRootVectors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PositiveRootVectors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PositiveRootVectors)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NegativeRootVectors","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "NegativeRootVectors: system getter","filters" : [["IsAttributeStoringRep","Tester(NegativeRootVectors)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NegativeRootVectors)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NegativeRootVectors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NegativeRootVectors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NegativeRootVectors)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SimpleSystem","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "SimpleSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(SimpleSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SimpleSystem)","type" : "GAP_Operation","filters" : [[["IsRootSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SimpleSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SimpleSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SimpleSystem)","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CartanMatrix","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "CartanMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(CartanMatrix)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CartanMatrix)","type" : "GAP_Operation","filters" : [[["IsRootSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CartanMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CartanMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CartanMatrix)","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BilinearFormMat","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "BilinearFormMat: system getter","filters" : [["IsAttributeStoringRep","Tester(BilinearFormMat)"]]},{"rank" : 2,"comment" : "BilinearFormMat: for a root system from a Lie algebra","filters" : [["IsRootSystemFromLieAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BilinearFormMat)","type" : "GAP_Operation","filters" : [[["IsRootSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BilinearFormMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BilinearFormMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BilinearFormMat)","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalGenerators","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "CanonicalGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalGenerators)"]]},{"rank" : 2,"comment" : "CanonicalGenerators: for a root system from a (semisimple) Lie algebra","filters" : [["IsRootSystemFromLieAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalGenerators)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalGenerators)","type" : "GAP_Operation","filters" : [[["IsRootSystemFromLieAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ChevalleyBasis","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "ChevalleyBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(ChevalleyBasis)"]]},{"rank" : 42,"comment" : "ChevalleyBasis: for a semisimple Lie algebra with a split Cartan subalgebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "ChevalleyBasis: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ChevalleyBasis)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ChevalleyBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ChevalleyBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ChevalleyBasis)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UniversalEnvelopingAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "UniversalEnvelopingAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(UniversalEnvelopingAlgebra)"]]},{"rank" : 42,"comment" : "UniversalEnvelopingAlgebra: for a finite dimensional Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "UniversalEnvelopingAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [{"rank" : 49,"comment" : "UniversalEnvelopingAlgebra: for a finite dimensional Lie algebra and a basis of it","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsBasis"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UniversalEnvelopingAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UniversalEnvelopingAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UniversalEnvelopingAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UniversalEnvelopingAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "JenningsLieAlgebra","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "JenningsLieAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(JenningsLieAlgebra)"]]},{"rank" : 33,"comment" : "JenningsLieAlgebra: for a p-group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "JenningsLieAlgebra: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(JenningsLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(JenningsLieAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(JenningsLieAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(JenningsLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PCentralLieAlgebra","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PCentralLieAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(PCentralLieAlgebra)"]]},{"rank" : 33,"comment" : "PCentralLieAlgebra: for a p-group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "PCentralLieAlgebra: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PCentralLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PCentralLieAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PCentralLieAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PCentralLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)"]]},{"rank" : -55,"comment" : "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullSCAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20040,"comment" : "IsFullSCAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullSCAlgebra)"]]},{"rank" : 41,"comment" : "IsFullSCAlgebra: for s. c. algebra elements collection","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCAlgebraObj)"]]},{"rank" : -59,"comment" : "IsFullSCAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullSCAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullSCAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullSCAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullSCAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCanonicalBasisFullSCAlgebra","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsCanonicalBasisFullSCAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCanonicalBasisFullSCAlgebra)"]]},{"rank" : 7,"comment" : "IsCanonicalBasisFullSCAlgebra: for a basis","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCanonicalBasisFullSCAlgebra)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCanonicalBasisFullSCAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCanonicalBasisFullSCAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCanonicalBasisFullSCAlgebra)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlgebraGeneralMappingByImages","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 76,"comment" : "AlgebraGeneralMappingByImages: for two FLMLORs and two homogeneous lists","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "AlgebraHomomorphismByImagesNC","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 76,"comment" : "AlgebraHomomorphismByImagesNC: for two FLMLORs and two homogeneous lists","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "AlgebraWithOneGeneralMappingByImages","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 76,"comment" : "AlgebraWithOneGeneralMappingByImages: for two FLMLORs and two homogeneous lists","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "AlgebraWithOneHomomorphismByImagesNC","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 76,"comment" : "AlgebraWithOneHomomorphismByImagesNC: for two FLMLORs and two homogeneous lists","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "OperationAlgebraHomomorphism","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsBasis"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "OperationAlgebraHomomorphism: for a FLMLOR and a collection (add `OnRight' argument)","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsCollection"]]}],"3args" : [{"rank" : 61,"comment" : "OperationAlgebraHomomorphism: for a FLMLOR, a free left module with known generators, and a function","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsFreeLeftModule","IsFiniteDimensional","Tester(IsFiniteDimensional)","Tester(GeneratorsOfLeftOperatorAdditiveGroup)"],["IsFunction"]]},{"rank" : 50,"comment" : "OperationAlgebraHomomorphism: for a full f.p. associative FLMLOR, a collection, and a function","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"],["IsCollection"],["IsFunction"]]},{"rank" : 42,"comment" : "OperationAlgebraHomomorphism: for a FLMLOR, a basis, and a function","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsBasis"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MakePreImagesInfoOperationAlgebraHomomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 29,"comment" : "MakePreImagesInfoOperationAlgebraHomomorphism: for an alg. hom. from f. p. algebra","filters" : [["IsAlgebraHomomorphismFromFpRep"]]},{"rank" : 29,"comment" : "MakePreImagesInfoOperationAlgebraHomomorphism: for an operation algebra homomorphism","filters" : [["IsOperationAlgebraHomomorphismDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpFLMLOR","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "IsomorphismFpFLMLOR: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismFpFLMLOR)"]]},{"rank" : 10037,"comment" : "IsomorphismFpFLMLOR: for f.p. FLMLOR (return the identity mapping)","filters" : [["IsSubalgebraFpAlgebra"]]},{"rank" : 37,"comment" : "IsomorphismFpFLMLOR: for a finite dimensional FLMLOR-with-one","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : -46,"comment" : "IsomorphismFpFLMLOR: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsFreeLeftModule"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismFpFLMLOR)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismFpFLMLOR): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismFpFLMLOR): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismFpFLMLOR)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismMatrixFLMLOR","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "IsomorphismMatrixFLMLOR: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismMatrixFLMLOR)"]]},{"rank" : 47,"comment" : "IsomorphismMatrixFLMLOR: for a full f.p. associative FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsSubalgebraFpAlgebra","IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]]},{"rank" : 44,"comment" : "IsomorphismMatrixFLMLOR: for a matrix FLMLOR","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 37,"comment" : "IsomorphismMatrixFLMLOR: for a f.p. FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsSubalgebraFpAlgebra"]]},{"rank" : 34,"comment" : "IsomorphismMatrixFLMLOR: for a finite dimensional associative FLMLOR with identity","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : -46,"comment" : "IsomorphismMatrixFLMLOR: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsFreeLeftModule"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismMatrixFLMLOR)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismMatrixFLMLOR): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismMatrixFLMLOR): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismMatrixFLMLOR)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismSCFLMLOR","type" : "GAP_Operation","filters" : [[["IsBasis"]],[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsomorphismSCFLMLOR: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismSCFLMLOR)"]]},{"rank" : 10039,"comment" : "IsomorphismSCFLMLOR: for s.c. FLMLOR (return the identity mapping)","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","CategoryCollections(IsSCAlgebraObj)"]]},{"rank" : 34,"comment" : "IsomorphismSCFLMLOR: for a finite dimensional FLMLOR (delegate to the method for a basis)","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 7,"comment" : "IsomorphismSCFLMLOR: for a basis (of a finite dimensional FLMLOR)","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismSCFLMLOR)","type" : "GAP_Operation","filters" : [[["IsBasis"],[]],[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismSCFLMLOR): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismSCFLMLOR): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismSCFLMLOR)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativeLinearOperation","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 95,"comment" : "RepresentativeLinearOperation: for a matrix FLMLOR, two lists of row vectors, and `OnTuples'","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"]]},{"rank" : 69,"comment" : "RepresentativeLinearOperation: for a matrix FLMLOR, two row vectors, and `OnRight'","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsFunction"]]},{"rank" : 49,"comment" : "RepresentativeLinearOperation: for a FLMLOR, two elements in it, and `OnRight'","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"],["IsFunction"]]},{"rank" : 43,"comment" : "RepresentativeLinearOperation: for a FLMLOR, two tuples of elements in it, and `OnTuples'","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsHomogeneousList"],["IsHomogeneousList"],["IsFunction"]]}],"5args" : [],"6args" : []}},{"name" : "LieFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "LieFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(LieFamily)"]]},{"rank" : 3,"comment" : "LieFamily: for family of ring elements","filters" : [["CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))"]]},{"rank" : 2,"comment" : "LieFamily: for a collections family (special case of Lie matrices)","filters" : [["CategoryFamily(IsCollection)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingFamily","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "UnderlyingFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingFamily)"]]},{"rank" : 18,"comment" : "UnderlyingFamily","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 2,"comment" : "UnderlyingFamily","filters" : [["IsRewritingSystem"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingFamily)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingFamily)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieObject","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "LieObject: system getter","filters" : [["IsAttributeStoringRep","Tester(LieObject)"]]},{"rank" : 8,"comment" : "LieObject: for a ring element","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieObject)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieObject): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieObject): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieObject)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingRingElement","type" : "GAP_Operation","filters" : [[["IsLieObject"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "UnderlyingRingElement: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingRingElement)"]]},{"rank" : 13,"comment" : "UnderlyingRingElement: for a Lie object in default representation","filters" : [["IsPackedElementDefaultRep","IsLieObject"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingRingElement)","type" : "GAP_Operation","filters" : [[["IsLieObject"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingRingElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingRingElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingRingElement)","type" : "GAP_Operation","filters" : [[["IsLieObject"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAlgebraModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsAlgebraModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAlgebraModule)"]]},{"rank" : -44,"comment" : "IsAlgebraModule: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAlgebraModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAlgebraModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLeftAlgebraModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsLeftAlgebraModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLeftAlgebraModule)"]]},{"rank" : -44,"comment" : "IsLeftAlgebraModule: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLeftAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLeftAlgebraModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLeftAlgebraModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLeftAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRightAlgebraModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsRightAlgebraModule: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRightAlgebraModule)"]]},{"rank" : -44,"comment" : "IsRightAlgebraModule: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRightAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRightAlgebraModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRightAlgebraModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRightAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftActingAlgebra","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20027,"comment" : "LeftActingAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(LeftActingAlgebra)"]]},{"rank" : 0,"comment" : "LeftActingAlgebra: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeftActingAlgebra)","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LeftActingAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeftActingAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeftActingAlgebra)","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightActingAlgebra","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20027,"comment" : "RightActingAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(RightActingAlgebra)"]]},{"rank" : 0,"comment" : "RightActingAlgebra: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RightActingAlgebra)","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RightActingAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RightActingAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RightActingAlgebra)","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ActingAlgebra","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 24,"comment" : "ActingAlgebra: for an algebra module","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfAlgebraModule","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20027,"comment" : "GeneratorsOfAlgebraModule: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfAlgebraModule)"]]},{"rank" : 0,"comment" : "GeneratorsOfAlgebraModule: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfAlgebraModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfAlgebraModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfAlgebraModule)","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftAlgebraModuleByGenerators","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 41,"comment" : "LeftAlgebraModuleByGenerators: for algebra, function of 2 args, module generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsHomogeneousList"]]}],"4args" : [{"rank" : 46,"comment" : "LeftAlgebraModuleByGenerators: for algebra, function of 2 args, generators, string","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsHomogeneousList"],["IsString"]]}],"5args" : [],"6args" : []}},{"name" : "RightAlgebraModuleByGenerators","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 41,"comment" : "RightAlgebraModuleByGenerators: for algebra, function of 2 args, module generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsHomogeneousList"]]}],"4args" : [{"rank" : 46,"comment" : "RightAlgebraModuleByGenerators: for algebra, function of 2 args, generators, string","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsHomogeneousList"],["IsString"]]}],"5args" : [],"6args" : []}},{"name" : "BiAlgebraModuleByGenerators","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsFunction"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 78,"comment" : "BiAlgebraModuleByGenerators: for 2 algebras, function of 2 args, function of 2 args, module generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsFunction"],["IsHomogeneousList"]]}],"6args" : [{"rank" : 83,"comment" : "BiAlgebraModuleByGenerators: for 2 algebras, function of 2 args, function of 2 args, generators, string","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsFunction"],["IsHomogeneousList"],["IsString"]]}]}},{"name" : "LeftAlgebraModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 62,"comment" : "LeftAlgebraModule: for algebra, function of 2 args, underlying space","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightAlgebraModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 62,"comment" : "RightAlgebraModule: for algebra, function of 2 args, underlying space","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BiAlgebraModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsFunction"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 99,"comment" : "BiAlgebraModule: for 2 algebras, function of 2 args, function of 2 args, module generators","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsFunction"],["IsFunction"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"6args" : []}},{"name" : "SubAlgebraModule","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["CategoryCollections(IsAlgebraModuleElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 45,"comment" : "SubAlgebraModule: for algebra module, and a list of submodule generators","filters" : [["IsFreeLeftModule","IsAlgebraModule","Tester(IsAlgebraModule)"],["IsList","CategoryCollections(IsAlgebraModuleElement)"]]}],"3args" : [{"rank" : 50,"comment" : "SubAlgebraModule: for algebra module, and a list of submodule generators, and string","filters" : [["IsFreeLeftModule","IsAlgebraModule","Tester(IsAlgebraModule)"],["IsList","CategoryCollections(IsAlgebraModuleElement)"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftModuleByHomomorphismToMatAlg","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 57,"comment" : "LeftModuleByHomomorphismToMatAlg: for an algebra and a homomorphism to a matrix algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightModuleByHomomorphismToMatAlg","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 57,"comment" : "RightModuleByHomomorphismToMatAlg: for an algebra and a homomorphism to a matrix algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdjointModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "AdjointModule: system getter","filters" : [["IsAttributeStoringRep","Tester(AdjointModule)"]]},{"rank" : 36,"comment" : "AdjointModule: for an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "AdjointModule: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdjointModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdjointModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdjointModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdjointModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FaithfulModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "FaithfulModule: system getter","filters" : [["IsAttributeStoringRep","Tester(FaithfulModule)"]]},{"rank" : 42,"comment" : "FaithfulModule: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : 36,"comment" : "FaithfulModule: for an algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "FaithfulModule: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FaithfulModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FaithfulModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FaithfulModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FaithfulModule)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ModuleByRestriction","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 60,"comment" : "ModuleByRestriction: for an algebra module and a subalgebra","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [{"rank" : 96,"comment" : "ModuleByRestriction: for a bi-algebra module and a subalgebra and a subalgebra","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismBySubAlgebraModule","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsAlgebraModule","Tester(IsAlgebraModule)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 48,"comment" : "NaturalHomomorphismBySubAlgebraModule: for algebra module and a submodule","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsAlgebraModule","Tester(IsAlgebraModule)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MatrixOfAction","type" : "GAP_Operation","filters" : [[["IsBasisOfAlgebraModuleElementSpace"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "MatrixOfAction: for a basis of an algebra module and an algebra element","filters" : [["IsBasisOfAlgebraModuleElementSpace"],[]]}],"3args" : [{"rank" : 8,"comment" : "MatrixOfAction: for a basis of an algebra module, an algebra element and a side","filters" : [["IsBasisOfAlgebraModuleElementSpace"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConvertToNormalFormMonomialElement","type" : "GAP_Operation","filters" : [[["IsMonomialElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 9,"comment" : "ConvertToNormalFormMonomialElement: for a symmetric element","filters" : [["IsSymmetricPowerElement"]]},{"rank" : 9,"comment" : "ConvertToNormalFormMonomialElement: for a wedge element","filters" : [["IsWedgeElement"]]},{"rank" : 9,"comment" : "ConvertToNormalFormMonomialElement: for a tensor element","filters" : [["IsTensorElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TensorProductOp","type" : "GAP_Operation","filters" : [[["IsList"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "TensorProductOp: for a list of finite dimensional vector spaces, and a space (for method selection)","filters" : [["IsDenseList"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TensorProductOfAlgebraModules","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "TensorProductOfAlgebraModules: for a list of algebra modules","filters" : [["IsDenseList"]]}],"2args" : [{"rank" : 48,"comment" : "TensorProductOfAlgebraModules: for two algebra modules","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsAlgebraModule","Tester(IsAlgebraModule)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExteriorPower","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 49,"comment" : "ExteriorPower: for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "ExteriorPower: for a vector space and an integer","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExteriorPowerOfAlgebraModule","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "ExteriorPowerOfAlgebraModule: for an algebra module and an integer","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymmetricPower","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 49,"comment" : "SymmetricPower: for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "SymmetricPower: for an algebra module and an integer","filters" : [["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymmetricPowerOfAlgebraModule","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "SymmetricPowerOfAlgebraModule: for an algebra module and an integer","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectSumOfAlgebraModules","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "DirectSumOfAlgebraModules: for a list of algebra modules","filters" : [["IsDenseList"]]}],"2args" : [{"rank" : 48,"comment" : "DirectSumOfAlgebraModules: for two algebra modules","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsAlgebraModule","Tester(IsAlgebraModule)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FullSparseRowSpace","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "FullSparseRowSpace: for a ring and an integer","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TranslatorSubalgebra","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsFreeLeftModule"],["IsFreeLeftModule"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 70,"comment" : "TranslatorSubalgebra: for an algebra, an algebra module and two subspaces","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsFreeLeftModule"],["IsFreeLeftModule"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cochain","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"],["IsInt"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 42,"comment" : "Cochain: for a module over a Lie algebra, an integer and an object","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CochainSpace","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "CochainSpace: for a module over a Lie algebra and an integer","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cocycles","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "Cocycles: for module over a Lie algebra and an integer","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Coboundaries","type" : "GAP_Operation","filters" : [[["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "Coboundaries: for module over a Lie algebra and an integer","filters" : [["IsAlgebraModule","Tester(IsAlgebraModule)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsWeylGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsWeylGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsWeylGroup)"]]},{"rank" : 0,"comment" : "IsWeylGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsWeylGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsWeylGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsWeylGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsWeylGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WeylGroup","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "WeylGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(WeylGroup)"]]},{"rank" : 1,"comment" : "WeylGroup: for a root system","filters" : [["IsRootSystem"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WeylGroup)","type" : "GAP_Operation","filters" : [[["IsRootSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WeylGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WeylGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WeylGroup)","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SparseCartanMatrix","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "SparseCartanMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(SparseCartanMatrix)"]]},{"rank" : 0,"comment" : "SparseCartanMatrix: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SparseCartanMatrix)","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SparseCartanMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SparseCartanMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SparseCartanMatrix)","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ApplySimpleReflection","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 22,"comment" : "ApplySimpleReflection: for a sparse Cartan matrix, index and weight","filters" : [["IsList"],["IsInt"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LongestWeylWordPerm","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "LongestWeylWordPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(LongestWeylWordPerm)"]]},{"rank" : 35,"comment" : "LongestWeylWordPerm: for Weyl group","filters" : [["IsWeylGroup","Tester(IsWeylGroup)"]]},{"rank" : 0,"comment" : "LongestWeylWordPerm: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LongestWeylWordPerm)","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LongestWeylWordPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LongestWeylWordPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LongestWeylWordPerm)","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugateDominantWeight","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "ConjugateDominantWeight: for Weyl group and weight","filters" : [["IsWeylGroup","Tester(IsWeylGroup)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugateDominantWeightWithWord","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "ConjugateDominantWeightWithWord: for Weyl group and weight","filters" : [["IsWeylGroup","Tester(IsWeylGroup)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WeylOrbitIterator","type" : "GAP_Operation","filters" : [[["IsWeylGroup","Tester(IsWeylGroup)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "WeylOrbitIterator: for weights of a W-orbit","filters" : [["IsWeylGroup","Tester(IsWeylGroup)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositiveRootsAsWeights","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "PositiveRootsAsWeights: system getter","filters" : [["IsAttributeStoringRep","Tester(PositiveRootsAsWeights)"]]},{"rank" : 1,"comment" : "PositiveRootsAsWeights: for a root system","filters" : [["IsRootSystem"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PositiveRootsAsWeights)","type" : "GAP_Operation","filters" : [[["IsRootSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PositiveRootsAsWeights): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PositiveRootsAsWeights): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PositiveRootsAsWeights)","type" : "GAP_Operation","filters" : [[["IsRootSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DominantWeights","type" : "GAP_Operation","filters" : [[["IsRootSystem"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 3,"comment" : "DominantWeights: for a root system and a dominant weight","filters" : [["IsRootSystem"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DominantCharacter","type" : "GAP_Operation","filters" : [[["IsRootSystem"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "DominantCharacter: for a semisimple Lie algebra and a highest weight","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList"]]},{"rank" : 3,"comment" : "DominantCharacter: for a root system and a highest weight","filters" : [["IsRootSystem"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DecomposeTensorProduct","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 46,"comment" : "DecomposeTensorProduct: for a semisimple Lie algebra and two dominant weights","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DimensionOfHighestWeightModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "DimensionOfHighestWeightModule: for a semisimple Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LatticeGeneratorsInUEA","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LatticeGeneratorsInUEA: system getter","filters" : [["IsAttributeStoringRep","Tester(LatticeGeneratorsInUEA)"]]},{"rank" : 42,"comment" : "LatticeGeneratorsInUEA: for semsimple Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LatticeGeneratorsInUEA: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LatticeGeneratorsInUEA)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LatticeGeneratorsInUEA): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LatticeGeneratorsInUEA): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LatticeGeneratorsInUEA)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HighestWeightModule","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "HighestWeightModule: for a Lie algebra and a list of non-negative integers","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadingUEALatticeMonomial","type" : "GAP_Operation","filters" : [[["IsInt"],["IsUEALatticeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "LeadingUEALatticeMonomial: for an integer and a UEALattice element","filters" : [["IsInt"],["IsUEALatticeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Search","type" : "GAP_Operation","filters" : [[["IsSearchTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "Search: for vector search tables in default representation","filters" : [["IsVectorSearchTableDefaultRep"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Insert","type" : "GAP_Operation","filters" : [[["IsSearchTable"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 9,"comment" : "Insert: for a vector search table in default representation","filters" : [["IsVectorSearchTableDefaultRep"],["IsHomogeneousList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsQadic","type" : "GAP_Operation","filters" : [[["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "CoefficientsQadic: for two integers","filters" : [["IsInt"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimeDivisors","type" : "GAP_Operation","filters" : [[["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20021,"comment" : "PrimeDivisors: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimeDivisors)"]]},{"rank" : 18,"comment" : "PrimeDivisors: for integer","filters" : [["IsInt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimeDivisors)","type" : "GAP_Operation","filters" : [[["IsInt"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimeDivisors): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimeDivisors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimeDivisors)","type" : "GAP_Operation","filters" : [[["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PartialFactorization","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "PartialFactorization: for integers","filters" : [["IsInt"]]}],"2args" : [{"rank" : 38,"comment" : "PartialFactorization: try harder (FactInt)","filters" : [["IsInt"],["IsInt","IsPosRat"]]},{"rank" : 36,"comment" : "PartialFactorization: generic method","filters" : [["IsInt"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Phi","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "Phi: value of Euler's totient function of an integer","filters" : [["IsInt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Lambda","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "Lambda: exponent of the group of prime residues modulo an integer","filters" : [["IsInt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Sigma","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "Sigma: sum of divisors of an integer","filters" : [["IsInt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tau","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "Tau: number of divisors of an integer","filters" : [["IsInt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StandardGeneratorsSubringSCRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20032,"comment" : "StandardGeneratorsSubringSCRing: system getter","filters" : [["IsAttributeStoringRep","Tester(StandardGeneratorsSubringSCRing)"]]},{"rank" : 29,"comment" : "StandardGeneratorsSubringSCRing: for sc rings and their subrings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]},{"rank" : -26,"comment" : "StandardGeneratorsSubringSCRing: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","CategoryCollections(IsSCRingObj)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StandardGeneratorsSubringSCRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StandardGeneratorsSubringSCRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StandardGeneratorsSubringSCRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StandardGeneratorsSubringSCRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Subrings","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "Subrings: system getter","filters" : [["IsAttributeStoringRep","Tester(Subrings)"]]},{"rank" : 29,"comment" : "Subrings: for SC Rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]},{"rank" : -14,"comment" : "Subrings: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Subrings)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Subrings): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Subrings): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Subrings)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Ideals","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "Ideals: system getter","filters" : [["IsAttributeStoringRep","Tester(Ideals)"]]},{"rank" : 29,"comment" : "Ideals: for SC Rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]},{"rank" : -14,"comment" : "Ideals: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Ideals)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Ideals): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Ideals): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Ideals)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectSumOp","type" : "GAP_Operation","filters" : [[["IsList"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 31,"comment" : "DirectSumOp: for SC Rings","filters" : [["IsList"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]},{"rank" : 28,"comment" : "DirectSumOp: for a list (of rings), and a ring","filters" : [["IsList"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectSumInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DirectSumInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(DirectSumInfo)"]]},{"rank" : 0,"comment" : "DirectSumInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DirectSumInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DirectSumInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DirectSumInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DirectSumInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RingGeneralMappingByImages","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 60,"comment" : "RingGeneralMappingByImages: for two rings and two homogeneous lists","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "RingHomomorphismByImagesNC","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 60,"comment" : "RingHomomorphismByImagesNC: for two rings and two homogeneous lists","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismByIdeal","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10087,"comment" : "NaturalHomomorphismByIdeal: for FLMLOR and trivial FLMLOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsTrivial","Tester(IsTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 69,"comment" : "NaturalHomomorphismByIdeal: for free algebra and ideal","filters" : [["IsMagmaRingModuloRelations"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 68,"comment" : "NaturalHomomorphismByIdeal: for two finite dimensional FLMLORs","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"],["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule"]]},{"rank" : 58,"comment" : "NaturalHomomorphismByIdeal: sc rings","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsSCRingObj)"]]},{"rank" : 53,"comment" : "NaturalHomomorphismByIdeal: polynomial rings","filters" : [["IsPolynomialRing"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LucasMod","type" : "GAP_Operation","filters" : [[["IsInt"],["IsInt"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 73,"comment" : "LucasMod: iterative method","filters" : [["IsInt"],["IsInt"],["IsInt"],["IsInt"]]},{"rank" : 72,"comment" : "LucasMod: recursive version, reduce mod N regularly","filters" : [["IsInt"],["IsInt"],["IsInt"],["IsInt"]]}],"5args" : [],"6args" : []}},{"name" : "RationalFunctionsFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "RationalFunctionsFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(RationalFunctionsFamily)"]]},{"rank" : 37,"comment" : "RationalFunctionsFamily: floats pseudofield","filters" : [["IsFloatPseudoField"]]},{"rank" : 2,"comment" : "RationalFunctionsFamily","filters" : [["IsFamily"]]},{"rank" : 0,"comment" : "RationalFunctionsFamily: not UFD ring","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RationalFunctionsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RationalFunctionsFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RationalFunctionsFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RationalFunctionsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "CoefficientsFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(CoefficientsFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoefficientsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoefficientsFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoefficientsFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoefficientsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumeratorOfRationalFunction","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "NumeratorOfRationalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(NumeratorOfRationalFunction)"]]},{"rank" : 15,"comment" : "NumeratorOfRationalFunction: univariate using ExtRepNumerator","filters" : [["IsRationalFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 13,"comment" : "NumeratorOfRationalFunction: call ExtRepNumerator","filters" : [["IsRationalFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NumeratorOfRationalFunction)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NumeratorOfRationalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NumeratorOfRationalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NumeratorOfRationalFunction)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DenominatorOfRationalFunction","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "DenominatorOfRationalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(DenominatorOfRationalFunction)"]]},{"rank" : 15,"comment" : "DenominatorOfRationalFunction: univariate using ExtRepDenominator","filters" : [["IsRationalFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 13,"comment" : "DenominatorOfRationalFunction: call ExtRepDenominator","filters" : [["IsRationalFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DenominatorOfRationalFunction)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DenominatorOfRationalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DenominatorOfRationalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DenominatorOfRationalFunction)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "IsPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPolynomial)"]]},{"rank" : 20,"comment" : "IsPolynomial: laurent rep.","filters" : [["IsLaurentPolynomialDefaultRep"]]},{"rank" : 16,"comment" : "IsPolynomial: rational function rep.","filters" : [["IsRationalFunctionDefaultRep"]]},{"rank" : 15,"comment" : "IsPolynomial: univariate","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "IsPolynomial: fallback for non-ratfun","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsPolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "AsPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(AsPolynomial)"]]},{"rank" : 15,"comment" : "AsPolynomial: call ExtRepPolynomial","filters" : [["IsRationalFunction","IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "AsPolynomial: default method requiring categories and checking properties","filters" : [["IsPolynomialFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsPolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsPolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUnivariateRationalFunction","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsUnivariateRationalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 13,"comment" : "IsUnivariateRationalFunction: ratfun","filters" : [["IsRationalFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsUnivariateRationalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsUnivariateRationalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLaurentPolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "IsLaurentPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLaurentPolynomial)"]]},{"rank" : 15,"comment" : "IsLaurentPolynomial: univariate","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "IsLaurentPolynomial","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 13,"comment" : "IsLaurentPolynomial: ratfun","filters" : [["IsRationalFunction"]]},{"rank" : 0,"comment" : "IsLaurentPolynomial: fallback for non-ratfun","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLaurentPolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLaurentPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLaurentPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLaurentPolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsConstantRationalFunction","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "IsConstantRationalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(IsConstantRationalFunction)"]]},{"rank" : 14,"comment" : "IsConstantRationalFunction: polynomial","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 12,"comment" : "IsConstantRationalFunction: rational function","filters" : [["IsPolynomialFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsConstantRationalFunction)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsConstantRationalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsConstantRationalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsConstantRationalFunction)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtRepNumeratorRatFun","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "ExtRepNumeratorRatFun: system getter","filters" : [["IsAttributeStoringRep","Tester(ExtRepNumeratorRatFun)"]]},{"rank" : 20,"comment" : "ExtRepNumeratorRatFun: laurent polynomial rep.","filters" : [["IsLaurentPolynomialDefaultRep"]]},{"rank" : 17,"comment" : "ExtRepNumeratorRatFun: polynomial rep -> ExtRepPolynomialRatFun","filters" : [["IsPolynomialDefaultRep"]]},{"rank" : 15,"comment" : "ExtRepNumeratorRatFun: univariate","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ExtRepNumeratorRatFun)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExtRepNumeratorRatFun): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExtRepNumeratorRatFun): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExtRepNumeratorRatFun)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtRepDenominatorRatFun","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "ExtRepDenominatorRatFun: system getter","filters" : [["IsAttributeStoringRep","Tester(ExtRepDenominatorRatFun)"]]},{"rank" : 20,"comment" : "ExtRepDenominatorRatFun: laurent polynomial rep.","filters" : [["IsRationalFunction","IsLaurentPolynomialDefaultRep"]]},{"rank" : 15,"comment" : "ExtRepDenominatorRatFun: univariate","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 13,"comment" : "ExtRepDenominatorRatFun: polynomial, return constant","filters" : [["IsRationalFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ExtRepDenominatorRatFun)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExtRepDenominatorRatFun): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExtRepDenominatorRatFun): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExtRepDenominatorRatFun)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroCoefficientRatFun","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 12,"comment" : "ZeroCoefficientRatFun: via family","filters" : [["IsPolynomialFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtRepPolynomialRatFun","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "ExtRepPolynomialRatFun: system getter","filters" : [["IsAttributeStoringRep","Tester(ExtRepPolynomialRatFun)"]]},{"rank" : 22,"comment" : "ExtRepPolynomialRatFun: laurent polynomial rep.","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsLaurentPolynomialDefaultRep"]]},{"rank" : 18,"comment" : "ExtRepPolynomialRatFun: rational function rep.","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsRationalFunctionDefaultRep"]]},{"rank" : 15,"comment" : "ExtRepPolynomialRatFun: univariate","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "ExtRepPolynomialRatFun: default method requiring categories and checking properties","filters" : [["IsPolynomialFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ExtRepPolynomialRatFun)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExtRepPolynomialRatFun): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExtRepPolynomialRatFun): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExtRepPolynomialRatFun)","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsOfLaurentPolynomial","type" : "GAP_Operation","filters" : [[["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "CoefficientsOfLaurentPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(CoefficientsOfLaurentPolynomial)"]]},{"rank" : 17,"comment" : "CoefficientsOfLaurentPolynomial: ratfun","filters" : [["IsRationalFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 0,"comment" : "CoefficientsOfLaurentPolynomial:  fallback method to test conditions","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "CoefficientsOfLaurentPolynomial: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoefficientsOfLaurentPolynomial)","type" : "GAP_Operation","filters" : [[["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoefficientsOfLaurentPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoefficientsOfLaurentPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoefficientsOfLaurentPolynomial)","type" : "GAP_Operation","filters" : [[["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndeterminateNumberOfUnivariateRationalFunction","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IndeterminateNumberOfUnivariateRationalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(IndeterminateNumberOfUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "IndeterminateNumberOfUnivariateRationalFunction: ratfun","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "IndeterminateNumberOfUnivariateRationalFunction: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndeterminateNumberOfUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndeterminateNumberOfUnivariateRationalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndeterminateNumberOfUnivariateRationalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndeterminateNumberOfUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LaurentPolynomialByCoefficients","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 21,"comment" : "LaurentPolynomialByCoefficients: fam, cof,val","filters" : [["IsFamily"],["IsList"],["IsInt"]]}],"4args" : [{"rank" : 75,"comment" : "LaurentPolynomialByCoefficients: ring","filters" : [["IsFloatPseudoField"],["IsList"],["IsInt"],["IsInt"]]},{"rank" : 40,"comment" : "LaurentPolynomialByCoefficients: warn about iterated polynomials","filters" : [["IsFamily","Tester(CoefficientsFamily)"],["IsList"],["IsInt"],["IsInt"]]},{"rank" : 39,"comment" : "LaurentPolynomialByCoefficients: with indeterminate","filters" : [["IsFamily"],["IsList"],["IsInt"],["IsInt"]]}],"5args" : [],"6args" : []}},{"name" : "IndeterminateOfUnivariateRationalFunction","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IndeterminateOfUnivariateRationalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(IndeterminateOfUnivariateRationalFunction)"]]},{"rank" : 15,"comment" : "IndeterminateOfUnivariateRationalFunction: use `IndeterminateNumber'","filters" : [["IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "IndeterminateOfUnivariateRationalFunction: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndeterminateOfUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndeterminateOfUnivariateRationalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndeterminateOfUnivariateRationalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndeterminateOfUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndeterminateName","type" : "GAP_Operation","filters" : [[["IsPolynomialFunctionsFamily"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "IndeterminateName: for rational function families","filters" : [["IsPolynomialFunctionsFamily"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasIndeterminateName","type" : "GAP_Operation","filters" : [[["IsPolynomialFunctionsFamily"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "HasIndeterminateName: for rational function families","filters" : [["IsPolynomialFunctionsFamily"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetIndeterminateName","type" : "GAP_Operation","filters" : [[["IsPolynomialFunctionsFamily"],["IsInt","IsPosRat"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 26,"comment" : "SetIndeterminateName: for rational function families","filters" : [["IsPolynomialFunctionsFamily"],["IsInt","IsPosRat"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsOfUnivariatePolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "CoefficientsOfUnivariatePolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(CoefficientsOfUnivariatePolynomial)"]]},{"rank" : 19,"comment" : "CoefficientsOfUnivariatePolynomial: use laurent coeffs","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "CoefficientsOfUnivariatePolynomial:  fallback method to test conditions","filters" : [["IsPolynomialFunction"]]},{"rank" : 0,"comment" : "CoefficientsOfUnivariatePolynomial: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoefficientsOfUnivariatePolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoefficientsOfUnivariatePolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoefficientsOfUnivariatePolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoefficientsOfUnivariatePolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOfLaurentPolynomial","type" : "GAP_Operation","filters" : [[["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "DegreeOfLaurentPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOfLaurentPolynomial)"]]},{"rank" : 17,"comment" : "DegreeOfLaurentPolynomial","filters" : [["IsPolynomialFunction","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 0,"comment" : "DegreeOfLaurentPolynomial: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOfLaurentPolynomial)","type" : "GAP_Operation","filters" : [[["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOfLaurentPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOfLaurentPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOfLaurentPolynomial)","type" : "GAP_Operation","filters" : [[["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnivariatePolynomialByCoefficients","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 3,"comment" : "UnivariatePolynomialByCoefficients: fam,cof","filters" : [["IsFamily"],["IsList"]]}],"3args" : [{"rank" : 57,"comment" : "UnivariatePolynomialByCoefficients: ring","filters" : [["IsFloatPseudoField"],["IsList"],["IsInt"]]},{"rank" : 22,"comment" : "UnivariatePolynomialByCoefficients: fam, cof,ind","filters" : [["IsFamily"],["IsList"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnivariatePolynomial","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 39,"comment" : "UnivariatePolynomial: ring,cof","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"]]},{"rank" : 29,"comment" : "UnivariatePolynomial: ring,empty cof","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsEmpty","Tester(IsEmpty)"]]}],"3args" : [{"rank" : 58,"comment" : "UnivariatePolynomial: ring,cof,indn","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],["IsInt","IsPosRat"]]},{"rank" : 54,"comment" : "UnivariatePolynomial: ring,cof,indpol","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsMultiplicativeElement)"],["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 29,"comment" : "UnivariatePolynomial: ring,empty cof, indnr","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsEmpty","Tester(IsEmpty)"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsOfUnivariateRationalFunction","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "CoefficientsOfUnivariateRationalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(CoefficientsOfUnivariateRationalFunction)"]]},{"rank" : 17,"comment" : "CoefficientsOfUnivariateRationalFunction: laurent polynomial","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 15,"comment" : "CoefficientsOfUnivariateRationalFunction: ratfun","filters" : [["IsRationalFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "CoefficientsOfUnivariateRationalFunction: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoefficientsOfUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoefficientsOfUnivariateRationalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoefficientsOfUnivariateRationalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoefficientsOfUnivariateRationalFunction)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnivariateRationalFunctionByCoefficients","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsList"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 59,"comment" : "UnivariateRationalFunctionByCoefficients: ring","filters" : [["IsFloatPseudoField"],["IsList"],["IsList"],["IsInt"]]},{"rank" : 23,"comment" : "UnivariateRationalFunctionByCoefficients: fam, ncof,dcof,val","filters" : [["IsFamily"],["IsList"],["IsList"],["IsInt"]]}],"5args" : [{"rank" : 77,"comment" : "UnivariateRationalFunctionByCoefficients: ring","filters" : [["IsFloatPseudoField"],["IsList"],["IsList"],["IsInt"],["IsInt"]]},{"rank" : 41,"comment" : "UnivariateRationalFunctionByCoefficients: with indeterminate","filters" : [["IsFamily"],["IsList"],["IsList"],["IsInt"],["IsInt"]]}],"6args" : []}},{"name" : "Value","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],["IsList"],["IsList"]],[["IsFloatRationalFunction"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "Value: supply `one'","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 0,"comment" : "Value:  fallback method to test conditions","filters" : [["IsPolynomialFunction"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [{"rank" : 33,"comment" : "Value: Laurent, ring element, and mult. neutral element","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 31,"comment" : "Value: univariate rational function","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]},{"rank" : 16,"comment" : "Value: rational function: supply `one'","filters" : [["IsPolynomialFunction"],["IsList"],["IsList"]]}],"4args" : [{"rank" : 24,"comment" : "Value: rat.fun., with one","filters" : [["IsPolynomialFunction"],["IsList"],["IsList"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"5args" : [],"6args" : []}},{"name" : "LeadingMonomial","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 17,"comment" : "LeadingMonomial: for a univariate laurent polynomial","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 14,"comment" : "LeadingMonomial: multivariate polynomials wrt total degree","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadingCoefficient","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 17,"comment" : "LeadingCoefficient: laurent","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 17,"comment" : "LeadingCoefficient: multivariate polynomials wrt total degree","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsPolynomialDefaultRep"]]}],"2args" : [{"rank" : 33,"comment" : "LeadingCoefficient: multivariate","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PolynomialCoefficientsOfPolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "PolynomialCoefficientsOfPolynomial: polynomial,integer","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]},{"rank" : 28,"comment" : "PolynomialCoefficientsOfPolynomial: polynomial,indet","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeIndeterminate","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "DegreeIndeterminate: laurent,indetnr","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"],["IsInt","IsPosRat"]]},{"rank" : 33,"comment" : "DegreeIndeterminate: pol,indetnr","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]},{"rank" : 31,"comment" : "DegreeIndeterminate: pol,indet","filters" : [["IsPolynomial","Tester(IsPolynomial)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Derivative","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]],[["IsPolynomialFunction"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "Derivative: system getter","filters" : [["IsAttributeStoringRep","Tester(Derivative)"]]},{"rank" : 18,"comment" : "Derivative: for float laurent polynomial","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)","IsFloatRationalFunction"]]},{"rank" : 17,"comment" : "Derivative: Laurent Polynomials","filters" : [["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 15,"comment" : "Derivative: uratfun,ind","filters" : [["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "Derivative:  fallback method to test conditions","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "Derivative:  fallback method to test conditions","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "Derivative: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [{"rank" : 31,"comment" : "Derivative: ratfun,inum","filters" : [["IsPolynomialFunction"],["IsInt","IsPosRat"]]},{"rank" : 28,"comment" : "Derivative: poly,ind","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 26,"comment" : "Derivative: ratfun,ind","filters" : [["IsPolynomialFunction"],["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Derivative)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Derivative): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Derivative): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Derivative)","type" : "GAP_Operation","filters" : [[["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Resultant","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"],["IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 47,"comment" : "Resultant: pol,pol,inum","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]},{"rank" : 42,"comment" : "Resultant: pol,pol,indet","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Discriminant","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"]],[["IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "Discriminant: system getter","filters" : [["IsAttributeStoringRep","Tester(Discriminant)"]]},{"rank" : 19,"comment" : "Discriminant: univariate","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "Discriminant:  fallback method to test conditions","filters" : [["IsRationalFunction"]]},{"rank" : 0,"comment" : "Discriminant: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [{"rank" : 33,"comment" : "Discriminant: poly,inum","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsInt","IsPosRat"]]},{"rank" : 28,"comment" : "Discriminant: poly,ind","filters" : [["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"],["IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Discriminant)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Discriminant): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Discriminant): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Discriminant)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HeuristicCancelPolynomialsExtRep","type" : "GAP_Operation","filters" : [[["IsRationalFunctionsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 9,"comment" : "HeuristicCancelPolynomialsExtRep: rationals","filters" : [["IsRationalFunctionsFamily"],["IsList"],["IsList"]]},{"rank" : 8,"comment" : "HeuristicCancelPolynomialsExtRep: ignore","filters" : [["IsRationalFunctionsFamily"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZippedSum","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"],[],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 6,"comment" : "ZippedSum","filters" : [["IsList"],["IsList"],[],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "ZippedProduct","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"],[],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 6,"comment" : "ZippedProduct","filters" : [["IsList"],["IsList"],[],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "PrimeField","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20052,"comment" : "PrimeField: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimeField)"]]},{"rank" : 82,"comment" : "PrimeField: for finite field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 65,"comment" : "PrimeField: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 54,"comment" : "PrimeField: for a prime field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 50,"comment" : "PrimeField: for a division ring","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "PrimeField: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimeField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimeField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimeField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimeField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimeField","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20052,"comment" : "IsPrimeField: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPrimeField)"]]},{"rank" : 50,"comment" : "IsPrimeField: for a division ring","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "IsPrimeField: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPrimeField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPrimeField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPrimeField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPrimeField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefiningPolynomial","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]],[["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "DefiningPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(DefiningPolynomial)"]]},{"rank" : 419,"comment" : "DefiningPolynomial: for a field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 56,"comment" : "DefiningPolynomial: for matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : -100,"comment" : "DefiningPolynomial: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DefiningPolynomial)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]],[["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DefiningPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DefiningPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DefiningPolynomial)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOverPrimeField","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20052,"comment" : "DegreeOverPrimeField: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOverPrimeField)"]]},{"rank" : 56,"comment" : "DegreeOverPrimeField: for matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 52,"comment" : "DegreeOverPrimeField","filters" : [["IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : -100,"comment" : "DegreeOverPrimeField: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOverPrimeField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOverPrimeField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOverPrimeField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOverPrimeField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfDivisionRing","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20052,"comment" : "GeneratorsOfDivisionRing: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfDivisionRing)"]]},{"rank" : 65,"comment" : "GeneratorsOfDivisionRing: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 54,"comment" : "GeneratorsOfDivisionRing: for a prime field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : -100,"comment" : "GeneratorsOfDivisionRing: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfDivisionRing)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsOfDivisionRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfDivisionRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfDivisionRing)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalBase","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "NormalBase: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalBase)"]]},{"rank" : 52,"comment" : "NormalBase: for a field (in characteristic zero)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "NormalBase: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [{"rank" : 66,"comment" : "NormalBase: for a finite field and scalar","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 62,"comment" : "NormalBase: for a field (in characteristic zero), and a scalar","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalBase)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalBase): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalBase): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalBase)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimitiveElement","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20052,"comment" : "PrimitiveElement: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimitiveElement)"]]},{"rank" : 56,"comment" : "PrimitiveElement: for matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 50,"comment" : "PrimitiveElement: for a division ring","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "PrimitiveElement: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimitiveElement)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimitiveElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimitiveElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimitiveElement)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimitiveRoot","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20058,"comment" : "PrimitiveRoot: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimitiveRoot)"]]},{"rank" : 432,"comment" : "PrimitiveRoot","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 56,"comment" : "PrimitiveRoot: for a finite prime field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "PrimitiveRoot: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimitiveRoot)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimitiveRoot): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimitiveRoot): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimitiveRoot)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RootOfDefiningPolynomial","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "RootOfDefiningPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(RootOfDefiningPolynomial)"]]},{"rank" : 419,"comment" : "RootOfDefiningPolynomial: for a small field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "RootOfDefiningPolynomial: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RootOfDefiningPolynomial)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RootOfDefiningPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RootOfDefiningPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RootOfDefiningPolynomial)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsDivisionRing","type" : "GAP_Operation","filters" : [[["IsCollection"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "AsDivisionRing: for a collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 100,"comment" : "AsDivisionRing: for two division rings","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 52,"comment" : "AsDivisionRing: for a division ring, and a collection","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClosureDivisionRing","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10062,"comment" : "ClosureDivisionRing: for a division ring containing the whole family, and a scalar","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsWholeFamily","Tester(IsWholeFamily)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 67,"comment" : "ClosureDivisionRing: for division ring and empty list","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 60,"comment" : "ClosureDivisionRing: for a division ring and a scalar","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 52,"comment" : "ClosureDivisionRing: for division ring and collection of elements","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Subfields","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "Subfields: system getter","filters" : [["IsAttributeStoringRep","Tester(Subfields)"]]},{"rank" : 82,"comment" : "Subfields: for finite field of FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 65,"comment" : "Subfields: for abelian number field of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 56,"comment" : "Subfields: for finite fields that are not FFEs","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "Subfields: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Subfields)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Subfields): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Subfields): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Subfields)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FieldExtension","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 436,"comment" : "FieldExtension: for a field of FFEs, and a univ. Laurent polynomial","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 82,"comment" : "FieldExtension: for field of cyclotomics, and univ. polynomial (degree <= 2)","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]]},{"rank" : 71,"comment" : "FieldExtension: generic","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Conjugates","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20013,"comment" : "Conjugates: system getter","filters" : [["IsAttributeStoringRep","Tester(Conjugates)"]]},{"rank" : 10,"comment" : "Conjugates: for a scalar (delegate to version with default field)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"2args" : [{"rank" : 62,"comment" : "Conjugates: for a field and a scalar (delegate to version with two fields)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"3args" : [{"rank" : 879,"comment" : "Conjugates: for two fields of FFEs, and a FFE","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFFE"]]},{"rank" : 155,"comment" : "Conjugates: for Rationals, Rationals, and a rational","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsRat"]]},{"rank" : 148,"comment" : "Conjugates: for cycl. field of cyclotomics, ab. number field, and cyclotomic","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsCyc"]]},{"rank" : 146,"comment" : "Conjugates: for two abelian number fields of cyclotomics, and cyclotomic","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsCyc"]]},{"rank" : 115,"comment" : "Conjugates: for two fields and a scalar (call `GaloisGroup')","filters" : [["IsFieldControlledByGaloisGroup"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 114,"comment" : "Conjugates: for two fields and a scalar (call `TracePolynomial')","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Conjugates)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Conjugates): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Conjugates): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Conjugates)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Norm","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsClassFunction"]],[["IsOrdinaryTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20013,"comment" : "Norm: system getter","filters" : [["IsAttributeStoringRep","Tester(Norm)"]]},{"rank" : 31,"comment" : "Norm: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 12,"comment" : "Norm: for floats","filters" : [["IsFloat"]]},{"rank" : 10,"comment" : "Norm: for a scalar (delegate to version with default field)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"2args" : [{"rank" : 10059,"comment" : "Norm: for matrix fields","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"],["IsMultiplicativeElement"]]},{"rank" : 62,"comment" : "Norm: for a field and a scalar (delegate to version with two fields)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 26,"comment" : "Norm: for an ordinary character table and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 879,"comment" : "Norm: for two fields of FFEs, and a FFE","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFFE"]]},{"rank" : 148,"comment" : "Norm: for cycl. field of cyclotomics, ab. number field, and cyclotomic","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsCyc"]]},{"rank" : 146,"comment" : "Norm: for two abelian number fields of cyclotomics, and cyclotomic","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsCyc"]]},{"rank" : 115,"comment" : "Norm: for two fields and a scalar (use `Conjugates')","filters" : [["IsFieldControlledByGaloisGroup"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 114,"comment" : "Norm: for two fields and a scalar (use the trace pol.)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Norm)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],[]],[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Norm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Norm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Norm)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Trace","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20013,"comment" : "Trace: system getter","filters" : [["IsAttributeStoringRep","Tester(Trace)"]]},{"rank" : 30,"comment" : "Trace: generic method for matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 10,"comment" : "Trace: for a scalar (delegate to version with default field)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"2args" : [{"rank" : 62,"comment" : "Trace: for a field and a scalar (delegate to version with two fields)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"3args" : [{"rank" : 879,"comment" : "Trace: for two fields of FFEs, and a FFE","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFFE"]]},{"rank" : 148,"comment" : "Trace: for cycl. field of cyclotomics, ab. number field, and cyclotomic","filters" : [["CategoryCollections(IsCyclotomic)","IsCyclotomicField","Tester(IsCyclotomicField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsCyc"]]},{"rank" : 146,"comment" : "Trace: for two abelian number fields of cyclotomics, and cyclotomic","filters" : [["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["CategoryCollections(IsCyclotomic)","IsAbelianNumberField","Tester(IsAbelianNumberField)"],["IsCyc"]]},{"rank" : 115,"comment" : "Trace: for two fields and a scalar (use `Conjugates')","filters" : [["IsFieldControlledByGaloisGroup"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 114,"comment" : "Trace: for two fields and a scalar (use the trace pol.)","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Trace)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],[]],[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Trace): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Trace): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Trace)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TracePolynomial","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 114,"comment" : "TracePolynomial: add default indet. 1","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]}],"4args" : [{"rank" : 133,"comment" : "TracePolynomial: using minimal polynomial","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "GaloisGroup","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]],[["IsRationalClassGroupRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "GaloisGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(GaloisGroup)"]]},{"rank" : 57,"comment" : "GaloisGroup: for abelian number field ","filters" : [["IsAbelianNumberField","Tester(IsAbelianNumberField)"]]},{"rank" : 56,"comment" : "GaloisGroup: for a finite field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 11,"comment" : "GaloisGroup","filters" : [["IsRationalClassGroupRep"]]},{"rank" : -100,"comment" : "GaloisGroup: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GaloisGroup)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]],[["IsRationalClassGroupRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GaloisGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GaloisGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GaloisGroup)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComplexConjugate","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20013,"comment" : "ComplexConjugate: system getter","filters" : [["IsAttributeStoringRep","Tester(ComplexConjugate)"]]},{"rank" : 38,"comment" : "ComplexConjugate: for a class function","filters" : [["CategoryCollections(IsCyclotomic)","IsClassFunction"]]},{"rank" : 23,"comment" : "ComplexConjugate: for a quaternion","filters" : [["IsQuaternion","IsSCAlgebraObj"]]},{"rank" : 16,"comment" : "ComplexConjugate: for a cyclotomic","filters" : [["IsCyc"]]},{"rank" : 15,"comment" : "ComplexConjugate: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 2,"comment" : "ComplexConjugate: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComplexConjugate)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],[]],[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComplexConjugate): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComplexConjugate): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComplexConjugate)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RealPart","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20013,"comment" : "RealPart: system getter","filters" : [["IsAttributeStoringRep","Tester(RealPart)"]]},{"rank" : 23,"comment" : "RealPart: for a quaternion","filters" : [["IsQuaternion","IsSCAlgebraObj"]]},{"rank" : 15,"comment" : "RealPart: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 10,"comment" : "RealPart: for a scalar","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]},{"rank" : 2,"comment" : "RealPart: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RealPart)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],[]],[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RealPart): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RealPart): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RealPart)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImaginaryPart","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]],[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20013,"comment" : "ImaginaryPart: system getter","filters" : [["IsAttributeStoringRep","Tester(ImaginaryPart)"]]},{"rank" : 23,"comment" : "ImaginaryPart: for a quaternion","filters" : [["IsQuaternion","IsSCAlgebraObj"]]},{"rank" : 16,"comment" : "ImaginaryPart: for a cyclotomic","filters" : [["IsCyc"]]},{"rank" : 15,"comment" : "ImaginaryPart: for macfloats","filters" : [["IsIEEE754FloatRep"]]},{"rank" : 2,"comment" : "ImaginaryPart: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImaginaryPart)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],[]],[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImaginaryPart): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImaginaryPart): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImaginaryPart)","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DivisionRingByGenerators","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "DivisionRingByGenerators: for collection of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)"]]},{"rank" : 2,"comment" : "DivisionRingByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 441,"comment" : "DivisionRingByGenerators: for two coll. of FFEs, the first a field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsFFE)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["CategoryCollections(IsFFE)"]]},{"rank" : 82,"comment" : "DivisionRingByGenerators: for field and collection, both collections of cyclotomics","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["CategoryCollections(IsCyclotomic)"]]},{"rank" : 52,"comment" : "DivisionRingByGenerators: for a division ring, and a collection","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FieldOverItselfByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "FieldOverItselfByGenerators: for a collection of FFEs","filters" : [["CategoryCollections(IsFFE)"]]},{"rank" : 2,"comment" : "FieldOverItselfByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefaultFieldByGenerators","type" : "GAP_Operation","filters" : [[["IsCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 29,"comment" : "DefaultFieldByGenerators: for a collection of FFEs that is a list","filters" : [["IsList","CategoryCollections(IsFFE)"]]},{"rank" : 29,"comment" : "DefaultFieldByGenerators: alg elms","filters" : [["IsList","CategoryCollections(IsAlgebraicElement)"]]},{"rank" : 22,"comment" : "DefaultFieldByGenerators: for collection of cyclotomics","filters" : [["CategoryCollections(IsCyclotomic)"]]},{"rank" : 2,"comment" : "DefaultFieldByGenerators: for a collection","filters" : [["IsCollection"]]}],"2args" : [{"rank" : 85,"comment" : "DefaultFieldByGenerators: for a finite field, and a collection of FFEs that is a list","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList","CategoryCollections(IsFFE)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FrobeniusAutomorphism","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "FrobeniusAutomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(FrobeniusAutomorphism)"]]},{"rank" : 52,"comment" : "FrobeniusAutomorphism: for a field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "FrobeniusAutomorphism: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FrobeniusAutomorphism)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FrobeniusAutomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FrobeniusAutomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FrobeniusAutomorphism)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NthRoot","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 86,"comment" : "NthRoot: for a field of FFEs, and a FFE","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsFFE"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZmodnZObj","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsZmodnZObjNonprime)"],["IsInt"]],[["IsInt"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "ZmodnZObj: for a positive integer, and an integer -- check small primes","filters" : [["IsInt"],["IsInt","IsPosRat"]]},{"rank" : 23,"comment" : "ZmodnZObj: for family of FFE elements, and integer","filters" : [["CategoryFamily(IsFFE)"],["IsInt"]]},{"rank" : 23,"comment" : "ZmodnZObj: for family of elements in Z\/nZ (nonprime), and integer","filters" : [["CategoryFamily(IsZmodnZObjNonprime)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ModulusOfZmodnZObj","type" : "GAP_Operation","filters" : [[["IsZmodnZObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "ModulusOfZmodnZObj: system getter","filters" : [["IsAttributeStoringRep","Tester(ModulusOfZmodnZObj)"]]},{"rank" : 16,"comment" : "ModulusOfZmodnZObj: for element in Z\/pZ (prime)","filters" : [["IsFFE","IsZmodnZObj"]]},{"rank" : 15,"comment" : "ModulusOfZmodnZObj: for FFE","filters" : [["IsFFE"]]},{"rank" : 15,"comment" : "ModulusOfZmodnZObj: for element in Z\/nZ (nonprime)","filters" : [["IsZmodnZObjNonprime"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ModulusOfZmodnZObj)","type" : "GAP_Operation","filters" : [[["IsZmodnZObj"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ModulusOfZmodnZObj): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ModulusOfZmodnZObj): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ModulusOfZmodnZObj)","type" : "GAP_Operation","filters" : [[["IsZmodnZObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cyclotomic","type" : "GAP_Operation","filters" : [[["IsZmodnZepsObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "Cyclotomic: system getter","filters" : [["IsAttributeStoringRep","Tester(Cyclotomic)"]]},{"rank" : 13,"comment" : "Cyclotomic: zmodnze : for element in Z\/nZ(m) (ZmodnZepsRep)","filters" : [["IsZmodnZepsObj","IsZmodnZepsRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Cyclotomic)","type" : "GAP_Operation","filters" : [[["IsZmodnZepsObj"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Cyclotomic): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Cyclotomic): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Cyclotomic)","type" : "GAP_Operation","filters" : [[["IsZmodnZepsObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRingOfIntegralCyclotomics","type" : "GAP_Operation","filters" : [[["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20031,"comment" : "IsRingOfIntegralCyclotomics: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRingOfIntegralCyclotomics)"]]},{"rank" : -25,"comment" : "IsRingOfIntegralCyclotomics: default method requiring categories and checking properties","filters" : [["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRingOfIntegralCyclotomics)","type" : "GAP_Operation","filters" : [[["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRingOfIntegralCyclotomics): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRingOfIntegralCyclotomics): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRingOfIntegralCyclotomics)","type" : "GAP_Operation","filters" : [[["IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RoundCyc","type" : "GAP_Operation","filters" : [[["IsCyclotomic"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "RoundCyc: Integer","filters" : [["IsInt"]]},{"rank" : 17,"comment" : "RoundCyc: Rational","filters" : [["IsRat"]]},{"rank" : 15,"comment" : "RoundCyc: general cyclotomic","filters" : [["IsCyclotomic"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RoundCycDown","type" : "GAP_Operation","filters" : [[["IsCyclotomic"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "RoundCycDown: Integer","filters" : [["IsInt"]]},{"rank" : 17,"comment" : "RoundCycDown: Rational","filters" : [["IsRat"]]},{"rank" : 15,"comment" : "RoundCycDown: general cyclotomic","filters" : [["IsCyclotomic"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GaloisMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "GaloisMat: system getter","filters" : [["IsAttributeStoringRep","Tester(GaloisMat)"]]},{"rank" : 42,"comment" : "GaloisMat: for a matrix of cyclotomics","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GaloisMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GaloisMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GaloisMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GaloisMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RationalizedMat","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "RationalizedMat: system getter","filters" : [["IsAttributeStoringRep","Tester(RationalizedMat)"]]},{"rank" : 30,"comment" : "RationalizedMat: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 17,"comment" : "RationalizedMat: for an empty list","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RationalizedMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RationalizedMat): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RationalizedMat): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RationalizedMat)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNumberField","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "IsNumberField: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNumberField)"]]},{"rank" : 52,"comment" : "IsNumberField: for a field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "IsNumberField: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNumberField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNumberField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNumberField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNumberField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAbelianNumberField","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "IsAbelianNumberField: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAbelianNumberField)"]]},{"rank" : 52,"comment" : "IsAbelianNumberField: for a field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "IsAbelianNumberField: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAbelianNumberField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAbelianNumberField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAbelianNumberField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAbelianNumberField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCyclotomicField","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20054,"comment" : "IsCyclotomicField: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCyclotomicField)"]]},{"rank" : 54,"comment" : "IsCyclotomicField: for number fields","filters" : [["IsNumberField","Tester(IsNumberField)"]]},{"rank" : 52,"comment" : "IsCyclotomicField: for a field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -100,"comment" : "IsCyclotomicField: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsNearAdditiveMagma","IsNearAdditiveGroup","IsEuclideanRing"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCyclotomicField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCyclotomicField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCyclotomicField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCyclotomicField)","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GaloisStabilizer","type" : "GAP_Operation","filters" : [[["IsAbelianNumberField","Tester(IsAbelianNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20059,"comment" : "GaloisStabilizer: system getter","filters" : [["IsAttributeStoringRep","Tester(GaloisStabilizer)"]]},{"rank" : 0,"comment" : "GaloisStabilizer: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GaloisStabilizer)","type" : "GAP_Operation","filters" : [[["IsAbelianNumberField","Tester(IsAbelianNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GaloisStabilizer): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GaloisStabilizer): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GaloisStabilizer)","type" : "GAP_Operation","filters" : [[["IsAbelianNumberField","Tester(IsAbelianNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentOfPowering","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "ExponentOfPowering: system getter","filters" : [["IsAttributeStoringRep","Tester(ExponentOfPowering)"]]},{"rank" : 17,"comment" : "ExponentOfPowering: for an identity mapping","filters" : [["IsOne","Tester(IsOne)","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 14,"comment" : "ExponentOfPowering: for an ANFAutomorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsANFAutomorphismRep"]]},{"rank" : 11,"comment" : "ExponentOfPowering: for a mapping (check whether it is the identity mapping)","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 0,"comment" : "ExponentOfPowering: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ExponentOfPowering)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExponentOfPowering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExponentOfPowering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExponentOfPowering)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Valuation","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 14,"comment" : "Valuation","filters" : [["IsPadicExtensionNumber"]]},{"rank" : 14,"comment" : "Valuation","filters" : [["IsPurePadicNumber"]]}],"2args" : [{"rank" : 36,"comment" : "Valuation: for two integers","filters" : [["IsInt"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PadicNumber","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsPadicNumber)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 27,"comment" : "PadicNumber: for a pure p-adic family and a list","filters" : [["CategoryFamily(IsPurePadicNumber)"],["CategoryCollections(IsCyclotomic)"]]},{"rank" : 22,"comment" : "PadicNumber: for a p-adic extension family and a rational","filters" : [["CategoryFamily(IsPadicExtensionNumber)"],["IsRat"]]},{"rank" : 22,"comment" : "PadicNumber: for a pure p-adic family and a rational","filters" : [["CategoryFamily(IsPurePadicNumber)"],["IsRat"]]},{"rank" : 7,"comment" : "PadicNumber: for a p-adic extension family and a list","filters" : [["CategoryFamily(IsPadicExtensionNumber)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ShiftedPadicNumber","type" : "GAP_Operation","filters" : [[["IsPadicNumber"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 31,"comment" : "ShiftedPadicNumber","filters" : [["IsPadicNumber"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsRing","type" : "GAP_Operation","filters" : [[["IsPolynomialRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20030,"comment" : "CoefficientsRing: system getter","filters" : [["IsAttributeStoringRep","Tester(CoefficientsRing)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoefficientsRing)","type" : "GAP_Operation","filters" : [[["IsPolynomialRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoefficientsRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoefficientsRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoefficientsRing)","type" : "GAP_Operation","filters" : [[["IsPolynomialRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Indeterminate","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 37,"comment" : "Indeterminate: number 1","filters" : [["IsFloatPseudoField"]]},{"rank" : 26,"comment" : "Indeterminate: number 1","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"2args" : [{"rank" : 56,"comment" : "Indeterminate: number","filters" : [["IsFloatPseudoField"],["IsInt","IsPosRat"]]},{"rank" : 45,"comment" : "Indeterminate: number","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]]},{"rank" : 42,"comment" : "Indeterminate: number, name","filters" : [["IsFloatPseudoField"],["IsString"]]},{"rank" : 39,"comment" : "Indeterminate: number, avoid","filters" : [["IsFloatPseudoField"],["IsList"]]},{"rank" : 31,"comment" : "Indeterminate: number, name","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsString"]]},{"rank" : 28,"comment" : "Indeterminate: number, avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]},{"rank" : 23,"comment" : "Indeterminate","filters" : [["CategoryFamily(IsFloat)"],["IsInt","IsPosRat"]]},{"rank" : 20,"comment" : "Indeterminate: fam,number","filters" : [["IsFamily"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 44,"comment" : "Indeterminate: number, name, avoid","filters" : [["IsFloatPseudoField"],["IsString"],["IsList"]]},{"rank" : 33,"comment" : "Indeterminate: number, name, avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsString"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnivariatePolynomialRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "UnivariatePolynomialRing: indet 1","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"2args" : [{"rank" : 45,"comment" : "UnivariatePolynomialRing: indet number","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]]},{"rank" : 31,"comment" : "UnivariatePolynomialRing: name","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsString"]]},{"rank" : 28,"comment" : "UnivariatePolynomialRing: avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]}],"3args" : [{"rank" : 33,"comment" : "UnivariatePolynomialRing: name,avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsString"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndeterminatesOfPolynomialRing","type" : "GAP_Operation","filters" : [[["IsPolynomialRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20030,"comment" : "IndeterminatesOfPolynomialRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IndeterminatesOfPolynomialRing)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndeterminatesOfPolynomialRing)","type" : "GAP_Operation","filters" : [[["IsPolynomialRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndeterminatesOfPolynomialRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndeterminatesOfPolynomialRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndeterminatesOfPolynomialRing)","type" : "GAP_Operation","filters" : [[["IsPolynomialRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PolynomialRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "PolynomialRing","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"2args" : [{"rank" : 45,"comment" : "PolynomialRing: rank","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "PolynomialRing: indetlist","filters" : [["IsFloatPseudoField"],["IsList"]]},{"rank" : 31,"comment" : "PolynomialRing: name","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsString"]]},{"rank" : 29,"comment" : "PolynomialRing: indetlist","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]},{"rank" : 28,"comment" : "PolynomialRing: names","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]}],"3args" : [{"rank" : 47,"comment" : "PolynomialRing: rank,avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"],["IsList"]]},{"rank" : 30,"comment" : "PolynomialRing: names,avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalPolynomial","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsAdditiveElement","IsMultiplicativeElement"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "MinimalPolynomial: supply field and indeterminate 1","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [{"rank" : 49,"comment" : "MinimalPolynomial: supply field","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsInt","IsPosRat"]]},{"rank" : 32,"comment" : "MinimalPolynomial: supply indeterminate 1","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [{"rank" : 102,"comment" : "MinimalPolynomial: spinning over field","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsOrdinaryMatrix"],["IsInt","IsPosRat"]]},{"rank" : 101,"comment" : "MinimalPolynomial: for floats","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsFloat"],["IsInt","IsPosRat"]]},{"rank" : 88,"comment" : "MinimalPolynomial","filters" : [["IsPrimeField","Tester(IsPrimeField)"],["IsFFE","IsCoeffsModConwayPolRep"],["IsInt","IsPosRat"]]},{"rank" : 86,"comment" : "MinimalPolynomial: AlgElm","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsAlgebraicElement"],["IsInt","IsPosRat"]]},{"rank" : 85,"comment" : "MinimalPolynomial: finite field, finite field element, and indet. number","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]},{"rank" : 81,"comment" : "MinimalPolynomial: for field, scalar, and indet. number","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FunctionField","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "FunctionField","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"2args" : [{"rank" : 45,"comment" : "FunctionField: rank","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]]},{"rank" : 29,"comment" : "FunctionField: indetlist","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]},{"rank" : 28,"comment" : "FunctionField: names","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]}],"3args" : [{"rank" : 47,"comment" : "FunctionField: rank,avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"],["IsList"]]},{"rank" : 30,"comment" : "FunctionField: names,avoid","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SplittingField","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "SplittingField: system getter","filters" : [["IsAttributeStoringRep","Tester(SplittingField)"]]},{"rank" : 46,"comment" : "SplittingField: use MeatAxe","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 19,"comment" : "SplittingField: rational polynomials","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 19,"comment" : "SplittingField: finite field polynomials","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "SplittingField: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SplittingField)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"],[]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SplittingField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SplittingField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SplittingField)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IrrFacsPol","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "IrrFacsPol: system getter","filters" : [["IsAttributeStoringRep","Tester(IrrFacsPol)"]]},{"rank" : 14,"comment" : "IrrFacsPol","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "IrrFacsPol: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IrrFacsPol)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IrrFacsPol): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IrrFacsPol): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IrrFacsPol)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorsSquarefree","type" : "GAP_Operation","filters" : [[["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 49,"comment" : "FactorsSquarefree: univariate rational poly","filters" : [["IsRationalsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRecord"]]},{"rank" : 48,"comment" : "FactorsSquarefree: for a polynomial over a field of cyclotomics","filters" : [["IsAbelianNumberFieldPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRecord"]]},{"rank" : 48,"comment" : "FactorsSquarefree: polynomial\/alg. ext.","filters" : [["IsAlgebraicExtensionPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRecord"]]},{"rank" : 48,"comment" : "FactorsSquarefree: univariate polynomial over finite field","filters" : [["IsFiniteFieldPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitivePolynomial","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 65,"comment" : "IsPrimitivePolynomial: for a (finite) field, and a polynomial","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsRationalFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimitivePolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "PrimitivePolynomial: univariate polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 14,"comment" : "PrimitivePolynomial: rational polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimizedBombieriNorm","type" : "GAP_Operation","filters" : [[["IsRationalFunctionsFamilyElement","IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "MinimizedBombieriNorm: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimizedBombieriNorm)"]]},{"rank" : 17,"comment" : "MinimizedBombieriNorm","filters" : [["IsRationalFunctionsFamilyElement","IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "MinimizedBombieriNorm: default method requiring categories and checking properties","filters" : [["IsRationalFunctionsFamilyElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimizedBombieriNorm)","type" : "GAP_Operation","filters" : [[["IsRationalFunctionsFamilyElement","IsPolynomial","Tester(IsPolynomial)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimizedBombieriNorm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimizedBombieriNorm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimizedBombieriNorm)","type" : "GAP_Operation","filters" : [[["IsRationalFunctionsFamilyElement","IsPolynomial","Tester(IsPolynomial)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlgebraicElementsFamilies","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "AlgebraicElementsFamilies: system getter","filters" : [["IsAttributeStoringRep","Tester(AlgebraicElementsFamilies)"]]},{"rank" : 19,"comment" : "AlgebraicElementsFamilies","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "AlgebraicElementsFamilies: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AlgebraicElementsFamilies)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AlgebraicElementsFamilies): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AlgebraicElementsFamilies): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AlgebraicElementsFamilies)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlgebraicElementsFamily","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "AlgebraicElementsFamily: generic","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlgebraicExtension","type" : "GAP_Operation","filters" : [[["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "AlgebraicExtension: generic","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "AlgebraicExtension:  fallback method to test conditions","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsRationalFunction"]]}],"3args" : [{"rank" : 76,"comment" : "AlgebraicExtension: with name","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsString"]]},{"rank" : 0,"comment" : "AlgebraicExtension:  fallback method to test conditions","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsRationalFunction"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaxNumeratorCoeffAlgElm","type" : "GAP_Operation","filters" : [[["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 17,"comment" : "MaxNumeratorCoeffAlgElm: algebraic element","filters" : [["IsAlgebraicElement","IsKroneckerConstRep"]]},{"rank" : 17,"comment" : "MaxNumeratorCoeffAlgElm: algebraic element","filters" : [["IsAlgebraicElement","IsAlgBFRep"]]},{"rank" : 17,"comment" : "MaxNumeratorCoeffAlgElm: rational","filters" : [["IsRat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefectApproximation","type" : "GAP_Operation","filters" : [[["IsAlgebraicExtension"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20055,"comment" : "DefectApproximation: system getter","filters" : [["IsAttributeStoringRep","Tester(DefectApproximation)"]]},{"rank" : 53,"comment" : "DefectApproximation: Algebraic Extension","filters" : [["IsAlgebraicExtension"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DefectApproximation)","type" : "GAP_Operation","filters" : [[["IsAlgebraicExtension"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DefectApproximation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DefectApproximation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DefectApproximation)","type" : "GAP_Operation","filters" : [[["IsAlgebraicExtension"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Unknown","type" : "GAP_Operation","filters" : [[],[["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "Unknown: for positive integer","filters" : [["IsInt","IsPosRat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MappedWord","type" : "GAP_Operation","filters" : [[["IsWord"],["CategoryCollections(IsWord)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 123,"comment" : "MappedWord: for a straight line program word, and two lists","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"],["CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]},{"rank" : 22,"comment" : "MappedWord: for fp group element","filters" : [["IsPackedElementDefaultRep"],["IsList","CategoryCollections(IsElementOfFpGroup)"],["IsList"]]},{"rank" : 20,"comment" : "MappedWord: for a letter assoc. word, a homogeneous list, and a list","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]},{"rank" : 20,"comment" : "MappedWord: for a syllable assoc. word, a homogeneous list, and a list","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]},{"rank" : 16,"comment" : "MappedWord: for a nonassoc. word, a homogeneous list, and a list","filters" : [["IsNonassocWord"],["CategoryCollections(IsNonassocWord)"],["IsList"]]},{"rank" : 5,"comment" : "MappedWord: empty generators list","filters" : [[],["IsEmpty","Tester(IsEmpty)"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFreeSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20021,"comment" : "IsFreeSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFreeSemigroup)"]]},{"rank" : -5,"comment" : "IsFreeSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections((IsWord and IsAssociativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFreeSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFreeSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFreeSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFreeSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections((IsWord and IsAssociativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFreeMonoid","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "IsFreeMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFreeMonoid)"]]},{"rank" : -4,"comment" : "IsFreeMonoid: default method requiring categories and checking properties","filters" : [["IsMagmaWithOne","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFreeMonoid)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFreeMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFreeMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFreeMonoid)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AssignGeneratorVariables","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "AssignGeneratorVariables: default method for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 29,"comment" : "AssignGeneratorVariables: default method for a LOR","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsDistributiveLOpDSum","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 27,"comment" : "AssignGeneratorVariables: default method for a ring","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(GeneratorsOfRing)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Subword","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 145,"comment" : "Subword: for a straight line program word","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"],["IsInt"],["IsInt"]]},{"rank" : 43,"comment" : "Subword: for letter associative word and two positions","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsInt","IsPosRat"],["IsInt"]]},{"rank" : 43,"comment" : "Subword: for syllable associative word and two positions","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsInt","IsPosRat"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionWord","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10,"comment" : "PositionWord: for two associative words,start at 1","filters" : [["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]}],"3args" : [{"rank" : 30,"comment" : "PositionWord: for two associative words and a positive integer, using letters","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"]]},{"rank" : 30,"comment" : "PositionWord: for two associative words and a positive integer, using syllables","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubstitutedWord","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsAssociativeElement","IsWord"]],[["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"],["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 48,"comment" : "SubstitutedWord: for assoc. word, two positive integers, and assoc. word","filters" : [["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsAssociativeElement","IsWord"]]},{"rank" : 34,"comment" : "SubstitutedWord: for three associative words","filters" : [["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"],["IsAssociativeElement","IsWord"]]}],"5args" : [],"6args" : []}},{"name" : "EliminatedWord","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 15,"comment" : "EliminatedWord: for three associative words, using the external rep.","filters" : [["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentSumWord","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "ExponentSumWord: letter rep as.word, gen","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsAssociativeElement","IsWord"]]},{"rank" : 11,"comment" : "ExponentSumWord: syllable rep as.word, gen","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsAssociativeElement","IsWord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumberSyllables","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "NumberSyllables: system getter","filters" : [["IsAttributeStoringRep","Tester(NumberSyllables)"]]},{"rank" : 109,"comment" : "NumberSyllables: for a straight line program word","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"]]},{"rank" : 8,"comment" : "NumberSyllables: for an inf. bits assoc. word","filters" : [["IsInfBitsAssocWord"]]},{"rank" : 8,"comment" : "NumberSyllables: for a 32 bits assoc. word","filters" : [["Is32BitsAssocWord"]]},{"rank" : 8,"comment" : "NumberSyllables: for a 16 bits assoc. word","filters" : [["Is16BitsAssocWord"]]},{"rank" : 8,"comment" : "NumberSyllables: for an 8 bits assoc. word","filters" : [["Is8BitsAssocWord"]]},{"rank" : 6,"comment" : "NumberSyllables: assoc word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]},{"rank" : 6,"comment" : "NumberSyllables: for an assoc. word in syllable rep","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NumberSyllables)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NumberSyllables): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NumberSyllables): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NumberSyllables)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentSyllable","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 128,"comment" : "ExponentSyllable: for a straight line program word","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"],["IsInt","IsPosRat"]]},{"rank" : 27,"comment" : "ExponentSyllable: for an inf. bits assoc. word, and a pos. integer","filters" : [["IsInfBitsAssocWord"],["IsInt","IsPosRat"]]},{"rank" : 27,"comment" : "ExponentSyllable: for a 32 bits assoc. word, and pos. integer","filters" : [["Is32BitsAssocWord"],["IsInt","IsPosRat"]]},{"rank" : 27,"comment" : "ExponentSyllable: for a 16 bits assoc. word, and pos. integer","filters" : [["Is16BitsAssocWord"],["IsInt","IsPosRat"]]},{"rank" : 27,"comment" : "ExponentSyllable: for an 8 bits assoc. word, and a pos. integer","filters" : [["Is8BitsAssocWord"],["IsInt","IsPosRat"]]},{"rank" : 25,"comment" : "ExponentSyllable: assoc word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsInt","IsPosRat"]]},{"rank" : 25,"comment" : "ExponentSyllable: for an assoc. word in syllable rep, and a positive integer","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorSyllable","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 128,"comment" : "GeneratorSyllable: for a straight line program word","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"],["IsInt","IsPosRat"]]},{"rank" : 27,"comment" : "GeneratorSyllable: for a 32 bits assoc. word, and pos. integer","filters" : [["Is32BitsAssocWord"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "GeneratorSyllable: assoc word in B letter rep","filters" : [["IsAssociativeElement","IsWord","IsBLetterAssocWordRep"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "GeneratorSyllable: assoc word in W letter rep","filters" : [["IsAssociativeElement","IsWord","IsWLetterAssocWordRep"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "GeneratorSyllable: for an inf. bits assoc. word, and an integer","filters" : [["IsInfBitsAssocWord"],["IsInt"]]},{"rank" : 26,"comment" : "GeneratorSyllable: for a 16 bits assoc. word, and integer","filters" : [["Is16BitsAssocWord"],["IsInt"]]},{"rank" : 26,"comment" : "GeneratorSyllable: for an 8 bits assoc. word, and an integer","filters" : [["Is8BitsAssocWord"],["IsInt"]]},{"rank" : 25,"comment" : "GeneratorSyllable: for an assoc. word in syllable rep, and a positive integer","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubSyllables","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 42,"comment" : "SubSyllables: for associative word and two positions, using ext rep.","filters" : [["IsAssociativeElement","IsWord"],["IsInt","IsPosRat"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LetterRepAssocWord","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 109,"comment" : "LetterRepAssocWord: for a straight line program word","filters" : [["IsAssociativeElement","IsWord","IsStraightLineProgElm"]]},{"rank" : 7,"comment" : "LetterRepAssocWord: B letter rep","filters" : [["IsBLetterAssocWordRep"]]},{"rank" : 7,"comment" : "LetterRepAssocWord: W letter rep","filters" : [["IsWLetterAssocWordRep"]]},{"rank" : 6,"comment" : "LetterRepAssocWord: syllable rep","filters" : [["IsSyllableAssocWordRep"]]}],"2args" : [{"rank" : 10,"comment" : "LetterRepAssocWord: letter rep,gens","filters" : [["IsLetterAssocWordRep"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "LetterRepAssocWord: syllable rep, generators","filters" : [["IsSyllableAssocWordRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AssocWordByLetterRep","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "AssocWordByLetterRep: B letter words family","filters" : [["IsBLetterWordsFamily"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "AssocWordByLetterRep: W letter words family","filters" : [["IsWLetterWordsFamily"],["IsHomogeneousList"]]},{"rank" : 7,"comment" : "AssocWordByLetterRep: family, list: syllables","filters" : [["IsSyllableWordsFamily"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 11,"comment" : "AssocWordByLetterRep: letter words family","filters" : [["IsLetterWordsFamily"],["IsHomogeneousList"],["IsHomogeneousList"]]},{"rank" : 11,"comment" : "AssocWordByLetterRep: family, list, gens: syllables","filters" : [["IsSyllableWordsFamily"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SyllableRepAssocWord","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "SyllableRepAssocWord: assoc word in syllable rep","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]]},{"rank" : 5,"comment" : "SyllableRepAssocWord: assoc word: via extrep","filters" : [["IsAssociativeElement","IsWord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentSums","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "ExponentSums: for an inf. bits assoc. word","filters" : [["IsInfBitsAssocWord"]]},{"rank" : 8,"comment" : "ExponentSums: for a 32 bits assoc. word","filters" : [["Is32BitsAssocWord"]]},{"rank" : 8,"comment" : "ExponentSums: for a 16 bits assoc. word","filters" : [["Is16BitsAssocWord"]]},{"rank" : 8,"comment" : "ExponentSums: for an 8 bits assoc. word","filters" : [["Is8BitsAssocWord"]]},{"rank" : 6,"comment" : "ExponentSums: assoc word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]}],"2args" : [{"rank" : 38,"comment" : "ExponentSums: for a group and an assoc. word in syllable rep","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsAssociativeElement","IsWord"]]}],"3args" : [{"rank" : 45,"comment" : "ExponentSums: for an inf. bits assoc. word, and two integers","filters" : [["IsInfBitsAssocWord"],["IsInt"],["IsInt"]]},{"rank" : 44,"comment" : "ExponentSums: for a 32 bits assoc. word","filters" : [["Is32BitsAssocWord"],["IsInt"],["IsInt"]]},{"rank" : 44,"comment" : "ExponentSums: for a 16 bits assoc. word, and two integers","filters" : [["Is16BitsAssocWord"],["IsInt"],["IsInt"]]},{"rank" : 44,"comment" : "ExponentSums: for an 8 bits assoc. word, and two integers","filters" : [["Is8BitsAssocWord"],["IsInt"],["IsInt"]]},{"rank" : 42,"comment" : "ExponentSums: assoc word in letter rep,ints","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RenumberedWord","type" : "GAP_Operation","filters" : [[["IsAssociativeElement","IsWord"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "RenumberedWord: associative words in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"],["IsList"]]},{"rank" : 8,"comment" : "RenumberedWord: associative words in syllable rep","filters" : [["IsAssociativeElement","IsWord","IsSyllableAssocWordRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseDomain","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "BaseDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(BaseDomain)"]]},{"rank" : 15,"comment" : "BaseDomain: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "BaseDomain: for an 8bit matrix","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "BaseDomain: for a gf2 matrix","filters" : [["IsGF2MatrixRep"]]},{"rank" : 11,"comment" : "BaseDomain: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "BaseDomain: for an 8bit vector","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "BaseDomain: for a gf2 vector","filters" : [["IsGF2VectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BaseDomain)","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],[]],[["IsMatrixObj"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BaseDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BaseDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BaseDomain)","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionLastNonZero","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"]],[["IsMatrixObj"]],[["IsMatrixObj"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "PositionLastNonZero: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 12,"comment" : "PositionLastNonZero: for a matrix obj","filters" : [["IsMatrixObj"]]},{"rank" : 11,"comment" : "PositionLastNonZero: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 9,"comment" : "PositionLastNonZero: for a row vector obj","filters" : [["IsRowVectorObj"]]}],"2args" : [{"rank" : 33,"comment" : "PositionLastNonZero: for a plist matrix, and a position","filters" : [["IsPlistMatrixRep"],["IsInt"]]},{"rank" : 31,"comment" : "PositionLastNonZero: for a matrix obj, and an index","filters" : [["IsMatrixObj"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Unpack","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"]],[["IsRowListMatrix"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "Unpack: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "Unpack: for an 8bit matrix","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "Unpack: for a gf2 matrix","filters" : [["IsGF2MatrixRep"]]},{"rank" : 11,"comment" : "Unpack: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "Unpack: for an 8bit vector","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "Unpack: for a gf2 vector","filters" : [["IsGF2VectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtractSubVector","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "ExtractSubVector: generic method","filters" : [["IsRowVectorObj"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroVector","type" : "GAP_Operation","filters" : [[["IsInt"],["IsRowVectorObj"]],[["IsInt"],["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "ZeroVector: for an integer and a plist matrix","filters" : [["IsInt"],["IsPlistMatrixRep"]]},{"rank" : 33,"comment" : "ZeroVector: for an int and an 8bit matrix","filters" : [["IsInt"],["Is8BitMatrixRep"]]},{"rank" : 33,"comment" : "ZeroVector: for an int and a gf2 matrix","filters" : [["IsInt"],["IsGF2MatrixRep"]]},{"rank" : 29,"comment" : "ZeroVector: for an integer and a plist vector","filters" : [["IsInt"],["IsPlistVectorRep"]]},{"rank" : 29,"comment" : "ZeroVector: for an int and an 8bit vector","filters" : [["IsInt"],["Is8BitVectorRep"]]},{"rank" : 29,"comment" : "ZeroVector: for an int and a gf2 vector","filters" : [["IsInt"],["IsGF2VectorRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Vector","type" : "GAP_Operation","filters" : [[["IsList"],["IsRowVectorObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 40,"comment" : "Vector: for a plist of finite field elements and an 8bitvector","filters" : [["IsList","CategoryCollections(IsFFE)"],["Is8BitVectorRep"]]},{"rank" : 40,"comment" : "Vector: for a list of gf2 elements and a gf2 vector","filters" : [["IsList","CategoryCollections(IsFFE)"],["IsGF2VectorRep"]]},{"rank" : 32,"comment" : "Vector: for a plain list and a plist vector","filters" : [["IsList","IsPlistRep"],["IsPlistVectorRep"]]},{"rank" : 13,"comment" : "Vector: for a list and a plist vector","filters" : [["IsList"],["IsPlistVectorRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConstructingFilter","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"]],[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 16,"comment" : "ConstructingFilter: for a checking plist matrix","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"]]},{"rank" : 15,"comment" : "ConstructingFilter: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "ConstructingFilter: for an 8bit matrix","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "ConstructingFilter: for a gf2 matrix","filters" : [["IsGF2MatrixRep"]]},{"rank" : 12,"comment" : "ConstructingFilter: for a checking plist vector","filters" : [["IsPlistVectorRep","IsCheckingVector"]]},{"rank" : 11,"comment" : "ConstructingFilter: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "ConstructingFilter: for an 8bit vector","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "ConstructingFilter: for a gf2 vector","filters" : [["IsGF2VectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CompatibleMatrix","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 11,"comment" : "CompatibleMatrix: for a plist vector","filters" : [["IsPlistVectorRep"]]},{"rank" : 11,"comment" : "CompatibleMatrix: for an 8bit vector","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "CompatibleMatrix: for a gf2 vector","filters" : [["IsGF2VectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewRowVector","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -11,"comment" : "NewRowVector: for Is8BitVectorRep, GF(q), and a list","filters" : [["Is8BitVectorRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList"]]},{"rank" : -11,"comment" : "NewRowVector: for IsGF2VectorRep, GF(2), and a list","filters" : [["IsGF2VectorRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsList"]]},{"rank" : -12,"comment" : "NewRowVector: for IsPlistVectorRep, a ring, and a list","filters" : [["IsPlistVectorRep","IsCheckingVector"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewZeroVector","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -11,"comment" : "NewZeroVector: for Is8BitVectorRep, GF(q), and an int","filters" : [["Is8BitVectorRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]},{"rank" : -11,"comment" : "NewZeroVector: for IsGF2VectorRep, GF(2), and an int","filters" : [["IsGF2VectorRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]},{"rank" : -12,"comment" : "NewZeroVector: for IsPlistVectorRep, a ring, and an int","filters" : [["IsPlistVectorRep","IsCheckingVector"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ChangedBaseDomain","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]],[["IsMatrixObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "ChangedBaseDomain: for an 8bit matrix and a finite field","filters" : [["Is8BitMatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 71,"comment" : "ChangedBaseDomain: for a gf2 matrix and a finite field","filters" : [["IsGF2MatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 67,"comment" : "ChangedBaseDomain: for an 8bit vector and a finite field","filters" : [["Is8BitVectorRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 67,"comment" : "ChangedBaseDomain: for a gf2 vector and a finite field","filters" : [["IsGF2VectorRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 42,"comment" : "ChangedBaseDomain: for a checking plist matrix, and a domain","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 41,"comment" : "ChangedBaseDomain: for a plist matrix, and a domain","filters" : [["IsPlistMatrixRep"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 38,"comment" : "ChangedBaseDomain: for a checking plist vector, and a domain","filters" : [["IsPlistVectorRep","IsCheckingVector"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 37,"comment" : "ChangedBaseDomain: for a plist vector, and a domain","filters" : [["IsPlistVectorRep"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Randomize","type" : "GAP_Operation","filters" : [[["IsMutable","IsRowVectorObj"]],[["IsMutable","IsRowVectorObj"],["IsRandomSource"]],[["IsMutable","IsMatrixObj"]],[["IsMutable","IsMatrixObj"],["IsRandomSource"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 16,"comment" : "Randomize: for a mutable plist matrix","filters" : [["IsMutable","IsPlistMatrixRep"]]},{"rank" : 16,"comment" : "Randomize: for a mutable 8bit matrix","filters" : [["IsMutable","Is8BitMatrixRep"]]},{"rank" : 16,"comment" : "Randomize: for a mutable gf2 matrix","filters" : [["IsMutable","IsGF2MatrixRep"]]},{"rank" : 12,"comment" : "Randomize: for a mutable plist vector","filters" : [["IsMutable","IsPlistVectorRep"]]},{"rank" : 12,"comment" : "Randomize: for a mutable 8bit vector","filters" : [["IsMutable","Is8BitVectorRep"]]},{"rank" : 12,"comment" : "Randomize: for a mutable gf2 vector","filters" : [["IsMutable","IsGF2VectorRep"]]}],"2args" : [{"rank" : 18,"comment" : "Randomize: for a mutable 8bit matrix, and a random source","filters" : [["IsMutable","Is8BitMatrixRep"],["IsRandomSource"]]},{"rank" : 18,"comment" : "Randomize: for a mutable gf2 matrix, and a random source","filters" : [["IsMutable","IsGF2MatrixRep"],["IsRandomSource"]]},{"rank" : 14,"comment" : "Randomize: for a mutable 8bit vector and a random source","filters" : [["IsMutable","Is8BitVectorRep"],["IsRandomSource"]]},{"rank" : 14,"comment" : "Randomize: for a mutable gf2 vector and a random source","filters" : [["IsMutable","IsGF2VectorRep"],["IsRandomSource"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CopySubVector","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],["IsMutable","IsRowVectorObj"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 83,"comment" : "CopySubVector: for two gf2 vectors, and two ranges","filters" : [["IsGF2VectorRep"],["IsMutable","IsGF2VectorRep"],["IsRange"],["IsRange"]]},{"rank" : 28,"comment" : "CopySubVector: for two plist vectors and two lists","filters" : [["IsPlistVectorRep"],["IsMutable","IsPlistVectorRep","IsCheckingVector"],["IsList"],["IsList"]]},{"rank" : 27,"comment" : "CopySubVector: for two plist vectors and two lists","filters" : [["IsPlistVectorRep"],["IsMutable","IsPlistVectorRep"],["IsList"],["IsList"]]},{"rank" : 27,"comment" : "CopySubVector: for two 8bit vectors, and two lists","filters" : [["Is8BitVectorRep"],["IsMutable","Is8BitVectorRep"],["IsList"],["IsList"]]},{"rank" : 27,"comment" : "CopySubVector: for two gf2 vectors, and two lists","filters" : [["IsGF2VectorRep"],["IsMutable","IsGF2VectorRep"],["IsList"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "WeightOfVector","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 11,"comment" : "WeightOfVector: for an 8bit vector","filters" : [["Is8BitVectorRep"]]},{"rank" : 11,"comment" : "WeightOfVector: for a gf2 vector","filters" : [["IsGF2VectorRep"]]},{"rank" : 9,"comment" : "WeightOfVector: generic method","filters" : [["IsRowVectorObj"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DistanceOfVectors","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],["IsRowVectorObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "DistanceOfVectors: for two 8bit vectors","filters" : [["Is8BitVectorRep"],["Is8BitVectorRep"]]},{"rank" : 22,"comment" : "DistanceOfVectors: for two gf2 vectors","filters" : [["IsGF2VectorRep"],["IsGF2VectorRep"]]},{"rank" : 18,"comment" : "DistanceOfVectors: generic method","filters" : [["IsRowVectorObj"],["IsRowVectorObj"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RowLength","type" : "GAP_Operation","filters" : [[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20015,"comment" : "RowLength: system getter","filters" : [["IsAttributeStoringRep","Tester(RowLength)"]]},{"rank" : 15,"comment" : "RowLength: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "RowLength: for an 8bit matrix","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "RowLength: for a gf2 matrix","filters" : [["IsGF2MatrixRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RowLength)","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RowLength): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RowLength): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RowLength)","type" : "GAP_Operation","filters" : [[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtractSubMatrix","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 19,"comment" : "ExtractSubMatrix: for a plist matrix, and two lists","filters" : [["IsPlistMatrixRep"],["IsList"],["IsList"]]},{"rank" : 19,"comment" : "ExtractSubMatrix: for an 8bit matrix, and two lists","filters" : [["Is8BitMatrixRep"],["IsList"],["IsList"]]},{"rank" : 19,"comment" : "ExtractSubMatrix: for a gf2 matrix, and two lists","filters" : [["IsGF2MatrixRep"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CopySubMatrix","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsMatrixObj"],["IsList"],["IsList"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : [{"rank" : 94,"comment" : "CopySubMatrix: for two gf2 matrices, two lists and two ranges","filters" : [["IsGF2MatrixRep"],["IsGF2MatrixRep"],["IsList"],["IsList"],["IsRange"],["IsRange"]]},{"rank" : 40,"comment" : "CopySubMatrix: for a plist matrix and a checking plist matrix and four lists","filters" : [["IsPlistMatrixRep"],["IsMutable","IsPlistMatrixRep","IsCheckingMatrix"],["IsList"],["IsList"],["IsList"],["IsList"]]},{"rank" : 39,"comment" : "CopySubMatrix: for two plist matrices and four lists","filters" : [["IsPlistMatrixRep"],["IsMutable","IsPlistMatrixRep"],["IsList"],["IsList"],["IsList"],["IsList"]]},{"rank" : 38,"comment" : "CopySubMatrix: for two 8bit matrices, and four lists","filters" : [["Is8BitMatrixRep"],["Is8BitMatrixRep"],["IsList"],["IsList"],["IsList"],["IsList"]]},{"rank" : 38,"comment" : "CopySubMatrix: for two gf2 matrices, and four lists","filters" : [["IsGF2MatrixRep"],["IsGF2MatrixRep"],["IsList"],["IsList"],["IsList"],["IsList"]]}]}},{"name" : "MatElm","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 53,"comment" : "MatElm: for a plist matrix and two positions","filters" : [["IsPlistMatrixRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "MatElm: for an 8bit matrix and two integers","filters" : [["Is8BitMatrixRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 53,"comment" : "MatElm: for a gf2 matrix and two integers","filters" : [["IsGF2MatrixRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetMatElm","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 68,"comment" : "SetMatElm: for an 8bit matrix, two integers, and a ffe","filters" : [["Is8BitMatrixRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsFFE"]]},{"rank" : 68,"comment" : "SetMatElm: for a gf2 matrix, two integers, and a ffe","filters" : [["IsGF2MatrixRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsFFE"]]},{"rank" : 55,"comment" : "SetMatElm: for a checking plist matrix, two positions, and an object","filters" : [["IsMutable","IsPlistMatrixRep","IsCheckingMatrix"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],[]]},{"rank" : 54,"comment" : "SetMatElm: for a plist matrix, two positions, and an object","filters" : [["IsMutable","IsPlistMatrixRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],[]]}],"5args" : [],"6args" : []}},{"name" : "AddMatrix","type" : "GAP_Operation","filters" : [[["IsMutable","IsMatrixObj"],["IsMatrixObj"]],[["IsMutable","IsMatrixObj"],["IsMatrixObj"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 27,"comment" : "AddMatrix: for two row list matrices","filters" : [["IsMutable","IsRowListMatrix"],["IsRowListMatrix"]]}],"3args" : [{"rank" : 30,"comment" : "AddMatrix: for two row list matrices and a scalar","filters" : [["IsMutable","IsRowListMatrix"],["IsRowListMatrix"],["IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MultMatrix","type" : "GAP_Operation","filters" : [[["IsMutable","IsMatrixObj"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 17,"comment" : "MultMatrix: for a row list matrix","filters" : [["IsMutable","IsRowListMatrix"],["IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProductTransposedMatMat","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 24,"comment" : "ProductTransposedMatMat: generic method","filters" : [["IsMatrixObj"],["IsMatrixObj"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZeroMatrix","type" : "GAP_Operation","filters" : [[["IsInt"],["IsInt"],["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 51,"comment" : "ZeroMatrix: for two integers and a plist matrix","filters" : [["IsInt"],["IsInt"],["IsPlistMatrixRep"]]},{"rank" : 51,"comment" : "ZeroMatrix: for a compressed 8bit matrix","filters" : [["IsInt"],["IsInt"],["Is8BitMatrixRep"]]},{"rank" : 51,"comment" : "ZeroMatrix: for a compressed gf2 matrix","filters" : [["IsInt"],["IsInt"],["IsGF2MatrixRep"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewZeroMatrix","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : -15,"comment" : "NewZeroMatrix: for Is8BitMatrixRep, GF(q), and two ints","filters" : [["Is8BitMatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"],["IsInt"]]},{"rank" : -15,"comment" : "NewZeroMatrix: for IsGF2MatrixRep, GF(2), and two ints","filters" : [["IsGF2MatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"],["IsInt"]]},{"rank" : -16,"comment" : "NewZeroMatrix: for IsPlistMatrixRep, a ring, and two ints","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"],["IsInt"]]}],"5args" : [],"6args" : []}},{"name" : "IdentityMatrix","type" : "GAP_Operation","filters" : [[["IsInt"],["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "IdentityMatrix: for an integer and a plist matrix","filters" : [["IsInt"],["IsPlistMatrixRep"]]},{"rank" : 33,"comment" : "IdentityMatrix: for a compressed 8bit matrix","filters" : [["IsInt"],["Is8BitMatrixRep"]]},{"rank" : 33,"comment" : "IdentityMatrix: for a compressed gf2 matrix","filters" : [["IsInt"],["IsGF2MatrixRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewIdentityMatrix","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -15,"comment" : "NewIdentityMatrix: for Is8BitMatrixRep, GF(q), and an int","filters" : [["Is8BitMatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]},{"rank" : -15,"comment" : "NewIdentityMatrix: for IsGF2MatrixRep, GF(2), and an int","filters" : [["IsGF2MatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]},{"rank" : -16,"comment" : "NewIdentityMatrix: for IsPlistMatrixRep, a ring, and an int","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CompanionMatrix","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 31,"comment" : "CompanionMatrix: for a polynomial and a matrix","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsMatrixObj"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewCompanionMatrix","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -15,"comment" : "NewCompanionMatrix: for IsPlistMatrixRep, a polynomial and a ring","filters" : [["IsPlistMatrixRep"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -15,"comment" : "NewCompanionMatrix: for Is8BitMatrixRep, a polynomial and a ring","filters" : [["Is8BitMatrixRep"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -15,"comment" : "NewCompanionMatrix: for IsGF2MatrixRep, a polynomial and a ring","filters" : [["IsGF2MatrixRep"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -16,"comment" : "NewCompanionMatrix: for IsPlistMatrixRep and IsCheckingMatrix, a polynomial and a ring","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"],["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Matrix","type" : "GAP_Operation","filters" : [[["IsList"],["IsInt"],["IsMatrixObj"]],[["IsList"],["IsMatrixObj"]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "Matrix: system getter","filters" : [["IsAttributeStoringRep","Tester(Matrix)"]]},{"rank" : 18,"comment" : "Matrix: for a Rees 0-matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 18,"comment" : "Matrix: for a Rees matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : -5,"comment" : "Matrix: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsReesMatrixSemigroupElement)"]]}],"2args" : [{"rank" : 14,"comment" : "Matrix: generic convenience method with 2 args","filters" : [["IsList"],["IsMatrixObj"]]}],"3args" : [{"rank" : 35,"comment" : "Matrix: for a list and a plist matrix","filters" : [["IsList"],["IsInt"],["IsPlistMatrixRep"]]},{"rank" : 35,"comment" : "Matrix: for a list of vecs, an integer, and an 8bit mat","filters" : [["IsList"],["IsInt"],["Is8BitMatrixRep"]]},{"rank" : 35,"comment" : "Matrix: for a list of vecs, an integer, and a gf2 mat","filters" : [["IsList"],["IsInt"],["IsGF2MatrixRep"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewMatrix","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : -15,"comment" : "NewMatrix: for Is8BitMatrixRep, GF(q), an int, and a list","filters" : [["Is8BitMatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"],["IsList"]]},{"rank" : -15,"comment" : "NewMatrix: for IsGF2MatrixRep, GF(2), an int, and a list","filters" : [["IsGF2MatrixRep"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"],["IsList"]]},{"rank" : -16,"comment" : "NewMatrix: for IsPlistMatrixRep, a ring, an int, and a list","filters" : [["IsPlistMatrixRep","IsCheckingMatrix"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "CompatibleVector","type" : "GAP_Operation","filters" : [[["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 15,"comment" : "CompatibleVector: for a plist matrix","filters" : [["IsPlistMatrixRep"]]},{"rank" : 15,"comment" : "CompatibleVector: for an 8bit matrix","filters" : [["Is8BitMatrixRep"]]},{"rank" : 15,"comment" : "CompatibleVector: for a gf2 matrix","filters" : [["IsGF2MatrixRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Unfold","type" : "GAP_Operation","filters" : [[["IsMatrixObj"],["IsRowVectorObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "Unfold: for a plist matrix","filters" : [["IsPlistMatrixRep"],["IsPlistVectorRep"]]},{"rank" : 21,"comment" : "Unfold: for a matrix object, and a vector object","filters" : [["IsMatrixObj"],["IsRowVectorObj"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Fold","type" : "GAP_Operation","filters" : [[["IsRowVectorObj"],["IsInt","IsPosRat"],["IsMatrixObj"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 45,"comment" : "Fold: for a plist vector, a positive int, and a plist matrix","filters" : [["IsPlistVectorRep"],["IsInt","IsPosRat"],["IsPlistMatrixRep"]]},{"rank" : 45,"comment" : "Fold: for an 8bit vector, a positive int, and an 8bit matrix","filters" : [["IsRowVectorObj","Is8BitVectorRep"],["IsInt","IsPosRat"],["Is8BitMatrixRep"]]},{"rank" : 45,"comment" : "Fold: for a gf2 vector, a positive int, and a gf2 matrix","filters" : [["IsRowVectorObj","IsGF2VectorRep"],["IsInt","IsPosRat"],["IsGF2MatrixRep"]]},{"rank" : 40,"comment" : "Fold: for a vector, a positive int, and a matrix","filters" : [["IsRowVectorObj"],["IsInt","IsPosRat"],["IsMatrixObj"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBuiltFromAdditiveMagmaWithInverses","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsBuiltFromAdditiveMagmaWithInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBuiltFromAdditiveMagmaWithInverses)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBuiltFromAdditiveMagmaWithInverses)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBuiltFromAdditiveMagmaWithInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBuiltFromAdditiveMagmaWithInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBuiltFromAdditiveMagmaWithInverses)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBuiltFromMagma","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsBuiltFromMagma: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBuiltFromMagma)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBuiltFromMagma)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBuiltFromMagma): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBuiltFromMagma): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBuiltFromMagma)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBuiltFromMagmaWithOne","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsBuiltFromMagmaWithOne: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBuiltFromMagmaWithOne)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBuiltFromMagmaWithOne)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBuiltFromMagmaWithOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBuiltFromMagmaWithOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBuiltFromMagmaWithOne)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBuiltFromMagmaWithInverses","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsBuiltFromMagmaWithInverses: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBuiltFromMagmaWithInverses)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBuiltFromMagmaWithInverses)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBuiltFromMagmaWithInverses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBuiltFromMagmaWithInverses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBuiltFromMagmaWithInverses)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBuiltFromGroup","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsBuiltFromGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBuiltFromGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBuiltFromGroup)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBuiltFromGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBuiltFromGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBuiltFromGroup)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBuiltFromSemigroup","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsBuiltFromSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBuiltFromSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBuiltFromSemigroup)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBuiltFromSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBuiltFromSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBuiltFromSemigroup)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBuiltFromMonoid","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsBuiltFromMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBuiltFromMonoid)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBuiltFromMonoid)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBuiltFromMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBuiltFromMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBuiltFromMonoid)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemigroupOfRewritingSystem","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "SemigroupOfRewritingSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(SemigroupOfRewritingSystem)"]]},{"rank" : 4,"comment" : "SemigroupOfRewritingSystem: for a Knuth Bendix rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemigroupOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemigroupOfRewritingSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemigroupOfRewritingSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemigroupOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MonoidOfRewritingSystem","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "MonoidOfRewritingSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(MonoidOfRewritingSystem)"]]},{"rank" : 4,"comment" : "MonoidOfRewritingSystem: for a Knuth Bendix rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MonoidOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MonoidOfRewritingSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MonoidOfRewritingSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MonoidOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeStructureOfRewritingSystem","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConfluentRws","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "ConfluentRws: system getter","filters" : [["IsAttributeStoringRep","Tester(ConfluentRws)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConfluentRws)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConfluentRws): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConfluentRws): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConfluentRws)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfRws","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "GeneratorsOfRws: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsOfRws)"]]},{"rank" : 18,"comment" : "GeneratorsOfRws","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 14,"comment" : "GeneratorsOfRws","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"]]},{"rank" : 4,"comment" : "GeneratorsOfRws: for a monoid rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)"]]},{"rank" : 4,"comment" : "GeneratorsOfRws: for a monoid rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsOfRws)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "Setter(GeneratorsOfRws)","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsList"]]},{"rank" : 2,"comment" : "Setter(GeneratorsOfRws): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsOfRws): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsOfRws)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumberGeneratorsOfRws","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "NumberGeneratorsOfRws: system getter","filters" : [["IsAttributeStoringRep","Tester(NumberGeneratorsOfRws)"]]},{"rank" : 18,"comment" : "NumberGeneratorsOfRws","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 14,"comment" : "NumberGeneratorsOfRws","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"]]},{"rank" : 2,"comment" : "NumberGeneratorsOfRws","filters" : [["IsRewritingSystem"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NumberGeneratorsOfRws)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "Setter(NumberGeneratorsOfRws)","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsInt"]]},{"rank" : 2,"comment" : "Setter(NumberGeneratorsOfRws): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NumberGeneratorsOfRws): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NumberGeneratorsOfRws)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Rules","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "Rules: system getter","filters" : [["IsAttributeStoringRep","Tester(Rules)"]]},{"rank" : 18,"comment" : "Rules","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 14,"comment" : "Rules: Deep Thought","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"]]},{"rank" : 5,"comment" : "Rules: for a Knuth Bendix rewriting system","filters" : [["IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Rules)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Rules): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Rules): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Rules)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrderingOfRewritingSystem","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "OrderingOfRewritingSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(OrderingOfRewritingSystem)"]]},{"rank" : 5,"comment" : "OrderingOfRewritingSystem: for a Knuth Bendix rewriting system","filters" : [["IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrderingOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrderingOfRewritingSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrderingOfRewritingSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrderingOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsConfluent","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsConfluent: system getter","filters" : [["IsAttributeStoringRep","Tester(IsConfluent)"]]},{"rank" : 43,"comment" : "IsConfluent: for pc group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 15,"comment" : "IsConfluent: method for finite polycylic rewriting systems","filters" : [["IsFinite","Tester(IsFinite)","IsPolycyclicCollector"]]},{"rank" : 13,"comment" : "IsConfluent: FromTheLeftCollector","filters" : [["IsFromTheLeftCollectorRep"]]},{"rank" : 11,"comment" : "IsConfluent: generic method for polycyclic rewriting systems","filters" : [["IsPolycyclicCollector"]]},{"rank" : 2,"comment" : "IsConfluent: for a monoid or a semigroup rewriting system","filters" : [["IsRewritingSystem"]]}],"2args" : [{"rank" : 17,"comment" : "IsConfluent","filters" : [["IsFinite","Tester(IsFinite)","IsPolycyclicCollector"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsConfluent)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsConfluent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsConfluent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsConfluent)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsReduced","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "IsReduced: system getter","filters" : [["IsAttributeStoringRep","Tester(IsReduced)"]]},{"rank" : 6,"comment" : "IsReduced: for a Knuth Bendix rewriting system","filters" : [["IsMutable","IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsReduced)","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsReduced): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsReduced): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsReduced)","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AddRule","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AddRuleReduced","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "AddRuleReduced: for a Knuth Bendix rewriting system and a rule","filters" : [["IsMutable","IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AddGenerators","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "AddGenerators","filters" : [["IsMutable","IsRewritingSystem"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MakeConfluent","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "MakeConfluent: for Knuth Bendix Rewriting System","filters" : [["IsMutable","IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)","IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]},{"rank" : 8,"comment" : "MakeConfluent: for Knuth Bendix Rewriting System","filters" : [["IsMutable","IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)","IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReduceRules","type" : "GAP_Operation","filters" : [[["IsMutable","IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "ReduceRules","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 6,"comment" : "ReduceRules: for a Knuth Bendix rewriting system","filters" : [["IsMutable","IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]},{"rank" : 3,"comment" : "ReduceRules","filters" : [["IsMutable","IsRewritingSystem"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedAdditiveInverse","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "ReducedAdditiveInverse: ReducedForm","filters" : [["IsRewritingSystem","IsBuiltFromAdditiveMagmaWithInverses","Tester(IsBuiltFromAdditiveMagmaWithInverses)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedComm","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsMultiplicativeElement"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "ReducedComm","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is32BitsAssocWord"],["Is32BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedComm","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is16BitsAssocWord"],["Is16BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedComm","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is8BitsAssocWord"],["Is8BitsAssocWord"]]},{"rank" : 25,"comment" : "ReducedComm: DeepThoughtReducedComm","filters" : [["IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsDeepThoughtCollectorRep"],["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]},{"rank" : 20,"comment" : "ReducedComm: ReducedLeftQuotient\/ReducedProduct","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedConjugate","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsMultiplicativeElement"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 25,"comment" : "ReducedConjugate: DeepThoughtReducedConjugate","filters" : [["IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsDeepThoughtCollectorRep"],["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]},{"rank" : 20,"comment" : "ReducedConjugate: ReducedLeftQuotient\/ReducedProduct","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedDifference","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsAdditiveElement"],["IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 14,"comment" : "ReducedDifference: ReducedSum\/ReducedAdditiveInverse","filters" : [["IsRewritingSystem","IsBuiltFromAdditiveMagmaWithInverses","Tester(IsBuiltFromAdditiveMagmaWithInverses)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement"],["IsNearAdditiveElementWithInverse","IsAdditiveElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedForm","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "ReducedForm","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is32BitsAssocWord"]]},{"rank" : 29,"comment" : "ReducedForm","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is16BitsAssocWord"]]},{"rank" : 29,"comment" : "ReducedForm","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is8BitsAssocWord"]]},{"rank" : 16,"comment" : "ReducedForm: CollectWordOrFail","filters" : [["IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 9,"comment" : "ReducedForm: for a monoid rewriting system and a word on the underlying free monoid","filters" : [["IsRewritingSystem","IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)"],["IsAssociativeElement","IsWord"]]},{"rank" : 9,"comment" : "ReducedForm: for a semigroup rewriting system and a word on the underlying free semigroup","filters" : [["IsRewritingSystem","IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)"],["IsAssociativeElement","IsWord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsReducedForm","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "IsReducedForm: for a rewriting system and an object","filters" : [["IsRewritingSystem"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedInverse","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "ReducedInverse","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsAssociativeElement","IsWord"]]},{"rank" : 20,"comment" : "ReducedInverse: DeepThoughtReducedInverse","filters" : [["IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsDeepThoughtCollectorRep"],["IsAssociativeElement","IsWord"]]},{"rank" : 13,"comment" : "ReducedInverse: ReducedForm","filters" : [["IsRewritingSystem","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedLeftQuotient","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsMultiplicativeElement"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "ReducedLeftQuotient","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is32BitsAssocWord"],["Is32BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedLeftQuotient","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is16BitsAssocWord"],["Is16BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedLeftQuotient","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is8BitsAssocWord"],["Is8BitsAssocWord"]]},{"rank" : 25,"comment" : "ReducedLeftQuotient: DeepThoughtReducedLeftQuotient","filters" : [["IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsDeepThoughtCollectorRep"],["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]},{"rank" : 18,"comment" : "ReducedLeftQuotient: ReducedProduct\/ReducedInverse","filters" : [["IsRewritingSystem","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedOne","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "ReducedOne","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 6,"comment" : "ReducedOne: ReducedForm","filters" : [["IsRewritingSystem","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)"]]},{"rank" : 4,"comment" : "ReducedOne: ReducedForm","filters" : [["IsRewritingSystem","IsBuiltFromAdditiveMagmaWithInverses","Tester(IsBuiltFromAdditiveMagmaWithInverses)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedPower","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsMultiplicativeElement"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 49,"comment" : "ReducedPower","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is32BitsAssocWord"],["IsInt","IsSmallIntRep"]]},{"rank" : 49,"comment" : "ReducedPower","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is16BitsAssocWord"],["IsInt","IsSmallIntRep"]]},{"rank" : 49,"comment" : "ReducedPower","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is8BitsAssocWord"],["IsInt","IsSmallIntRep"]]},{"rank" : 38,"comment" : "ReducedPower: DeepThoughtReducedPower","filters" : [["IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsDeepThoughtCollectorRep"],["IsAssociativeElement","IsWord"],["IsInt"]]},{"rank" : 34,"comment" : "ReducedPower: ReducedInverse\/CollectWordOrFail","filters" : [["IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsInt"]]},{"rank" : 31,"comment" : "ReducedPower: ReducedProduct\/ReducedInverse","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"],["IsMultiplicativeElement"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedProduct","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsMultiplicativeElement"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "ReducedProduct","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is32BitsAssocWord"],["Is32BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedProduct","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is16BitsAssocWord"],["Is16BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedProduct","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is8BitsAssocWord"],["Is8BitsAssocWord"]]},{"rank" : 25,"comment" : "ReducedProduct: DeepThoughtReducedProduct","filters" : [["IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsDeepThoughtCollectorRep"],["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]},{"rank" : 10,"comment" : "ReducedProduct: ReducedForm","filters" : [["IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)"],["IsMultiplicativeElement"],["IsMultiplicativeElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedQuotient","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsMultiplicativeElement"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "ReducedQuotient","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is32BitsAssocWord"],["Is32BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedQuotient","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is16BitsAssocWord"],["Is16BitsAssocWord"]]},{"rank" : 37,"comment" : "ReducedQuotient","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["Is8BitsAssocWord"],["Is8BitsAssocWord"]]},{"rank" : 25,"comment" : "ReducedQuotient: DeepThoughtReducedQuotient","filters" : [["IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsDeepThoughtCollectorRep"],["IsAssociativeElement","IsWord"],["IsAssociativeElement","IsWord"]]},{"rank" : 18,"comment" : "ReducedQuotient: ReducedProduct\/ReducedInverse","filters" : [["IsRewritingSystem","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedScalarProduct","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElementWithInverse"],["IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedSum","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],["IsAdditiveElement"],["IsAdditiveElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 10,"comment" : "ReducedSum: ReducedForm","filters" : [["IsRewritingSystem","IsBuiltFromAdditiveMagmaWithInverses","Tester(IsBuiltFromAdditiveMagmaWithInverses)"],["IsAdditiveElement"],["IsAdditiveElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedZero","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelativeOrders","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]],[["IsGeneralPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "RelativeOrders: system getter","filters" : [["IsAttributeStoringRep","Tester(RelativeOrders)"]]},{"rank" : 24,"comment" : "RelativeOrders: fp","filters" : [["IsModuloPcgsFpGroupRep"]]},{"rank" : 21,"comment" : "RelativeOrders: pc series","filters" : [["IsPcgs"]]},{"rank" : 18,"comment" : "RelativeOrders","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 14,"comment" : "RelativeOrders: Method for Deep Thought","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"]]},{"rank" : 13,"comment" : "RelativeOrders: from-the-left collector","filters" : [["IsFromTheLeftCollectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelativeOrders)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]],[["IsGeneralPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "Setter(RelativeOrders): setting orders for prime orders pcgs","filters" : [["IsComponentObjectRep","IsAttributeStoringRep","IsPcgs","Tester(IsPrimeOrdersPcgs)","Tester(IsFiniteOrdersPcgs)"],["IsList"]]},{"rank" : 25,"comment" : "Setter(RelativeOrders): setting orders and checking for prime orders","filters" : [["IsComponentObjectRep","IsAttributeStoringRep","IsPcgs"],["IsList"]]},{"rank" : 16,"comment" : "Setter(RelativeOrders)","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsList"]]},{"rank" : 2,"comment" : "Setter(RelativeOrders): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelativeOrders): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelativeOrders)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OutdatePolycyclicCollector","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 12,"comment" : "OutdatePolycyclicCollector","filters" : [["IsMutable","IsPolycyclicCollector"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UpdatePolycyclicCollector","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "UpdatePolycyclicCollector: combinatorial collector rep","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsCombinatorialCollectorRep"]]},{"rank" : 18,"comment" : "UpdatePolycyclicCollector","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]},{"rank" : 14,"comment" : "UpdatePolycyclicCollector","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"]]},{"rank" : 13,"comment" : "UpdatePolycyclicCollector: FromTheLeftCollector","filters" : [["IsFromTheLeftCollectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CollectWord","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 18,"comment" : "CollectWord","filters" : [["IsPolycyclicCollector"],["IsList"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CollectWordOrFail","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 31,"comment" : "CollectWordOrFail","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["IsList"],["Is32BitsAssocWord"]]},{"rank" : 31,"comment" : "CollectWordOrFail","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["IsList"],["Is16BitsAssocWord"]]},{"rank" : 31,"comment" : "CollectWordOrFail","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"],["IsList"],["Is8BitsAssocWord"]]},{"rank" : 26,"comment" : "CollectWordOrFail","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsUpToDatePolycyclicCollector","IsSingleCollectorRep"],["IsList"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 21,"comment" : "CollectWordOrFail: DeepThought","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsList"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 20,"comment" : "CollectWordOrFail: FTL collector with Hall polynomials, exponent vector, gen-exp-pairs","filters" : [["IsUpToDatePolycyclicCollector","IsFromTheLeftCollectorRep","IsPolynomialCollector","Tester(IsPolynomialCollector)"],["IsList"],["IsList"]]},{"rank" : 20,"comment" : "CollectWordOrFail: CombinatorialFromTheLeftCollector","filters" : [["IsUpToDatePolycyclicCollector","IsFromTheLeftCollectorRep","IsWeightedCollector","Tester(IsWeightedCollector)"],["IsList"],["IsList"]]},{"rank" : 20,"comment" : "CollectWordOrFail: FromTheLeftCollector","filters" : [["IsUpToDatePolycyclicCollector","IsFromTheLeftCollectorRep","UseLibraryCollector","Tester(UseLibraryCollector)"],["IsList"],["IsList"]]},{"rank" : 19,"comment" : "CollectWordOrFail","filters" : [["IsPolycyclicCollector","IsUpToDatePolycyclicCollector"],["IsList"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 18,"comment" : "CollectWordOrFail: FromTheLeftCollector","filters" : [["IsUpToDatePolycyclicCollector","IsFromTheLeftCollectorRep"],["IsList"],["IsList"]]},{"rank" : 18,"comment" : "CollectWordOrFail","filters" : [["IsPolycyclicCollector"],["IsList"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 17,"comment" : "CollectWordOrFail: FromTheLeftCollector (outdated)","filters" : [["IsFromTheLeftCollectorRep"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NonTrivialRightHandSides","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "NonTrivialRightHandSides","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ObjByExponents","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "ObjByExponents","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsList"]]},{"rank" : 16,"comment" : "ObjByExponents: DeepThought","filters" : [["IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsList"]]},{"rank" : 15,"comment" : "ObjByExponents","filters" : [["IsFromTheLeftCollectorRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetCommutator","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 54,"comment" : "SetCommutator: from-the-left collector, words","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"],["IsWord"]]},{"rank" : 52,"comment" : "SetCommutator: for from-the-left collector, words as lists","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"],["IsList"]]},{"rank" : 49,"comment" : "SetCommutator: integers","filters" : [["IsMutable","IsPowerConjugateCollector"],["IsInt"],["IsInt"],[]]},{"rank" : 27,"comment" : "SetCommutator: elements","filters" : [["IsMutable","IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"5args" : [],"6args" : []}},{"name" : "SetCommutatorNC","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 54,"comment" : "SetCommutatorNC: integers","filters" : [["IsMutable","IsPowerConjugateCollector"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 28,"comment" : "SetCommutatorNC: elements","filters" : [["IsMutable","IsPowerConjugateCollector"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"5args" : [],"6args" : []}},{"name" : "SetCommutatorANC","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetConjugate","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 61,"comment" : "SetConjugate: combinatorial collector rep","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsCombinatorialCollectorRep"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 60,"comment" : "SetConjugate","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 56,"comment" : "SetConjugate","filters" : [["IsMutable","IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 54,"comment" : "SetConjugate: from-the-left collector, words","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"],["IsWord"]]},{"rank" : 54,"comment" : "SetConjugate","filters" : [["IsMutable","IsPowerCommutatorCollector"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 52,"comment" : "SetConjugate: for from-the-left collector, words as lists","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"],["IsList"]]},{"rank" : 27,"comment" : "SetConjugate","filters" : [["IsMutable","IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"5args" : [],"6args" : []}},{"name" : "SetConjugateNC","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 60,"comment" : "SetConjugateNC","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 54,"comment" : "SetConjugateNC","filters" : [["IsMutable","IsPowerCommutatorCollector"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 52,"comment" : "SetConjugateNC: for from-the-left collector, words as lists","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"],["IsList"]]},{"rank" : 27,"comment" : "SetConjugateNC","filters" : [["IsMutable","IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"5args" : [],"6args" : []}},{"name" : "SetConjugateANC","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 60,"comment" : "SetConjugateANC: pow conj single collector","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsInt"],["IsMultiplicativeElementWithInverse"]]}],"5args" : [],"6args" : []}},{"name" : "SetPower","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 43,"comment" : "SetPower: combinatorial collector rep","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsCombinatorialCollectorRep"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 42,"comment" : "SetPower","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 38,"comment" : "SetPower","filters" : [["IsMutable","IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 37,"comment" : "SetPower: from-the-left collector, word","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt","IsPosRat"],["IsWord"]]},{"rank" : 35,"comment" : "SetPower: for from-the-left collector, word as list","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt","IsPosRat"],["IsList"]]},{"rank" : 22,"comment" : "SetPower","filters" : [["IsMutable","IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPowerNC","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 42,"comment" : "SetPowerNC","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 35,"comment" : "SetPowerNC: for from-the-left collector, word as list","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt","IsPosRat"],["IsList"]]},{"rank" : 22,"comment" : "SetPowerNC","filters" : [["IsMutable","IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPowerANC","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 42,"comment" : "SetPowerANC: pow conj single collector","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetRelativeOrder","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 55,"comment" : "SetRelativeOrder","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsInt"]]},{"rank" : 51,"comment" : "SetRelativeOrder: for from-the-left collector","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt","IsPosRat"],["IsInt"]]},{"rank" : 35,"comment" : "SetRelativeOrder","filters" : [["IsMutable","IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsInt"]]},{"rank" : 33,"comment" : "SetRelativeOrder","filters" : [["IsMutable","IsPowerConjugateCollector","IsDeepThoughtCollectorRep"],["IsInt"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetRelativeOrderNC","type" : "GAP_Operation","filters" : [[["IsMutable","IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 55,"comment" : "SetRelativeOrderNC","filters" : [["IsMutable","IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsInt"]]},{"rank" : 51,"comment" : "SetRelativeOrderNC: for from-the-left collector","filters" : [["IsMutable","IsFromTheLeftCollectorRep"],["IsInt","IsPosRat"],["IsInt"]]},{"rank" : 35,"comment" : "SetRelativeOrderNC","filters" : [["IsMutable","IsPolycyclicCollector"],["IsMultiplicativeElementWithInverse"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetCommutatorNC","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 49,"comment" : "GetCommutatorNC: for from the left collector","filters" : [["IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetConjugateNC","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 54,"comment" : "GetConjugateNC: finite pow-conj single collector","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"],["IsInt"]]},{"rank" : 49,"comment" : "GetConjugateNC: from the left collector","filters" : [["IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetPowerNC","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "GetPowerNC","filters" : [["IsFinite","Tester(IsFinite)","IsPowerConjugateCollector","IsSingleCollectorRep"],["IsInt"]]},{"rank" : 32,"comment" : "GetPowerNC: from-the-left collector","filters" : [["IsFromTheLeftCollectorRep"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SingleCollector","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "SingleCollector","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsInt"]]},{"rank" : 47,"comment" : "SingleCollector","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsList"]]},{"rank" : 20,"comment" : "SingleCollector","filters" : [["IsList"],["IsInt"]]},{"rank" : 4,"comment" : "SingleCollector","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SingleCollectorByGenerators","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 5,"comment" : "SingleCollectorByGenerators","filters" : [["IsFamily"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CombinatorialCollector","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "CombinatorialCollector","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsInt"]]},{"rank" : 47,"comment" : "CombinatorialCollector","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsList"]]},{"rank" : 20,"comment" : "CombinatorialCollector","filters" : [["IsList"],["IsInt"]]},{"rank" : 4,"comment" : "CombinatorialCollector","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CombinatorialCollectorByGenerators","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 5,"comment" : "CombinatorialCollectorByGenerators","filters" : [["IsFamily"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeepThoughtCollector","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 65,"comment" : "DeepThoughtCollector","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsInt"]]},{"rank" : 49,"comment" : "DeepThoughtCollector","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeepThoughtCollectorByGenerators","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 5,"comment" : "DeepThoughtCollectorByGenerators","filters" : [["IsFamily"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EvaluateOverlapCBA","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],["IsList"],["IsList"],["IsInt"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : [{"rank" : 76,"comment" : "EvaluateOverlapCBA: polyc. collector, 2 hom. lists, 3 pos. integers","filters" : [["IsPolycyclicCollector"],["IsHomogeneousList"],["IsHomogeneousList"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}]}},{"name" : "EvaluateOverlapBNA","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],["IsList"],["IsList"],["IsInt"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : [{"rank" : 76,"comment" : "EvaluateOverlapBNA: polyc. collector, 2 hom. lists, 3 pos. integers","filters" : [["IsPolycyclicCollector"],["IsHomogeneousList"],["IsHomogeneousList"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}]}},{"name" : "EvaluateOverlapBAN","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],["IsList"],["IsList"],["IsInt"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : [{"rank" : 76,"comment" : "EvaluateOverlapBAN: polyc. collector, 2 hom. lists, 3 pos. integers","filters" : [["IsPolycyclicCollector"],["IsHomogeneousList"],["IsHomogeneousList"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}]}},{"name" : "EvaluateOverlapANA","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],["IsList"],["IsList"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 57,"comment" : "EvaluateOverlapANA: polyc. collector, 2 hom. lists, 3 pos. integers","filters" : [["IsPolycyclicCollector"],["IsHomogeneousList"],["IsHomogeneousList"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"6args" : []}},{"name" : "MultiplicativeElementsWithInversesFamilyByRws","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20,"comment" : "MultiplicativeElementsWithInversesFamilyByRws: 32 bits family","filters" : [["IsFinite","Tester(IsFinite)","IsPolycyclicCollector","IsUpToDatePolycyclicCollector","Is32BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"]]},{"rank" : 20,"comment" : "MultiplicativeElementsWithInversesFamilyByRws: 16 bits family","filters" : [["IsFinite","Tester(IsFinite)","IsPolycyclicCollector","IsUpToDatePolycyclicCollector","Is16BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"]]},{"rank" : 20,"comment" : "MultiplicativeElementsWithInversesFamilyByRws: 8 bits family","filters" : [["IsFinite","Tester(IsFinite)","IsPolycyclicCollector","IsUpToDatePolycyclicCollector","Is8BitsSingleCollectorRep","IsDefaultRhsTypeSingleCollector"]]},{"rank" : 11,"comment" : "MultiplicativeElementsWithInversesFamilyByRws: generic method","filters" : [["IsPolycyclicCollector"]]},{"rank" : 10,"comment" : "MultiplicativeElementsWithInversesFamilyByRws","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementByRws","type" : "GAP_Operation","filters" : [[["IsElementsFamilyByRws"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "ElementByRws: using 32Bits_AssocWord","filters" : [["IsElementsFamilyBy32BitsSingleCollector"],["Is32BitsAssocWord"]]},{"rank" : 11,"comment" : "ElementByRws: using 16Bits_AssocWord","filters" : [["IsElementsFamilyBy16BitsSingleCollector"],["Is16BitsAssocWord"]]},{"rank" : 11,"comment" : "ElementByRws: using 8Bits_AssocWord","filters" : [["IsElementsFamilyBy8BitsSingleCollector"],["Is8BitsAssocWord"]]},{"rank" : 4,"comment" : "ElementByRws","filters" : [["IsElementsFamilyByRws"],["IsList"]]},{"rank" : 2,"comment" : "ElementByRws","filters" : [["IsElementsFamilyByRws"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupByRws","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10,"comment" : "GroupByRws","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupByRwsNC","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 110,"comment" : "GroupByRwsNC: rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefiningPcgs","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "DefiningPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(DefiningPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DefiningPcgs)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DefiningPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DefiningPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DefiningPcgs)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PolycyclicFactorGroup","type" : "GAP_Operation","filters" : [[[],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 61,"comment" : "PolycyclicFactorGroup: for free group, empty list using ' PolycyclicFactorGroupByRelators'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 48,"comment" : "PolycyclicFactorGroup: for free group, list using ' PolycyclicFactorGroupByRelators'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PolycyclicFactorGroupNC","type" : "GAP_Operation","filters" : [[[],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 48,"comment" : "PolycyclicFactorGroupNC: for free group, list using ' PolycyclicFactorGroupByRelators'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PolycyclicFactorGroupByRelatorsNC","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 5,"comment" : "PolycyclicFactorGroupByRelatorsNC: generic method for family, generators, relators","filters" : [["IsFamily"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PolycyclicFactorGroupByRelators","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 5,"comment" : "PolycyclicFactorGroupByRelators: generic method for family, generators, relators","filters" : [["IsFamily"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MonomialComparisonFunction","type" : "GAP_Operation","filters" : [[["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MonomialComparisonFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(MonomialComparisonFunction)"]]},{"rank" : 5,"comment" : "MonomialComparisonFunction: default: use extrep","filters" : [["IsMonomialOrderingDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MonomialComparisonFunction)","type" : "GAP_Operation","filters" : [[["IsMonomialOrdering"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MonomialComparisonFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MonomialComparisonFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MonomialComparisonFunction)","type" : "GAP_Operation","filters" : [[["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MonomialExtrepComparisonFun","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "MonomialExtrepComparisonFun: system getter","filters" : [["IsAttributeStoringRep","Tester(MonomialExtrepComparisonFun)"]]},{"rank" : 1,"comment" : "MonomialExtrepComparisonFun: functions are themselves -- for compatibility","filters" : [["IsFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MonomialExtrepComparisonFun)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MonomialExtrepComparisonFun): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MonomialExtrepComparisonFun): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MonomialExtrepComparisonFun)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OccuringVariableIndices","type" : "GAP_Operation","filters" : [[["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "OccuringVariableIndices: system getter","filters" : [["IsAttributeStoringRep","Tester(OccuringVariableIndices)"]]},{"rank" : 14,"comment" : "OccuringVariableIndices: polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OccuringVariableIndices)","type" : "GAP_Operation","filters" : [[["IsMonomialOrdering"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OccuringVariableIndices): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OccuringVariableIndices): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OccuringVariableIndices)","type" : "GAP_Operation","filters" : [[["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadingMonomialOfPolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 13,"comment" : "LeadingMonomialOfPolynomial: with ordering","filters" : [["IsPolynomialFunction"],["IsMonomialOrdering"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadingCoefficientOfPolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 13,"comment" : "LeadingCoefficientOfPolynomial: with ordering","filters" : [["IsPolynomialFunction"],["IsMonomialOrdering"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadingTermOfPolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomialFunction"],["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 13,"comment" : "LeadingTermOfPolynomial: with ordering","filters" : [["IsPolynomialFunction"],["IsMonomialOrdering"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroebnerBasis","type" : "GAP_Operation","filters" : [[["IsHomogeneousList","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]],[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "GroebnerBasis: ideal with stored GB","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)","Tester(StoredGroebnerBasis)"],["IsMonomialOrdering"]]},{"rank" : 34,"comment" : "GroebnerBasis: ideal","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]]},{"rank" : 26,"comment" : "GroebnerBasis: polynomials","filters" : [["IsHomogeneousList","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]]},{"rank" : 1,"comment" : "GroebnerBasis: fix function","filters" : [[],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedGroebnerBasis","type" : "GAP_Operation","filters" : [[["IsHomogeneousList","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]],[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "ReducedGroebnerBasis: ideal","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]]},{"rank" : 26,"comment" : "ReducedGroebnerBasis: polynomials","filters" : [["IsHomogeneousList","CategoryCollections(IsRationalFunction)"],["IsMonomialOrdering"]]},{"rank" : 1,"comment" : "ReducedGroebnerBasis: fix function","filters" : [[],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StoredGroebnerBasis","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "StoredGroebnerBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(StoredGroebnerBasis)"]]},{"rank" : 33,"comment" : "StoredGroebnerBasis: ideal","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"]]},{"rank" : -26,"comment" : "StoredGroebnerBasis: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","CategoryCollections(IsRationalFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StoredGroebnerBasis)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StoredGroebnerBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StoredGroebnerBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StoredGroebnerBasis)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","Tester(LeftActingRingOfIdeal)","Tester(RightActingRingOfIdeal)","CategoryCollections(IsRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsByPcSequence","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 19,"comment" : "PcgsByPcSequence","filters" : [["IsElementsFamilyByRws"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 18,"comment" : "PcgsByPcSequence","filters" : [["IsFamily"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 6,"comment" : "PcgsByPcSequence","filters" : [["IsElementsFamilyByRws"],["IsHomogeneousList"]]},{"rank" : 5,"comment" : "PcgsByPcSequence","filters" : [["IsFamily"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsByPcSequenceNC","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 19,"comment" : "PcgsByPcSequenceNC: elements family by rws, empty sequence","filters" : [["IsElementsFamilyByRws"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 18,"comment" : "PcgsByPcSequenceNC: pc series, empty sequence","filters" : [["IsFamily"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 7,"comment" : "PcgsByPcSequenceNC: elements family by rws with defining pcgs","filters" : [["IsElementsFamilyByRws","Tester(DefiningPcgs)"],["IsHomogeneousList"]]},{"rank" : 6,"comment" : "PcgsByPcSequenceNC: elements family by rws","filters" : [["IsElementsFamilyByRws"],["IsHomogeneousList"]]},{"rank" : 5,"comment" : "PcgsByPcSequenceNC: pc series","filters" : [["IsFamily"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsByPcSequenceCons","type" : "GAP_Operation","filters" : [[[],[],["IsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : -3,"comment" : "PcgsByPcSequenceCons: generic constructor","filters" : [["IsPcgsDefaultRep"],[],["IsFamily"],["IsList"],["IsList"]]}],"6args" : []}},{"name" : "PcGroupWithPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "PcGroupWithPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(PcGroupWithPcgs)"]]},{"rank" : 21,"comment" : "PcGroupWithPcgs","filters" : [["IsPcgs"]]},{"rank" : 20,"comment" : "PcGroupWithPcgs: pcgs modulo pcgs","filters" : [["IsModuloPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcGroupWithPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcGroupWithPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcGroupWithPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcGroupWithPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupOfPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "GroupOfPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(GroupOfPcgs)"]]},{"rank" : 27,"comment" : "GroupOfPcgs","filters" : [["IsPcgs","IsPcgsPermGroupRep"]]},{"rank" : 21,"comment" : "GroupOfPcgs","filters" : [["IsPcgs"]]},{"rank" : 20,"comment" : "GroupOfPcgs","filters" : [["IsModuloPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GroupOfPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GroupOfPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GroupOfPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GroupOfPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OneOfPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "OneOfPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(OneOfPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OneOfPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OneOfPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OneOfPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OneOfPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcSeries","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "PcSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(PcSeries)"]]},{"rank" : 27,"comment" : "PcSeries","filters" : [["IsPcgs","IsPcgsPermGroupRep"]]},{"rank" : 21,"comment" : "PcSeries: construct subgroups","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPcgsElementaryAbelianSeries","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsPcgsElementaryAbelianSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPcgsElementaryAbelianSeries)"]]},{"rank" : 21,"comment" : "IsPcgsElementaryAbelianSeries: test if elm. abelian","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPcgsElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPcgsElementaryAbelianSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPcgsElementaryAbelianSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPcgsElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsElementaryAbelianSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PcgsElementaryAbelianSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(PcgsElementaryAbelianSeries)"]]},{"rank" : 93,"comment" : "PcgsElementaryAbelianSeries: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 66,"comment" : "PcgsElementaryAbelianSeries: for pc group with parent group","filters" : [["IsFinite","Tester(IsFinite)","Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 65,"comment" : "PcgsElementaryAbelianSeries: CRISP method for pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 55,"comment" : "PcgsElementaryAbelianSeries: perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "PcgsElementaryAbelianSeries: for PCgroups via SpecialPcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 34,"comment" : "PcgsElementaryAbelianSeries: for group with parent group","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 34,"comment" : "PcgsElementaryAbelianSeries: generic group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "PcgsElementaryAbelianSeries: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "PcgsElementaryAbelianSeries: if special pcgs is known","filters" : [["Tester(SpecialPcgs)"]]},{"rank" : 2,"comment" : "PcgsElementaryAbelianSeries: group list","filters" : [["IsList"]]},{"rank" : 0,"comment" : "PcgsElementaryAbelianSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcgsElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcgsElementaryAbelianSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcgsElementaryAbelianSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcgsElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicesEANormalSteps","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IndicesEANormalSteps: system getter","filters" : [["IsAttributeStoringRep","Tester(IndicesEANormalSteps)"]]},{"rank" : 25,"comment" : "IndicesEANormalSteps: special pcgs: LGFirst","filters" : [["IsSpecialPcgs","Tester(IsSpecialPcgs)"]]},{"rank" : 23,"comment" : "IndicesEANormalSteps: inherit from parent","filters" : [["IsInducedPcgs","Tester(ParentPcgs)"]]},{"rank" : 0,"comment" : "IndicesEANormalSteps: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndicesEANormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndicesEANormalSteps): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndicesEANormalSteps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndicesEANormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EANormalSeriesByPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "EANormalSeriesByPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(EANormalSeriesByPcgs)"]]},{"rank" : 30,"comment" : "EANormalSeriesByPcgs: perm group modulo rep","filters" : [["IsPcgsElementaryAbelianSeries","Tester(IsPcgsElementaryAbelianSeries)","IsModuloPcgsPermGroupRep"]]},{"rank" : 29,"comment" : "EANormalSeriesByPcgs: perm group rep","filters" : [["IsPcgs","IsPcgsElementaryAbelianSeries","Tester(IsPcgsElementaryAbelianSeries)","IsPcgsPermGroupRep"]]},{"rank" : 28,"comment" : "EANormalSeriesByPcgs: from indices","filters" : [["IsPcgs","Tester(IndicesEANormalSteps)","IsPcgsPermGroupRep"]]},{"rank" : 23,"comment" : "EANormalSeriesByPcgs: from PcSeries","filters" : [["IsPcgs","Tester(PcSeries)","Tester(IndicesEANormalSteps)"]]},{"rank" : 22,"comment" : "EANormalSeriesByPcgs: from indices","filters" : [["IsPcgs","Tester(IndicesEANormalSteps)"]]},{"rank" : 0,"comment" : "EANormalSeriesByPcgs: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EANormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EANormalSeriesByPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EANormalSeriesByPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EANormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPcgsCentralSeries","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsPcgsCentralSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPcgsCentralSeries)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPcgsCentralSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPcgsCentralSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPcgsCentralSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPcgsCentralSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsCentralSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PcgsCentralSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(PcgsCentralSeries)"]]},{"rank" : 93,"comment" : "PcgsCentralSeries: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 58,"comment" : "PcgsCentralSeries: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "PcgsCentralSeries: for pc groups use SpecialPcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 34,"comment" : "PcgsCentralSeries: for pcgs computable use SpecialPcgs","filters" : [["CanEasilyComputePcgs"]]},{"rank" : 22,"comment" : "PcgsCentralSeries: if special pcgs is known","filters" : [["Tester(SpecialPcgs)"]]},{"rank" : 0,"comment" : "PcgsCentralSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcgsCentralSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcgsCentralSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcgsCentralSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcgsCentralSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicesCentralNormalSteps","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IndicesCentralNormalSteps: system getter","filters" : [["IsAttributeStoringRep","Tester(IndicesCentralNormalSteps)"]]},{"rank" : 0,"comment" : "IndicesCentralNormalSteps: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndicesCentralNormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndicesCentralNormalSteps): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndicesCentralNormalSteps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndicesCentralNormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralNormalSeriesByPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "CentralNormalSeriesByPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(CentralNormalSeriesByPcgs)"]]},{"rank" : 28,"comment" : "CentralNormalSeriesByPcgs: from indices","filters" : [["IsPcgs","Tester(IndicesCentralNormalSteps)","IsPcgsPermGroupRep"]]},{"rank" : 23,"comment" : "CentralNormalSeriesByPcgs: from PcSeries","filters" : [["IsPcgs","Tester(PcSeries)","Tester(IndicesCentralNormalSteps)"]]},{"rank" : 22,"comment" : "CentralNormalSeriesByPcgs: from indices","filters" : [["IsPcgs","Tester(IndicesCentralNormalSteps)"]]},{"rank" : 0,"comment" : "CentralNormalSeriesByPcgs: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CentralNormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CentralNormalSeriesByPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CentralNormalSeriesByPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CentralNormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPcgsPCentralSeriesPGroup","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsPcgsPCentralSeriesPGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPcgsPCentralSeriesPGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPcgsPCentralSeriesPGroup)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPcgsPCentralSeriesPGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPcgsPCentralSeriesPGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPcgsPCentralSeriesPGroup)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsPCentralSeriesPGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PcgsPCentralSeriesPGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(PcgsPCentralSeriesPGroup)"]]},{"rank" : 93,"comment" : "PcgsPCentralSeriesPGroup: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 58,"comment" : "PcgsPCentralSeriesPGroup: for permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "PcgsPCentralSeriesPGroup: for pc groups use SpecialPcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 34,"comment" : "PcgsPCentralSeriesPGroup: for pcgs computable use SpecialPcgs","filters" : [["CanEasilyComputePcgs"]]},{"rank" : 0,"comment" : "PcgsPCentralSeriesPGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcgsPCentralSeriesPGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcgsPCentralSeriesPGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcgsPCentralSeriesPGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcgsPCentralSeriesPGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicesPCentralNormalStepsPGroup","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IndicesPCentralNormalStepsPGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IndicesPCentralNormalStepsPGroup)"]]},{"rank" : 0,"comment" : "IndicesPCentralNormalStepsPGroup: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndicesPCentralNormalStepsPGroup)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndicesPCentralNormalStepsPGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndicesPCentralNormalStepsPGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndicesPCentralNormalStepsPGroup)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PCentralNormalSeriesByPcgsPGroup","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "PCentralNormalSeriesByPcgsPGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(PCentralNormalSeriesByPcgsPGroup)"]]},{"rank" : 28,"comment" : "PCentralNormalSeriesByPcgsPGroup: from indices","filters" : [["IsPcgs","Tester(IndicesPCentralNormalStepsPGroup)","IsPcgsPermGroupRep"]]},{"rank" : 23,"comment" : "PCentralNormalSeriesByPcgsPGroup: from PcSeries","filters" : [["IsPcgs","Tester(PcSeries)","Tester(IndicesPCentralNormalStepsPGroup)"]]},{"rank" : 22,"comment" : "PCentralNormalSeriesByPcgsPGroup: from indices","filters" : [["IsPcgs","Tester(IndicesPCentralNormalStepsPGroup)"]]},{"rank" : 0,"comment" : "PCentralNormalSeriesByPcgsPGroup: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PCentralNormalSeriesByPcgsPGroup)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PCentralNormalSeriesByPcgsPGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PCentralNormalSeriesByPcgsPGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PCentralNormalSeriesByPcgsPGroup)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPcgsChiefSeries","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsPcgsChiefSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPcgsChiefSeries)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPcgsChiefSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPcgsChiefSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPcgsChiefSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPcgsChiefSeries)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsChiefSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PcgsChiefSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(PcgsChiefSeries)"]]},{"rank" : 93,"comment" : "PcgsChiefSeries: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 33,"comment" : "PcgsChiefSeries: compute chief series and pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "PcgsChiefSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcgsChiefSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcgsChiefSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcgsChiefSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcgsChiefSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicesChiefNormalSteps","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IndicesChiefNormalSteps: system getter","filters" : [["IsAttributeStoringRep","Tester(IndicesChiefNormalSteps)"]]},{"rank" : 0,"comment" : "IndicesChiefNormalSteps: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndicesChiefNormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndicesChiefNormalSteps): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndicesChiefNormalSteps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndicesChiefNormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ChiefNormalSeriesByPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "ChiefNormalSeriesByPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(ChiefNormalSeriesByPcgs)"]]},{"rank" : 28,"comment" : "ChiefNormalSeriesByPcgs: from indices","filters" : [["IsPcgs","Tester(IndicesChiefNormalSteps)","IsPcgsPermGroupRep"]]},{"rank" : 23,"comment" : "ChiefNormalSeriesByPcgs: from PcSeries","filters" : [["IsPcgs","Tester(PcSeries)","Tester(IndicesChiefNormalSteps)"]]},{"rank" : 22,"comment" : "ChiefNormalSeriesByPcgs: from indices","filters" : [["IsPcgs","Tester(IndicesChiefNormalSteps)"]]},{"rank" : 0,"comment" : "ChiefNormalSeriesByPcgs: compatibility only","filters" : [["IsPcgs","Tester(IndicesNormalSteps)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ChiefNormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ChiefNormalSeriesByPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ChiefNormalSeriesByPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ChiefNormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicesNormalSteps","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IndicesNormalSteps: system getter","filters" : [["IsAttributeStoringRep","Tester(IndicesNormalSteps)"]]},{"rank" : 21,"comment" : "IndicesNormalSteps: generic","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndicesNormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndicesNormalSteps): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndicesNormalSteps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndicesNormalSteps)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalSeriesByPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "NormalSeriesByPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalSeriesByPcgs)"]]},{"rank" : 21,"comment" : "NormalSeriesByPcgs: generic","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalSeriesByPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalSeriesByPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalSeriesByPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimeOrdersPcgs","type" : "GAP_Operation","filters" : [[["IsGeneralPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "IsPrimeOrdersPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPrimeOrdersPcgs)"]]},{"rank" : 21,"comment" : "IsPrimeOrdersPcgs","filters" : [["IsPcgs"]]},{"rank" : 20,"comment" : "IsPrimeOrdersPcgs","filters" : [["IsModuloPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPrimeOrdersPcgs)","type" : "GAP_Operation","filters" : [[["IsGeneralPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPrimeOrdersPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPrimeOrdersPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPrimeOrdersPcgs)","type" : "GAP_Operation","filters" : [[["IsGeneralPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFiniteOrdersPcgs","type" : "GAP_Operation","filters" : [[["IsGeneralPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "IsFiniteOrdersPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFiniteOrdersPcgs)"]]},{"rank" : 21,"comment" : "IsFiniteOrdersPcgs","filters" : [["IsPcgs"]]},{"rank" : 20,"comment" : "IsFiniteOrdersPcgs","filters" : [["IsModuloPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFiniteOrdersPcgs)","type" : "GAP_Operation","filters" : [[["IsGeneralPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFiniteOrdersPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFiniteOrdersPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFiniteOrdersPcgs)","type" : "GAP_Operation","filters" : [[["IsGeneralPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RefinedPcGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20039,"comment" : "RefinedPcGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RefinedPcGroup)"]]},{"rank" : 43,"comment" : "RefinedPcGroup: group with refined pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 7,"comment" : "RefinedPcGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RefinedPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RefinedPcGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RefinedPcGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RefinedPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismRefinedPcGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsomorphismRefinedPcGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismRefinedPcGroup)"]]},{"rank" : 43,"comment" : "IsomorphismRefinedPcGroup: group with refined pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 0,"comment" : "IsomorphismRefinedPcGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismRefinedPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismRefinedPcGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismRefinedPcGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismRefinedPcGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DepthOfPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 360,"comment" : "DepthOfPcElement: handled by nice monomorphism: attribute CollElm","filters" : [["IsPcgs","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 185,"comment" : "DepthOfPcElement: family pcgs (32 bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is32BitsPcWordRep"]]},{"rank" : 185,"comment" : "DepthOfPcElement: family pcgs (16 bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is16BitsPcWordRep"]]},{"rank" : 185,"comment" : "DepthOfPcElement: family pcgs (8 bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is8BitsPcWordRep"]]},{"rank" : 82,"comment" : "DepthOfPcElement: family pcgs","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 40,"comment" : "DepthOfPcElement: for pcgs of direct product","filters" : [["IsPcgs","IsPcgsDirectProductRep"],["IsDirectProductElement"]]},{"rank" : 37,"comment" : "DepthOfPcElement: permpcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"]]},{"rank" : 27,"comment" : "DepthOfPcElement: pcgs by pcgs","filters" : [["IsPcgs","IsPcgsByPcgsRep"],[]]},{"rank" : 26,"comment" : "DepthOfPcElement: sorted pcgs","filters" : [["IsPcgs","IsSortedPcgsRep"],[]]},{"rank" : 26,"comment" : "DepthOfPcElement: induced pcgs","filters" : [["IsInducedPcgs","IsInducedPcgsRep"],[]]},{"rank" : 25,"comment" : "DepthOfPcElement: unsorted pcgs","filters" : [["IsPcgs","IsUnsortedPcgsRep"],[]]},{"rank" : 24,"comment" : "DepthOfPcElement: pcgs modulo pcgs","filters" : [["IsModuloPcgs","IsModuloPcgsRep"],[]]},{"rank" : 21,"comment" : "DepthOfPcElement: generic methods, ExponentsOfPcElement","filters" : [["IsPcgs"],[]]}],"3args" : [{"rank" : 379,"comment" : "DepthOfPcElement","filters" : [["IsPcgs","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]},{"rank" : 56,"comment" : "DepthOfPcElement: permpcgs,start","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"],["IsInt","IsPosRat"]]},{"rank" : 39,"comment" : "DepthOfPcElement: pcgs modulo pcgs, ignoring <min>","filters" : [["IsPcgs"],[],["IsInt"]]},{"rank" : 38,"comment" : "DepthOfPcElement: pcgs modulo pcgs, ignoring <min>","filters" : [["IsModuloPcgs"],[],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DifferenceOfPcElement","type" : "GAP_Operation","filters" : [[["IsPcgs"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 21,"comment" : "DifferenceOfPcElement: generic methods, PcElementByExponents\/ExponentsOfPcElement","filters" : [["IsPcgs"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentOfPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 379,"comment" : "ExponentOfPcElement: via nicoemorphism","filters" : [["IsPcgs","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]},{"rank" : 204,"comment" : "ExponentOfPcElement: family pcgs (32bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is32BitsPcWordRep"],["IsInt","IsPosRat"]]},{"rank" : 204,"comment" : "ExponentOfPcElement: family pcgs (16bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is16BitsPcWordRep"],["IsInt","IsPosRat"]]},{"rank" : 204,"comment" : "ExponentOfPcElement: family pcgs (8bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is8BitsPcWordRep"],["IsInt","IsPosRat"]]},{"rank" : 56,"comment" : "ExponentOfPcElement","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"],["IsInt","IsPosRat"]]},{"rank" : 49,"comment" : "ExponentOfPcElement: induced pcgs","filters" : [["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsInducedPcgs","IsInducedPcgsRep"],[],["IsInt","IsPosRat"]]},{"rank" : 45,"comment" : "ExponentOfPcElement: sorted pcgs","filters" : [["IsPcgs","IsSortedPcgsRep"],[],["IsInt","IsPosRat"]]},{"rank" : 44,"comment" : "ExponentOfPcElement: unsorted pcgs","filters" : [["IsPcgs","IsUnsortedPcgsRep"],[],["IsInt","IsPosRat"]]},{"rank" : 44,"comment" : "ExponentOfPcElement: pcgs modulo tail-pcgs, ExponentsOfPcElement","filters" : [["IsModuloPcgs","IsModuloTailPcgsRep"],[],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "ExponentOfPcElement: generic method, ExponentsOfPcElement","filters" : [["IsPcgs"],[],["IsInt","IsPosRat"]]},{"rank" : 39,"comment" : "ExponentOfPcElement: pcgs modulo pcgs, ExponentsOfPcElement","filters" : [["IsModuloPcgs"],[],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentsOfPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 360,"comment" : "ExponentsOfPcElement: handled by nice monomorphism: attribute CollElm","filters" : [["IsPcgs","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 179,"comment" : "ExponentsOfPcElement: family pcgs\/32 bit","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["Is32BitsPcWordRep"]]},{"rank" : 179,"comment" : "ExponentsOfPcElement: family pcgs\/16 bit","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["Is16BitsPcWordRep"]]},{"rank" : 179,"comment" : "ExponentsOfPcElement: family pcgs\/8 bit","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["Is8BitsPcWordRep"]]},{"rank" : 82,"comment" : "ExponentsOfPcElement: family pcgs","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 40,"comment" : "ExponentsOfPcElement: for pcgs of direct product","filters" : [["IsPcgs","IsPcgsDirectProductRep"],["IsDirectProductElement"]]},{"rank" : 37,"comment" : "ExponentsOfPcElement: perm group","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"]]},{"rank" : 30,"comment" : "ExponentsOfPcElement: subset of induced pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsSubsetInducedPcgsRep"],[]]},{"rank" : 30,"comment" : "ExponentsOfPcElement: induced pcgs","filters" : [["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsInducedPcgs","IsInducedPcgsRep"],[]]},{"rank" : 29,"comment" : "ExponentsOfPcElement: fp","filters" : [["IsModuloPcgsFpGroupRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 27,"comment" : "ExponentsOfPcElement: pcgs by pcgs","filters" : [["IsPcgs","IsPcgsByPcgsRep"],[]]},{"rank" : 26,"comment" : "ExponentsOfPcElement: sorted pcgs","filters" : [["IsPcgs","IsSortedPcgsRep"],[]]},{"rank" : 26,"comment" : "ExponentsOfPcElement: subset induced pcgs modulo tail-pcgs","filters" : [["IsModuloPcgs","IsModuloTailPcgsRep","IsNumeratorParentForExponentsRep"],[]]},{"rank" : 25,"comment" : "ExponentsOfPcElement: unsorted pcgs","filters" : [["IsPcgs","IsUnsortedPcgsRep"],[]]},{"rank" : 25,"comment" : "ExponentsOfPcElement: pcgs modulo tail-pcgs","filters" : [["IsModuloPcgs","IsModuloTailPcgsRep"],[]]},{"rank" : 25,"comment" : "ExponentsOfPcElement: modpcgs numerator parent layers","filters" : [["IsModuloPcgs","IsModuloPcgsRep","IsNumeratorParentLayersForExponentsRep"],[]]},{"rank" : 24,"comment" : "ExponentsOfPcElement: pcgs modulo pcgs","filters" : [["IsModuloPcgs","IsModuloPcgsRep"],[]]},{"rank" : 21,"comment" : "ExponentsOfPcElement: pc series","filters" : [["IsPcgs"],[]]}],"3args" : [{"rank" : 389,"comment" : "ExponentsOfPcElement","filters" : [["IsPcgs","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 377,"comment" : "ExponentsOfPcElement: perm group with 0 positions","filters" : [["IsPcgs","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 181,"comment" : "ExponentsOfPcElement: family pcgs\/32 bit","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["Is32BitsPcWordRep"],["IsList"]]},{"rank" : 181,"comment" : "ExponentsOfPcElement: family pcgs\/16 bit","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["Is16BitsPcWordRep"],["IsList"]]},{"rank" : 181,"comment" : "ExponentsOfPcElement: family pcgs\/8 bit","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["Is8BitsPcWordRep"],["IsList"]]},{"rank" : 66,"comment" : "ExponentsOfPcElement: perm group with positions","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 54,"comment" : "ExponentsOfPcElement: perm group with 0 positions","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 32,"comment" : "ExponentsOfPcElement: subset of induced pcgs, subrange","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsSubsetInducedPcgsRep"],[],["IsList"]]},{"rank" : 32,"comment" : "ExponentsOfPcElement: induced pcgs, subrange","filters" : [["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsInducedPcgs","IsInducedPcgsRep"],[],["IsList"]]},{"rank" : 28,"comment" : "ExponentsOfPcElement: sorted pcgs\/range","filters" : [["IsPcgs","IsSortedPcgsRep"],[],["IsList"]]},{"rank" : 28,"comment" : "ExponentsOfPcElement: subset induced pcgs modulo tail-pcgs, subrange","filters" : [["IsModuloPcgs","IsModuloTailPcgsRep","IsNumeratorParentForExponentsRep"],[],["IsList"]]},{"rank" : 27,"comment" : "ExponentsOfPcElement: unsorted pcgs\/range","filters" : [["IsPcgs","IsUnsortedPcgsRep"],[],["IsList"]]},{"rank" : 27,"comment" : "ExponentsOfPcElement: pcgs modulo tail-pcgs, subrange","filters" : [["IsModuloPcgs","IsModuloTailPcgsRep"],[],["IsList"]]},{"rank" : 26,"comment" : "ExponentsOfPcElement: pcgs modulo pcgs, subrange","filters" : [["IsModuloPcgs","IsModuloPcgsRep"],[],["IsList"]]},{"rank" : 23,"comment" : "ExponentsOfPcElement: with positions, falling back to ExponentsOfPcElement","filters" : [["IsPcgs"],[],["IsList"]]},{"rank" : 22,"comment" : "ExponentsOfPcElement: pcgs mod. pcgs,range, falling back to Exp.OfPcElement","filters" : [["IsModuloPcgs"],[],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentsOfConjugate","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 114,"comment" : "ExponentsOfConjugate: family pcgs: look up","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 64,"comment" : "ExponentsOfConjugate: subset induced pcgs modulo tail-pcgs","filters" : [["IsModuloPcgs","IsModuloTailPcgsRep","IsNumeratorParentForExponentsRep"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 58,"comment" : "ExponentsOfConjugate: generic: compute conjugate","filters" : [["IsModuloPcgs"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentsOfRelativePower","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 95,"comment" : "ExponentsOfRelativePower: family pcgs: look up","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsInt","IsPosRat"]]},{"rank" : 45,"comment" : "ExponentsOfRelativePower: subset induced pcgs modulo tail-pcgs","filters" : [["IsModuloPcgs","IsModuloTailPcgsRep","IsNumeratorParentForExponentsRep"],["IsInt","IsPosRat"]]},{"rank" : 39,"comment" : "ExponentsOfRelativePower: generic: compute power","filters" : [["IsModuloPcgs"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentsOfCommutator","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 58,"comment" : "ExponentsOfCommutator: generic: compute commutator","filters" : [["IsModuloPcgs"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadingExponentOfPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 360,"comment" : "LeadingExponentOfPcElement: handled by nice monomorphism: attribute CollElm","filters" : [["IsPcgs","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 185,"comment" : "LeadingExponentOfPcElement: family pcgs (32 bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is32BitsPcWordRep"]]},{"rank" : 185,"comment" : "LeadingExponentOfPcElement: family pcgs (16 bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is16BitsPcWordRep"]]},{"rank" : 185,"comment" : "LeadingExponentOfPcElement: family pcgs (8 bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is8BitsPcWordRep"]]},{"rank" : 82,"comment" : "LeadingExponentOfPcElement: family pcgs","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws"]]},{"rank" : 37,"comment" : "LeadingExponentOfPcElement","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"]]},{"rank" : 30,"comment" : "LeadingExponentOfPcElement: subset induced pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsSubsetInducedPcgsRep"],[]]},{"rank" : 26,"comment" : "LeadingExponentOfPcElement: sorted pcgs","filters" : [["IsPcgs","IsSortedPcgsRep"],[]]},{"rank" : 25,"comment" : "LeadingExponentOfPcElement: unsorted pcgs","filters" : [["IsPcgs","IsUnsortedPcgsRep"],[]]},{"rank" : 21,"comment" : "LeadingExponentOfPcElement: generic methods, ExponentsOfPcElement","filters" : [["IsPcgs"],[]]},{"rank" : 20,"comment" : "LeadingExponentOfPcElement: pcgs modulo pcgs, use ExponentsOfPcElement","filters" : [["IsModuloPcgs"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DepthAndLeadingExponentOfPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "DepthAndLeadingExponentOfPcElement: permpcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsPerm"]]},{"rank" : 20,"comment" : "DepthAndLeadingExponentOfPcElement: generic methods, ExponentsOfPcElement","filters" : [["IsModuloPcgs"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcElementByExponentsNC","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 107,"comment" : "PcElementByExponentsNC: family pcgs, FFE","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 107,"comment" : "PcElementByExponentsNC: family pcgs","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 83,"comment" : "PcElementByExponentsNC: subset induced wrt family pcgs, FFE","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsSubsetInducedPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 83,"comment" : "PcElementByExponentsNC: subset induced wrt family pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsSubsetInducedPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 63,"comment" : "PcElementByExponentsNC: modulo subset induced wrt family pcgs, FFE","filters" : [["IsModuloPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)","IsSubsetInducedNumeratorModuloTailPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 63,"comment" : "PcElementByExponentsNC: modulo subset induced wrt family pcgs","filters" : [["IsModuloPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)","IsSubsetInducedNumeratorModuloTailPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 51,"comment" : "PcElementByExponentsNC: generic method: modulo, FFE","filters" : [["IsModuloPcgs"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 51,"comment" : "PcElementByExponentsNC: generic method: modulo","filters" : [["IsModuloPcgs"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 38,"comment" : "PcElementByExponentsNC: generic method for empty lists","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 37,"comment" : "PcElementByExponentsNC: generic method for empty lists","filters" : [["IsModuloPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 33,"comment" : "PcElementByExponentsNC: generic method","filters" : [["IsList"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 33,"comment" : "PcElementByExponentsNC: generic method: call LinearCombinationPcgs","filters" : [["IsList"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]}],"3args" : [{"rank" : 10039,"comment" : "PcElementByExponentsNC: generic method for empty list as basis or basisindex, modulo","filters" : [["IsModuloPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"]]},{"rank" : 138,"comment" : "PcElementByExponentsNC: family pcgs, basisind, FFE","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 138,"comment" : "PcElementByExponentsNC: family pcgs, index","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 114,"comment" : "PcElementByExponentsNC: subset induced wrt family pcgs, FFE,index","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsSubsetInducedPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 114,"comment" : "PcElementByExponentsNC: subset induced wrt family pcgs, index","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsSubsetInducedPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 94,"comment" : "PcElementByExponentsNC: modulo subset induced wrt family pcgs, FFE, index","filters" : [["IsModuloPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)","IsSubsetInducedNumeratorModuloTailPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 94,"comment" : "PcElementByExponentsNC: modulo subset induced wrt family pcgs,index","filters" : [["IsModuloPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)","IsSubsetInducedNumeratorModuloTailPcgsRep"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 82,"comment" : "PcElementByExponentsNC: index: defer to basis,FFE","filters" : [["IsModuloPcgs"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 82,"comment" : "PcElementByExponentsNC: index: defer to basis","filters" : [["IsModuloPcgs"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 55,"comment" : "PcElementByExponentsNC: generic method for empty lists","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 54,"comment" : "PcElementByExponentsNC: multiply base elts., FFE","filters" : [["IsPcgs"],["IsList"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 54,"comment" : "PcElementByExponentsNC: multiply basis elements","filters" : [["IsPcgs"],["IsList"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]},{"rank" : 53,"comment" : "PcElementByExponentsNC: generic method: modulo, basis, FFE","filters" : [["IsModuloPcgs"],["IsList"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsFFE)"]]},{"rank" : 53,"comment" : "PcElementByExponentsNC: generic method: modulo, basis","filters" : [["IsModuloPcgs"],["IsList"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","CategoryCollections(IsCyclotomic)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SumOfPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 21,"comment" : "SumOfPcElement: generic methods, PcElementByExponents+ExponentsOfPcElement","filters" : [["IsPcgs"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 25,"comment" : "ReducedPcElement: generic method","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],[],[]]},{"rank" : 20,"comment" : "ReducedPcElement: pcgs modulo pcgs","filters" : [["IsModuloPcgs"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelativeOrderOfPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 29,"comment" : "RelativeOrderOfPcElement: fp","filters" : [["IsModuloPcgsFpGroupRep"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 25,"comment" : "RelativeOrderOfPcElement: for IsPrimeOrdersPcgs using RelativeOrders","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],[]]},{"rank" : 21,"comment" : "RelativeOrderOfPcElement: general method using RelativeOrders","filters" : [["IsPcgs"],[]]},{"rank" : 20,"comment" : "RelativeOrderOfPcElement: pcgs modulo pcgs","filters" : [["IsModuloPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HeadPcElementByNumber","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 203,"comment" : "HeadPcElementByNumber: family pcgs (32bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is32BitsPcWordRep"],["IsInt"]]},{"rank" : 203,"comment" : "HeadPcElementByNumber: family pcgs (16bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is16BitsPcWordRep"],["IsInt"]]},{"rank" : 203,"comment" : "HeadPcElementByNumber: family pcgs (8bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is8BitsPcWordRep"],["IsInt"]]},{"rank" : 39,"comment" : "HeadPcElementByNumber: using 'ExponentsOfPcElement', 'PcElementByExponents'","filters" : [["IsPcgs"],[],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CleanedTailPcElement","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 203,"comment" : "CleanedTailPcElement: family pcgs (32bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is32BitsPcWordRep"],["IsInt"]]},{"rank" : 203,"comment" : "CleanedTailPcElement: family pcgs (16bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is16BitsPcWordRep"],["IsInt"]]},{"rank" : 203,"comment" : "CleanedTailPcElement: family pcgs (8bits)","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverseByRws","Is8BitsPcWordRep"],["IsInt"]]},{"rank" : 100,"comment" : "CleanedTailPcElement: family pcgs","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]},{"rank" : 50,"comment" : "CleanedTailPcElement: sorted pcgs - defer to sorting pcgs","filters" : [["IsPcgs","IsSortedPcgsRep"],["IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]},{"rank" : 45,"comment" : "CleanedTailPcElement: generic: do nothing","filters" : [["IsPcgs"],["IsMultiplicativeElementWithInverse"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtendedIntersectionSumPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsList"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 29,"comment" : "ExtendedIntersectionSumPcgs: generic method for modulo pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsList"],[]]}],"5args" : [],"6args" : []}},{"name" : "IntersectionSumPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 55,"comment" : "IntersectionSumPcgs: prime orders pcgs, tail-pcgs, list","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsInducedPcgs","IsTailInducedPcgsRep"],["IsList"]]},{"rank" : 29,"comment" : "IntersectionSumPcgs: using 'ExtendedIntersectionSumPcgs'","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalIntersectionPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 79,"comment" : "NormalIntersectionPcgs: prime orders pcgs, tail-pcgs, induced-pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsInducedPcgs","IsTailInducedPcgsRep"],["IsInducedPcgs","IsInducedPcgsRep"]]},{"rank" : 55,"comment" : "NormalIntersectionPcgs: prime orders pcgs, tail-pcgs, list","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsInducedPcgs","IsTailInducedPcgsRep"],["IsList"]]},{"rank" : 29,"comment" : "NormalIntersectionPcgs: using 'ExtendedIntersectionSumPcgs'","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SumPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 29,"comment" : "SumPcgs: generic method","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SumFactorizationFunctionPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsList"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 29,"comment" : "SumFactorizationFunctionPcgs: generic method","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsList"],[]]}],"5args" : [],"6args" : []}},{"name" : "EnumeratorByPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "EnumeratorByPcgs: pcgs","filters" : [["IsPcgs"]]}],"2args" : [{"rank" : 23,"comment" : "EnumeratorByPcgs: pcgs, sublist","filters" : [["IsPcgs"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtendedPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 87,"comment" : "ExtendedPcgs: perm pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsList","CategoryCollections(IsPerm)"]]},{"rank" : 38,"comment" : "ExtendedPcgs: pcgs, empty list","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 24,"comment" : "ExtendedPcgs: induced pcgs","filters" : [["IsInducedPcgs"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsByPcSequence","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "InducedPcgsByPcSequence","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 26,"comment" : "InducedPcgsByPcSequence","filters" : [["IsPcgs"],["IsHomogeneousList","IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsByPcSequenceNC","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 87,"comment" : "InducedPcgsByPcSequenceNC: tail of perm pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsPcgsPermGroupRep"],["IsList","CategoryCollections(IsPerm)"]]},{"rank" : 38,"comment" : "InducedPcgsByPcSequenceNC: pcgs, empty list","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 26,"comment" : "InducedPcgsByPcSequenceNC: pcgs, homogeneous list","filters" : [["IsPcgs"],["IsHomogeneousList","IsCollection"]]}],"3args" : [{"rank" : 40,"comment" : "InducedPcgsByPcSequenceNC: pcgs, empty list,depths","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"]]},{"rank" : 28,"comment" : "InducedPcgsByPcSequenceNC: pcgs, homogeneous list, depths","filters" : [["IsPcgs"],["IsHomogeneousList","IsCollection"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadCoeffsIGS","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "LeadCoeffsIGS: system getter","filters" : [["IsAttributeStoringRep","Tester(LeadCoeffsIGS)"]]},{"rank" : 30,"comment" : "LeadCoeffsIGS: generic","filters" : [["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsInducedPcgs","IsInducedPcgsRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeadCoeffsIGS)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LeadCoeffsIGS): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeadCoeffsIGS): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeadCoeffsIGS)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsByPcSequenceAndGenerators","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 29,"comment" : "InducedPcgsByPcSequenceAndGenerators","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsByGenerators","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "InducedPcgsByGenerators","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 23,"comment" : "InducedPcgsByGenerators: pcgs, collection","filters" : [["IsPcgs"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsByGeneratorsNC","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "InducedPcgsByGeneratorsNC: pcgs, empty list","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 27,"comment" : "InducedPcgsByGeneratorsNC: prime order pcgs, collection","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsCollection"]]},{"rank" : 0,"comment" : "InducedPcgsByGeneratorsNC:  fallback method to test conditions","filters" : [["IsPcgs"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsByGeneratorsWithImages","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsCollection"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 59,"comment" : "InducedPcgsByGeneratorsWithImages","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 29,"comment" : "InducedPcgsByGeneratorsWithImages","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsCollection"],["IsCollection"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalPcgsByGeneratorsWithImages","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsCollection"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 29,"comment" : "CanonicalPcgsByGeneratorsWithImages","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsCollection"],["IsCollection"]]},{"rank" : 25,"comment" : "CanonicalPcgsByGeneratorsWithImages","filters" : [["IsPcgs"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsInducedPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "AsInducedPcgs","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 25,"comment" : "AsInducedPcgs","filters" : [["IsPcgs"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParentPcgs","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ParentPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(ParentPcgs)"]]},{"rank" : 21,"comment" : "ParentPcgs","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ParentPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ParentPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ParentPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ParentPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalPcgs","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "CanonicalPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalPcgs)"]]},{"rank" : 10024,"comment" : "CanonicalPcgs: of an canonical pcgs","filters" : [["IsCanonicalPcgs","Tester(IsCanonicalPcgs)"]]},{"rank" : 26,"comment" : "CanonicalPcgs: induced prime orders pcgs","filters" : [["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsInducedPcgs"]]},{"rank" : 0,"comment" : "CanonicalPcgs:  fallback method to test conditions","filters" : [["IsInducedPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCanonicalPcgs","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsCanonicalPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCanonicalPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCanonicalPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCanonicalPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCanonicalPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCanonicalPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsParentPcgsFamilyPcgs","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsParentPcgsFamilyPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsParentPcgsFamilyPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsParentPcgsFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsParentPcgsFamilyPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsParentPcgsFamilyPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsParentPcgsFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementaryAbelianSubseries","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "ElementaryAbelianSubseries: system getter","filters" : [["IsAttributeStoringRep","Tester(ElementaryAbelianSubseries)"]]},{"rank" : 21,"comment" : "ElementaryAbelianSubseries: generic method","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ElementaryAbelianSubseries)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ElementaryAbelianSubseries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ElementaryAbelianSubseries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ElementaryAbelianSubseries)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalPcElement","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 158,"comment" : "CanonicalPcElement: tail induced pcgs, 32bits word","filters" : [["IsInducedPcgs","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsTailInducedPcgsRep"],["IsMultiplicativeElementWithInverseByRws","Is32BitsPcWordRep"]]},{"rank" : 158,"comment" : "CanonicalPcElement: tail induced pcgs, 16bits word","filters" : [["IsInducedPcgs","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsTailInducedPcgsRep"],["IsMultiplicativeElementWithInverseByRws","Is16BitsPcWordRep"]]},{"rank" : 158,"comment" : "CanonicalPcElement: tail induced pcgs, 8bits word","filters" : [["IsInducedPcgs","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsTailInducedPcgsRep"],["IsMultiplicativeElementWithInverseByRws","Is8BitsPcWordRep"]]},{"rank" : 30,"comment" : "CanonicalPcElement: generic method","filters" : [["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsInducedPcgs","IsInducedPcgsRep"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SiftedPcElement","type" : "GAP_Operation","filters" : [[["IsInducedPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 81,"comment" : "SiftedPcElement: family pcgs","filters" : [["IsPcgs","IsFamilyPcgs","Tester(IsFamilyPcgs)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 30,"comment" : "SiftedPcElement: for induced pcgs","filters" : [["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsInducedPcgs","IsInducedPcgsRep"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HomomorphicCanonicalPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "HomomorphicCanonicalPcgs: pcgs, list","filters" : [["IsPcgs"],["IsList"]]}],"3args" : [{"rank" : 23,"comment" : "HomomorphicCanonicalPcgs: pcgs, list, object","filters" : [["IsPcgs"],["IsList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HomomorphicInducedPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "HomomorphicInducedPcgs","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 29,"comment" : "HomomorphicInducedPcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 39,"comment" : "HomomorphicInducedPcgs","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsFunction"]]},{"rank" : 38,"comment" : "HomomorphicInducedPcgs","filters" : [["IsPcgs"],["IsList","IsEmpty","Tester(IsEmpty)"],[]]},{"rank" : 30,"comment" : "HomomorphicInducedPcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsHomogeneousList"],["IsFunction"]]},{"rank" : 29,"comment" : "HomomorphicInducedPcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsHomogeneousList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFamilyPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsFamilyPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFamilyPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFamilyPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFamilyPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ModuloPcgsByPcSequenceNC","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"],["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 44,"comment" : "ModuloPcgsByPcSequenceNC: generic method for pcgs mod pcgs","filters" : [["IsPcgs"],["IsList"],["IsPcgs"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ModuloPcgsByPcSequence","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsList"],["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 45,"comment" : "ModuloPcgsByPcSequence: generic method","filters" : [["IsPcgs"],["IsList"],["IsInducedPcgs"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ModuloPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 110,"comment" : "ModuloPcgs: for permutation groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 70,"comment" : "ModuloPcgs: subgroups fp","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 66,"comment" : "ModuloPcgs: for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DenominatorOfModuloPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "DenominatorOfModuloPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(DenominatorOfModuloPcgs)"]]},{"rank" : 26,"comment" : "DenominatorOfModuloPcgs","filters" : [["IsModuloPcgsPermGroupRep"]]},{"rank" : 26,"comment" : "DenominatorOfModuloPcgs: modolo-tail-pcgs-by-list-rep","filters" : [["IsModuloPcgs","IsModuloTailPcgsByListRep"]]},{"rank" : 24,"comment" : "DenominatorOfModuloPcgs: fp","filters" : [["IsModuloPcgsFpGroupRep"]]},{"rank" : 21,"comment" : "DenominatorOfModuloPcgs: for pcgs","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DenominatorOfModuloPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DenominatorOfModuloPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DenominatorOfModuloPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DenominatorOfModuloPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumeratorOfModuloPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "NumeratorOfModuloPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(NumeratorOfModuloPcgs)"]]},{"rank" : 26,"comment" : "NumeratorOfModuloPcgs","filters" : [["IsModuloPcgsPermGroupRep"]]},{"rank" : 26,"comment" : "NumeratorOfModuloPcgs: modolo-tail-pcgs-by-list-rep","filters" : [["IsModuloPcgs","IsModuloTailPcgsByListRep"]]},{"rank" : 24,"comment" : "NumeratorOfModuloPcgs: fp","filters" : [["IsModuloPcgsFpGroupRep"]]},{"rank" : 21,"comment" : "NumeratorOfModuloPcgs: for pcgs","filters" : [["IsPcgs"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NumeratorOfModuloPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NumeratorOfModuloPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NumeratorOfModuloPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NumeratorOfModuloPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNumeratorParentPcgsFamilyPcgs","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsNumeratorParentPcgsFamilyPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNumeratorParentPcgsFamilyPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNumeratorParentPcgsFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNumeratorParentPcgsFamilyPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNumeratorParentPcgsFamilyPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNumeratorParentPcgsFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentsConjugateLayer","type" : "GAP_Operation","filters" : [[["IsModuloPcgs"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 59,"comment" : "ExponentsConjugateLayer: subset induced pcgs","filters" : [["IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsTailInducedPcgsRep"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 42,"comment" : "ExponentsConjugateLayer: subset induced modulo pcgs","filters" : [["IsModuloPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)","IsSubsetInducedNumeratorModuloTailPcgsRep"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 30,"comment" : "ExponentsConjugateLayer: default: compute brute force","filters" : [["IsModuloPcgs"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSpecialPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsSpecialPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSpecialPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSpecialPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpecialPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "SpecialPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(SpecialPcgs)"]]},{"rank" : 35,"comment" : "SpecialPcgs: method for special pcgs","filters" : [["IsSpecialPcgs","Tester(IsSpecialPcgs)"]]},{"rank" : 33,"comment" : "SpecialPcgs: last resort method which tests solvability","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "SpecialPcgs: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 25,"comment" : "SpecialPcgs: generic method for pcgs","filters" : [["IsPcgs","IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SpecialPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SpecialPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LGHeads","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "LGHeads: system getter","filters" : [["IsAttributeStoringRep","Tester(LGHeads)"]]},{"rank" : 25,"comment" : "LGHeads: for special pcgs","filters" : [["IsSpecialPcgs","Tester(IsSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LGHeads)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LGHeads): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LGHeads): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LGHeads)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LGTails","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "LGTails: system getter","filters" : [["IsAttributeStoringRep","Tester(LGTails)"]]},{"rank" : 25,"comment" : "LGTails: for special pcgs","filters" : [["IsSpecialPcgs","Tester(IsSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LGTails)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LGTails): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LGTails): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LGTails)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LGWeights","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "LGWeights: system getter","filters" : [["IsAttributeStoringRep","Tester(LGWeights)"]]},{"rank" : 23,"comment" : "LGWeights: for induced wrt special","filters" : [["IsInducedPcgsWrtSpecialPcgs","Tester(IsInducedPcgsWrtSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LGWeights)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LGWeights): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LGWeights): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LGWeights)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LGLayers","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "LGLayers: system getter","filters" : [["IsAttributeStoringRep","Tester(LGLayers)"]]},{"rank" : 23,"comment" : "LGLayers: for induced wrt special","filters" : [["IsInducedPcgsWrtSpecialPcgs","Tester(IsInducedPcgsWrtSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LGLayers)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LGLayers): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LGLayers): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LGLayers)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LGFirst","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "LGFirst: system getter","filters" : [["IsAttributeStoringRep","Tester(LGFirst)"]]},{"rank" : 23,"comment" : "LGFirst: for induced wrt special","filters" : [["IsInducedPcgsWrtSpecialPcgs","Tester(IsInducedPcgsWrtSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LGFirst)","type" : "GAP_Operation","filters" : [[["IsPcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LGFirst): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LGFirst): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LGFirst)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LGLength","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "LGLength: system getter","filters" : [["IsAttributeStoringRep","Tester(LGLength)"]]},{"rank" : 33,"comment" : "LGLength: for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "LGLength: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LGLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LGLength): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LGLength): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LGLength)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsWrtSpecialPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "InducedPcgsWrtSpecialPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(InducedPcgsWrtSpecialPcgs)"]]},{"rank" : 43,"comment" : "InducedPcgsWrtSpecialPcgs: method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 34,"comment" : "InducedPcgsWrtSpecialPcgs: for groups that have already an induced pcgs wrt family pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(InducedPcgsWrtFamilyPcgs)"]]},{"rank" : 34,"comment" : "InducedPcgsWrtSpecialPcgs: for groups that have already an induced pcgs wrt home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(InducedPcgsWrtHomePcgs)"]]},{"rank" : 33,"comment" : "InducedPcgsWrtSpecialPcgs: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "InducedPcgsWrtSpecialPcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InducedPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InducedPcgsWrtSpecialPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InducedPcgsWrtSpecialPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InducedPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalPcgsWrtSpecialPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CanonicalPcgsWrtSpecialPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalPcgsWrtSpecialPcgs)"]]},{"rank" : 0,"comment" : "CanonicalPcgsWrtSpecialPcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalPcgsWrtSpecialPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalPcgsWrtSpecialPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInducedPcgsWrtSpecialPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsInducedPcgsWrtSpecialPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsInducedPcgsWrtSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsInducedPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsInducedPcgsWrtSpecialPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsInducedPcgsWrtSpecialPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsInducedPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCanonicalPcgsWrtSpecialPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "IsCanonicalPcgsWrtSpecialPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCanonicalPcgsWrtSpecialPcgs)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCanonicalPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCanonicalPcgsWrtSpecialPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCanonicalPcgsWrtSpecialPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCanonicalPcgsWrtSpecialPcgs)","type" : "GAP_Operation","filters" : [[["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalPcgsWrtFamilyPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CanonicalPcgsWrtFamilyPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalPcgsWrtFamilyPcgs)"]]},{"rank" : 34,"comment" : "CanonicalPcgsWrtFamilyPcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FamilyPcgs)"]]},{"rank" : 0,"comment" : "CanonicalPcgsWrtFamilyPcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalPcgsWrtFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalPcgsWrtFamilyPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalPcgsWrtFamilyPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalPcgsWrtFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalPcgsWrtHomePcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CanonicalPcgsWrtHomePcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalPcgsWrtHomePcgs)"]]},{"rank" : 34,"comment" : "CanonicalPcgsWrtHomePcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 0,"comment" : "CanonicalPcgsWrtHomePcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalPcgsWrtHomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalPcgsWrtHomePcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalPcgsWrtHomePcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalPcgsWrtHomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FamilyPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "FamilyPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(FamilyPcgs)"]]},{"rank" : 0,"comment" : "FamilyPcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FamilyPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FamilyPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HomePcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "HomePcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(HomePcgs)"]]},{"rank" : 56,"comment" : "HomePcgs: use a perm pcgs if possible","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(Pcgs)"]]},{"rank" : 55,"comment" : "HomePcgs: try to compute a perm pcgs","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "HomePcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "HomePcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(HomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(HomePcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(HomePcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(HomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsWrtFamilyPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "InducedPcgsWrtFamilyPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(InducedPcgsWrtFamilyPcgs)"]]},{"rank" : 45,"comment" : "InducedPcgsWrtFamilyPcgs: whole family","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 34,"comment" : "InducedPcgsWrtFamilyPcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FamilyPcgs)"]]},{"rank" : 0,"comment" : "InducedPcgsWrtFamilyPcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InducedPcgsWrtFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InducedPcgsWrtFamilyPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InducedPcgsWrtFamilyPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InducedPcgsWrtFamilyPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgs","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 54,"comment" : "InducedPcgs: cache pcgs","filters" : [["IsPcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsOp","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 55,"comment" : "InducedPcgsOp: sift existing pcgs","filters" : [["IsPcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(Pcgs)"]]},{"rank" : 54,"comment" : "InducedPcgsOp: generic method","filters" : [["IsPcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedInducedPcgses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedInducedPcgses: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedInducedPcgses)"]]},{"rank" : 33,"comment" : "ComputedInducedPcgses: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedInducedPcgses: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedInducedPcgses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedInducedPcgses): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedInducedPcgses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedInducedPcgses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedPcgsWrtHomePcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "InducedPcgsWrtHomePcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(InducedPcgsWrtHomePcgs)"]]},{"rank" : 57,"comment" : "InducedPcgsWrtHomePcgs: tail of perm pcgs","filters" : [["Tester(HomePcgs)","IsMemberPcSeriesPermGroup"]]},{"rank" : 43,"comment" : "InducedPcgsWrtHomePcgs: pc group: home=family","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 33,"comment" : "InducedPcgsWrtHomePcgs: from generators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "InducedPcgsWrtHomePcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InducedPcgsWrtHomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InducedPcgsWrtHomePcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InducedPcgsWrtHomePcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InducedPcgsWrtHomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Pcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Pcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(Pcgs)"]]},{"rank" : 10034,"comment" : "Pcgs: take induced pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(InducedPcgsWrtHomePcgs)"]]},{"rank" : 10034,"comment" : "Pcgs: fail if insolvable","filters" : [["Tester(IsSolvableGroup)"]]},{"rank" : 367,"comment" : "Pcgs: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 156,"comment" : "Pcgs: tail of perm pcgs","filters" : [["IsMemberPcSeriesPermGroup"]]},{"rank" : 155,"comment" : "Pcgs: Sims's method","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 93,"comment" : "Pcgs: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 42,"comment" : "Pcgs: from independent generators of abelian group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CanEasilyComputeWithIndependentGensAbelianGroup"]]},{"rank" : 42,"comment" : "Pcgs: from independent generators of abelian group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(IndependentGeneratorsOfAbelianGroup)"]]},{"rank" : 36,"comment" : "Pcgs: for a group containing the whole family and with known family pcgs","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FamilyPcgs)"]]},{"rank" : 35,"comment" : "Pcgs: for a group with known home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 34,"comment" : "Pcgs: for a group with known family pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FamilyPcgs)"]]},{"rank" : 33,"comment" : "Pcgs: generic method using CompositionSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "Pcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Pcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "Setter(Pcgs)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]},{"rank" : 2,"comment" : "Setter(Pcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Pcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Pcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneralizedPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "GeneralizedPcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneralizedPcgs)"]]},{"rank" : 34,"comment" : "GeneralizedPcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(Pcgs)"]]},{"rank" : 0,"comment" : "GeneralizedPcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneralizedPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneralizedPcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneralizedPcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneralizedPcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubgroupByPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 54,"comment" : "SubgroupByPcgs: subgroup with pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPcgs"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AffineAction","type" : "GAP_Operation","filters" : [[["IsList"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 65,"comment" : "AffineAction: group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"],["IsFunction"]]},{"rank" : 53,"comment" : "AffineAction: pcgs","filters" : [["IsPcgs"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"],["IsFunction"]]},{"rank" : 34,"comment" : "AffineAction: generators","filters" : [["IsList"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"],["IsFunction"]]}],"5args" : [{"rank" : 67,"comment" : "AffineAction: group2","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"],["IsFunction"]]}],"6args" : []}},{"name" : "LinearAction","type" : "GAP_Operation","filters" : [[["IsList"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 64,"comment" : "LinearAction","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"]]},{"rank" : 52,"comment" : "LinearAction","filters" : [["IsPcgs"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"]]},{"rank" : 33,"comment" : "LinearAction","filters" : [["IsList"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"]]}],"4args" : [{"rank" : 66,"comment" : "LinearAction","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsFunction"]]}],"5args" : [],"6args" : []}},{"name" : "OmegaSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "OmegaSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(OmegaSeries)"]]},{"rank" : 50,"comment" : "OmegaSeries: for p-groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 0,"comment" : "OmegaSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OmegaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OmegaSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OmegaSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OmegaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerInHomePcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "NormalizerInHomePcgs: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizerInHomePcgs)"]]},{"rank" : 34,"comment" : "NormalizerInHomePcgs: for group with home pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]},{"rank" : 0,"comment" : "NormalizerInHomePcgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizerInHomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizerInHomePcgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizerInHomePcgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizerInHomePcgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(HomePcgs)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MultiplicationTable","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"]],[["IsMagma"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "MultiplicationTable: system getter","filters" : [["IsAttributeStoringRep","Tester(MultiplicationTable)"]]},{"rank" : 11,"comment" : "MultiplicationTable: for a magma","filters" : [["IsMagma"]]},{"rank" : 4,"comment" : "MultiplicationTable: for a list of elements","filters" : [["IsHomogeneousList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MultiplicationTable)","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"],[]],[["IsMagma"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MultiplicationTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MultiplicationTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MultiplicationTable)","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AllBlocks","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "AllBlocks: system getter","filters" : [["IsAttributeStoringRep","Tester(AllBlocks)"]]},{"rank" : 58,"comment" : "AllBlocks: generic","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "AllBlocks: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AllBlocks)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AllBlocks): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AllBlocks): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AllBlocks)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransitiveIdentification","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "TransitiveIdentification: system getter","filters" : [["IsAttributeStoringRep","Tester(TransitiveIdentification)"]]},{"rank" : 58,"comment" : "TransitiveIdentification: generic","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "TransitiveIdentification: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransitiveIdentification)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransitiveIdentification): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransitiveIdentification): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransitiveIdentification)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimitiveIdentification","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "PrimitiveIdentification: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimitiveIdentification)"]]},{"rank" : 58,"comment" : "PrimitiveIdentification: generic","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "PrimitiveIdentification: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimitiveIdentification)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimitiveIdentification): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimitiveIdentification): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimitiveIdentification)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ONanScottType","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "ONanScottType: system getter","filters" : [["IsAttributeStoringRep","Tester(ONanScottType)"]]},{"rank" : 58,"comment" : "ONanScottType: primitive permgroups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "ONanScottType: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ONanScottType)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ONanScottType): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ONanScottType): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ONanScottType)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SocleTypePrimitiveGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "SocleTypePrimitiveGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(SocleTypePrimitiveGroup)"]]},{"rank" : 58,"comment" : "SocleTypePrimitiveGroup: primitive permgroups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "SocleTypePrimitiveGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SocleTypePrimitiveGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SocleTypePrimitiveGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SocleTypePrimitiveGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SocleTypePrimitiveGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TwoClosure","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "TwoClosure: system getter","filters" : [["IsAttributeStoringRep","Tester(TwoClosure)"]]},{"rank" : 58,"comment" : "TwoClosure: permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "TwoClosure: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TwoClosure)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TwoClosure): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TwoClosure): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TwoClosure)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupGeneralMappingByImages","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "GroupGeneralMappingByImages: make onto","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]}],"4args" : [{"rank" : 70,"comment" : "GroupGeneralMappingByImages: for group, group, list, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "GroupGeneralMappingByImagesNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 372,"comment" : "GroupGeneralMappingByImagesNC: from a group handled by a niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsList"],["IsList"]]},{"rank" : 37,"comment" : "GroupGeneralMappingByImagesNC: make onto","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]}],"4args" : [{"rank" : 405,"comment" : "GroupGeneralMappingByImagesNC: from a group handled by a niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]},{"rank" : 100,"comment" : "GroupGeneralMappingByImagesNC: for pcp group, pcp group, list, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsList"],["IsList"]]},{"rank" : 85,"comment" : "GroupGeneralMappingByImagesNC: for group, pcp group, list, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsList"],["IsList"]]},{"rank" : 85,"comment" : "GroupGeneralMappingByImagesNC: for pcp group, group, list, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]},{"rank" : 70,"comment" : "GroupGeneralMappingByImagesNC: for group, group, list, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "GroupHomomorphismByImagesNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "GroupHomomorphismByImagesNC: for group, group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [{"rank" : 68,"comment" : "GroupHomomorphismByImagesNC: for group, group, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : 37,"comment" : "GroupHomomorphismByImagesNC: for group, list, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]}],"4args" : [{"rank" : 70,"comment" : "GroupHomomorphismByImagesNC: for group, group, list, list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "AsGroupGeneralMappingByImages","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AsGroupGeneralMappingByImages: system getter","filters" : [["IsAttributeStoringRep","Tester(AsGroupGeneralMappingByImages)"]]},{"rank" : 10017,"comment" : "AsGroupGeneralMappingByImages: for GHBI","filters" : [["IsGroupGeneralMappingByImages"]]},{"rank" : 347,"comment" : "AsGroupGeneralMappingByImages: for Niceomorphisms: avoid recursion","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsNiceMonomorphism"]]},{"rank" : 23,"comment" : "AsGroupGeneralMappingByImages: for conjugator isomorphism","filters" : [["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 17,"comment" : "AsGroupGeneralMappingByImages: for group homomorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 13,"comment" : "AsGroupGeneralMappingByImages: for group general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 0,"comment" : "AsGroupGeneralMappingByImages: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsGroupGeneralMappingByImages)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "Setter(AsGroupGeneralMappingByImages): assign MappingOfWhichItIsAsGGMBI","filters" : [["IsAttributeStoringRep","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 2,"comment" : "Setter(AsGroupGeneralMappingByImages): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsGroupGeneralMappingByImages): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsGroupGeneralMappingByImages)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MappingOfWhichItIsAsGGMBI","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "MappingOfWhichItIsAsGGMBI: system getter","filters" : [["IsAttributeStoringRep","Tester(MappingOfWhichItIsAsGGMBI)"]]},{"rank" : 0,"comment" : "MappingOfWhichItIsAsGGMBI: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MappingOfWhichItIsAsGGMBI)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MappingOfWhichItIsAsGGMBI): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MappingOfWhichItIsAsGGMBI): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MappingOfWhichItIsAsGGMBI)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismByNormalSubgroupNCOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10102,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: for group, and trivial group (delegate to `IdentityMapping')","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsTrivial","Tester(IsTrivial)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 401,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 116,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup, via pcp representation","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 116,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup, via pcp representation","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 116,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: test if known\/try solvable factor for permutation groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 96,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 96,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 92,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 73,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: trivial image fp case","filters" : [["IsSubgroupFpGroup"],["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"]]},{"rank" : 71,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: for subgroups of fp groups by quotient rep.","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 70,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: for subgroups of fp groups","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 66,"comment" : "NaturalHomomorphismByNormalSubgroupNCOp: search for operation","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismByNormalSubgroupNCInParent","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NaturalHomomorphismByNormalSubgroupNCInParent: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalHomomorphismByNormalSubgroupNCInParent)"]]},{"rank" : 33,"comment" : "NaturalHomomorphismByNormalSubgroupNCInParent: method that calls the two-argument operation NaturalHomomorphismByNormalSubgroupNCOp","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NaturalHomomorphismByNormalSubgroupNCInParent: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalHomomorphismByNormalSubgroupNCInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalHomomorphismByNormalSubgroupNCInParent): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalHomomorphismByNormalSubgroupNCInParent): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalHomomorphismByNormalSubgroupNCInParent)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismByNormalSubgroupNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 96,"comment" : "NaturalHomomorphismByNormalSubgroupNC: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 64,"comment" : "NaturalHomomorphismByNormalSubgroupNC: try to exploit the in-parent attribute NaturalHomomorphismByNormalSubgroupNCInParent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugatorIsomorphism","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "ConjugatorIsomorphism: for group and mult.-elm.-with-inverse","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugatorAutomorphismNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "ConjugatorAutomorphismNC: group and mult.-elm.-with-inverse","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InnerAutomorphismNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "InnerAutomorphismNC: for group and mult.-elm.-with-inverse","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMultiplicativeElementWithInverse"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsConjugatorIsomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsConjugatorIsomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 14,"comment" : "IsConjugatorIsomorphism: for a f.p. group general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 14,"comment" : "IsConjugatorIsomorphism: for a matrix group general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 14,"comment" : "IsConjugatorIsomorphism: perm group homomorphism","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 14,"comment" : "IsConjugatorIsomorphism: for a pc group general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 13,"comment" : "IsConjugatorIsomorphism: for a group general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 0,"comment" : "IsConjugatorIsomorphism: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsConjugatorIsomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsConjugatorIsomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsConjugatorIsomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsConjugatorIsomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInnerAutomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsInnerAutomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsInnerAutomorphism)"]]},{"rank" : 13,"comment" : "IsInnerAutomorphism: for a group general mapping","filters" : [["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 0,"comment" : "IsInnerAutomorphism: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsInnerAutomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsInnerAutomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsInnerAutomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsInnerAutomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugatorOfConjugatorIsomorphism","type" : "GAP_Operation","filters" : [[["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "ConjugatorOfConjugatorIsomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(ConjugatorOfConjugatorIsomorphism)"]]},{"rank" : 23,"comment" : "ConjugatorOfConjugatorIsomorphism: default -- try RepresentativeAction","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]},{"rank" : 0,"comment" : "ConjugatorOfConjugatorIsomorphism: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConjugatorOfConjugatorIsomorphism)","type" : "GAP_Operation","filters" : [[["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConjugatorOfConjugatorIsomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConjugatorOfConjugatorIsomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConjugatorOfConjugatorIsomorphism)","type" : "GAP_Operation","filters" : [[["IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImagesSmallestGenerators","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "ImagesSmallestGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(ImagesSmallestGenerators)"]]},{"rank" : 17,"comment" : "ImagesSmallestGenerators: group homomorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 0,"comment" : "ImagesSmallestGenerators: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImagesSmallestGenerators)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImagesSmallestGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImagesSmallestGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImagesSmallestGenerators)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RegularActionHomomorphism","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "RegularActionHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(RegularActionHomomorphism)"]]},{"rank" : 42,"comment" : "RegularActionHomomorphism: generic","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RegularActionHomomorphism:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "RegularActionHomomorphism: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RegularActionHomomorphism)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RegularActionHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RegularActionHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RegularActionHomomorphism)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalIsomorphismByPcgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 54,"comment" : "NaturalIsomorphismByPcgs: for group and pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPcgs"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectProductOp","type" : "GAP_Operation","filters" : [[["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 77,"comment" : "DirectProductOp: for a list of permutation groups, and a permutation group","filters" : [["IsList","CategoryCollections(CategoryCollections(IsPerm))"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 50,"comment" : "DirectProductOp: for pcp groups","filters" : [["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 48,"comment" : "DirectProductOp: for a list (of pc groups), and a pc group","filters" : [["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 45,"comment" : "DirectProductOp: matrix groups","filters" : [["IsList"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 38,"comment" : "DirectProductOp: for a list of fp groups, and a fp group","filters" : [["IsList"],["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 35,"comment" : "DirectProductOp: for a list (of groups), and a group","filters" : [["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubdirectProductOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 150,"comment" : "SubdirectProductOp: permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 126,"comment" : "SubdirectProductOp: pcgroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 100,"comment" : "SubdirectProductOp: groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]}],"5args" : [],"6args" : []}},{"name" : "SemidirectProduct","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "SemidirectProduct: generic method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 47,"comment" : "SemidirectProduct: generic method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsRecord"]]},{"rank" : 33,"comment" : "SemidirectProduct: automorphisms group with group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 133,"comment" : "SemidirectProduct: Induced permutation automorphisms","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 133,"comment" : "SemidirectProduct: generic method for permutation groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 101,"comment" : "SemidirectProduct: group with vector space: affine","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFullRowModule","Tester(IsFullRowModule)"]]},{"rank" : 93,"comment" : "SemidirectProduct: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["CanEasilyComputePcgs"]]},{"rank" : 85,"comment" : "SemidirectProduct: group with fp","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsSubgroupFpGroup"]]},{"rank" : 85,"comment" : "SemidirectProduct: fp with group","filters" : [["IsSubgroupFpGroup"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 81,"comment" : "SemidirectProduct: different representations","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WreathProduct","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 116,"comment" : "WreathProduct: permgroups: imprimitive","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 101,"comment" : "WreathProduct: imprimitive matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 88,"comment" : "WreathProduct: generic groups with perm","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "WreathProduct: generic groups, no perm","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [{"rank" : 124,"comment" : "WreathProduct: permgroups and action","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsSPGeneralMapping"]]},{"rank" : 107,"comment" : "WreathProduct","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 74,"comment" : "WreathProduct: generic groups with permhom","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsSPGeneralMapping"]]}],"4args" : [{"rank" : 126,"comment" : "WreathProduct","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "StandardWreathProduct","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "StandardWreathProduct: generic groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeProductOp","type" : "GAP_Operation","filters" : [[["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "FreeProductOp: for a list (of groups), and a group","filters" : [["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectProductInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DirectProductInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(DirectProductInfo)"]]},{"rank" : 0,"comment" : "DirectProductInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DirectProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DirectProductInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DirectProductInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DirectProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubdirectProductInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SubdirectProductInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(SubdirectProductInfo)"]]},{"rank" : 0,"comment" : "SubdirectProductInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SubdirectProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SubdirectProductInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SubdirectProductInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SubdirectProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemidirectProductInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SemidirectProductInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(SemidirectProductInfo)"]]},{"rank" : 0,"comment" : "SemidirectProductInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemidirectProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemidirectProductInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemidirectProductInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemidirectProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WreathProductInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "WreathProductInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(WreathProductInfo)"]]},{"rank" : 0,"comment" : "WreathProductInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WreathProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WreathProductInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WreathProductInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WreathProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeProductInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "FreeProductInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeProductInfo)"]]},{"rank" : 0,"comment" : "FreeProductInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeProductInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeProductInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeProductInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNaturalSymmetricGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsNaturalSymmetricGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 59,"comment" : "IsNaturalSymmetricGroup: knows size","filters" : [["Tester(Size)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "IsNaturalSymmetricGroup: comprehensive","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "IsNaturalSymmetricGroup: for non-permutation group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "IsNaturalSymmetricGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNaturalSymmetricGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNaturalSymmetricGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNaturalSymmetricGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNaturalSymmetricGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNaturalAlternatingGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsNaturalAlternatingGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 59,"comment" : "IsNaturalAlternatingGroup: knows size","filters" : [["Tester(Size)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "IsNaturalAlternatingGroup: comprehensive","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "IsNaturalAlternatingGroup: for non-permutation group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "IsNaturalAlternatingGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNaturalAlternatingGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNaturalAlternatingGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNaturalAlternatingGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNaturalAlternatingGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAlternatingGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsAlternatingGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAlternatingGroup)"]]},{"rank" : 33,"comment" : "IsAlternatingGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsAlternatingGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAlternatingGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAlternatingGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAlternatingGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAlternatingGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSymmetricGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSymmetricGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSymmetricGroup)"]]},{"rank" : 33,"comment" : "IsSymmetricGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsSymmetricGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSymmetricGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSymmetricGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSymmetricGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSymmetricGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymmetricParentGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "SymmetricParentGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(SymmetricParentGroup)"]]},{"rank" : 62,"comment" : "SymmetricParentGroup: natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 58,"comment" : "SymmetricParentGroup: symm(moved pts)","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "SymmetricParentGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SymmetricParentGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SymmetricParentGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SymmetricParentGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SymmetricParentGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlternatingSubgroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "AlternatingSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AlternatingSubgroup)"]]},{"rank" : 58,"comment" : "AlternatingSubgroup: for perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "AlternatingSubgroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AlternatingSubgroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AlternatingSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AlternatingSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AlternatingSubgroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrbitStabilizingParentGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "OrbitStabilizingParentGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(OrbitStabilizingParentGroup)"]]},{"rank" : 58,"comment" : "OrbitStabilizingParentGroup: direct product of S_n's","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "OrbitStabilizingParentGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrbitStabilizingParentGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrbitStabilizingParentGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrbitStabilizingParentGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrbitStabilizingParentGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTrivialNormalIntersection","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 100,"comment" : "IsTrivialNormalIntersection: if minimal normal subgroups are computed","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MinimalNormalSubgroups)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 99,"comment" : "IsTrivialNormalIntersection: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalComplement","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "NormalComplement: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalComplementNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "NormalComplementNC: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectFactorsOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DirectFactorsOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DirectFactorsOfGroup)"]]},{"rank" : 35,"comment" : "DirectFactorsOfGroup: for direct products if normal subgroups are computed","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(NormalSubgroups)","Tester(DirectProductInfo)"]]},{"rank" : 34,"comment" : "DirectFactorsOfGroup: if normal subgroups are computed","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(NormalSubgroups)"]]},{"rank" : 34,"comment" : "DirectFactorsOfGroup: for direct products","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DirectProductInfo)"]]},{"rank" : 33,"comment" : "DirectFactorsOfGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DirectFactorsOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DirectFactorsOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DirectFactorsOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DirectFactorsOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DirectFactorsOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemidirectFactorsOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SemidirectFactorsOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(SemidirectFactorsOfGroup)"]]},{"rank" : 33,"comment" : "SemidirectFactorsOfGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SemidirectFactorsOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemidirectFactorsOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemidirectFactorsOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemidirectFactorsOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemidirectFactorsOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DecompositionTypesOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DecompositionTypesOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DecompositionTypesOfGroup)"]]},{"rank" : 33,"comment" : "DecompositionTypesOfGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DecompositionTypesOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DecompositionTypesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DecompositionTypesOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DecompositionTypesOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DecompositionTypesOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsDihedralGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsDihedralGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsDihedralGroup)"]]},{"rank" : 33,"comment" : "IsDihedralGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsDihedralGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsDihedralGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsDihedralGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsDihedralGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsDihedralGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DihedralGenerators","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DihedralGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(DihedralGenerators)"]]},{"rank" : 0,"comment" : "DihedralGenerators: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DihedralGenerators)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DihedralGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DihedralGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DihedralGenerators)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsQuaternionGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsQuaternionGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsQuaternionGroup)"]]},{"rank" : 33,"comment" : "IsQuaternionGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsQuaternionGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsQuaternionGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsQuaternionGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsQuaternionGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsQuaternionGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuaternionGenerators","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "QuaternionGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(QuaternionGenerators)"]]},{"rank" : 0,"comment" : "QuaternionGenerators: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(QuaternionGenerators)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(QuaternionGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(QuaternionGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(QuaternionGenerators)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsQuasiDihedralGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsQuasiDihedralGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsQuasiDihedralGroup)"]]},{"rank" : 33,"comment" : "IsQuasiDihedralGroup: generic method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsQuasiDihedralGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsQuasiDihedralGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsQuasiDihedralGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsQuasiDihedralGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsQuasiDihedralGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuasiDihedralGenerators","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "QuasiDihedralGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(QuasiDihedralGenerators)"]]},{"rank" : 0,"comment" : "QuasiDihedralGenerators: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(QuasiDihedralGenerators)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(QuasiDihedralGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(QuasiDihedralGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(QuasiDihedralGenerators)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPSL","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsPSL: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPSL)"]]},{"rank" : 33,"comment" : "IsPSL: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsPSL: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPSL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPSL): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPSL): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPSL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParametersOfGroupViewedAsPSL","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ParametersOfGroupViewedAsPSL: system getter","filters" : [["IsAttributeStoringRep","Tester(ParametersOfGroupViewedAsPSL)"]]},{"rank" : 0,"comment" : "ParametersOfGroupViewedAsPSL: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ParametersOfGroupViewedAsPSL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ParametersOfGroupViewedAsPSL): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ParametersOfGroupViewedAsPSL): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ParametersOfGroupViewedAsPSL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParametersOfGroupViewedAsSL","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ParametersOfGroupViewedAsSL: system getter","filters" : [["IsAttributeStoringRep","Tester(ParametersOfGroupViewedAsSL)"]]},{"rank" : 0,"comment" : "ParametersOfGroupViewedAsSL: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ParametersOfGroupViewedAsSL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ParametersOfGroupViewedAsSL): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ParametersOfGroupViewedAsSL): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ParametersOfGroupViewedAsSL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParametersOfGroupViewedAsGL","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ParametersOfGroupViewedAsGL: system getter","filters" : [["IsAttributeStoringRep","Tester(ParametersOfGroupViewedAsGL)"]]},{"rank" : 0,"comment" : "ParametersOfGroupViewedAsGL: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ParametersOfGroupViewedAsGL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ParametersOfGroupViewedAsGL): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ParametersOfGroupViewedAsGL): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ParametersOfGroupViewedAsGL)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlternatingDegree","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "AlternatingDegree: system getter","filters" : [["IsAttributeStoringRep","Tester(AlternatingDegree)"]]},{"rank" : 33,"comment" : "AlternatingDegree: generic method, dispatch to `IsAlternatingGroup'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "AlternatingDegree: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AlternatingDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AlternatingDegree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AlternatingDegree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AlternatingDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymmetricDegree","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SymmetricDegree: system getter","filters" : [["IsAttributeStoringRep","Tester(SymmetricDegree)"]]},{"rank" : 33,"comment" : "SymmetricDegree: generic method, dispatch to `IsSymmetricGroup'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SymmetricDegree: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SymmetricDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SymmetricDegree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SymmetricDegree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SymmetricDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PSLDegree","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PSLDegree: system getter","filters" : [["IsAttributeStoringRep","Tester(PSLDegree)"]]},{"rank" : 33,"comment" : "PSLDegree: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "PSLDegree: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PSLDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PSLDegree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PSLDegree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PSLDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PSLUnderlyingField","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PSLUnderlyingField: system getter","filters" : [["IsAttributeStoringRep","Tester(PSLUnderlyingField)"]]},{"rank" : 33,"comment" : "PSLUnderlyingField: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "PSLUnderlyingField: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PSLUnderlyingField)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PSLUnderlyingField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PSLUnderlyingField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PSLUnderlyingField)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SLDegree","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SLDegree: system getter","filters" : [["IsAttributeStoringRep","Tester(SLDegree)"]]},{"rank" : 33,"comment" : "SLDegree: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SLDegree: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SLDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SLDegree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SLDegree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SLDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SLUnderlyingField","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SLUnderlyingField: system getter","filters" : [["IsAttributeStoringRep","Tester(SLUnderlyingField)"]]},{"rank" : 33,"comment" : "SLUnderlyingField: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SLUnderlyingField: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SLUnderlyingField)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SLUnderlyingField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SLUnderlyingField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SLUnderlyingField)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GLDegree","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "GLDegree: system getter","filters" : [["IsAttributeStoringRep","Tester(GLDegree)"]]},{"rank" : 33,"comment" : "GLDegree: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GLDegree: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GLDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GLDegree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GLDegree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GLDegree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GLUnderlyingField","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "GLUnderlyingField: system getter","filters" : [["IsAttributeStoringRep","Tester(GLUnderlyingField)"]]},{"rank" : 33,"comment" : "GLUnderlyingField: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GLUnderlyingField: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GLUnderlyingField)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GLUnderlyingField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GLUnderlyingField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GLUnderlyingField)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StructureDescription","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "StructureDescription: system getter","filters" : [["IsAttributeStoringRep","Tester(StructureDescription)"]]},{"rank" : 367,"comment" : "StructureDescription: for groups handled by nice monomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "StructureDescription: for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "StructureDescription: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StructureDescription)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StructureDescription): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StructureDescription): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StructureDescription)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPQuotientSystem","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsPQuotientSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPQuotientSystem)","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPQuotientSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPQuotientSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPQuotientSystem)","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpQuotientSystem","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsNilpQuotientSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNilpQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNilpQuotientSystem)","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNilpQuotientSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNilpQuotientSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNilpQuotientSystem)","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuotientSystem","type" : "GAP_Operation","filters" : [[[],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 76,"comment" : "QuotientSystem: pquotient","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"],["IsString"]]}],"5args" : [],"6args" : []}},{"name" : "GetDefinitionNC","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "GetDefinitionNC","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetDefinitionNC","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 22,"comment" : "SetDefinitionNC","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClearDefinitionNC","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "ClearDefinitionNC","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefineNewGenerators","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "DefineNewGenerators: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SplitWordTail","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "SplitWordTail: p-quotient system, word","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsAssociativeElement","IsWord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtRepByTailVector","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10,"comment" : "ExtRepByTailVector: p-quotient system, vector","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorNumberOfQuotient","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "GeneratorNumberOfQuotient: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TailsInverses","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "TailsInverses: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputeTails","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "ComputeTails: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EvaluateConsistency","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "EvaluateConsistency: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IncorporateCentralRelations","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "IncorporateCentralRelations: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RenumberHighestWeightGenerators","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "RenumberHighestWeightGenerators: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EvaluateRelators","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "EvaluateRelators: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LiftEpimorphism","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "LiftEpimorphism: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfLayer","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "GeneratorsOfLayer: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LengthOfDescendingSeries","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "LengthOfDescendingSeries: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RanksOfDescendingSeries","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "RanksOfDescendingSeries: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CheckConsistencyOfDefinitions","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "CheckConsistencyOfDefinitions: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupByQuotientSystem","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "GroupByQuotientSystem: p-group from a p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TraceDefinition","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "TraceDefinition: p-quotient system","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EpimorphismPGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 61,"comment" : "EpimorphismPGroup: finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 57,"comment" : "EpimorphismPGroup: for finitely presented groups","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : 54,"comment" : "EpimorphismPGroup: for subgroups of finitely presented groups","filters" : [["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 80,"comment" : "EpimorphismPGroup: finite group, class bound","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 76,"comment" : "EpimorphismPGroup: for finitely presented groups, class bound","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : 73,"comment" : "EpimorphismPGroup: for subgroups of finitely presented groups, class bound","filters" : [["IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EpimorphismQuotientSystem","type" : "GAP_Operation","filters" : [[["IsQuotientSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "EpimorphismQuotientSystem: for p-quotient systems","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EpimorphismNilpotentQuotientOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "EpimorphismNilpotentQuotientOp: full fp group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],[]]},{"rank" : 35,"comment" : "EpimorphismNilpotentQuotientOp: subgroup fp group","filters" : [["IsSubgroupFpGroup"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Nucleus","type" : "GAP_Operation","filters" : [[["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "Nucleus: for a p-quotient system and a group","filters" : [["IsPQuotientSystem","Tester(IsPQuotientSystem)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ActingDomain","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "ActingDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(ActingDomain)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ActingDomain)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ActingDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ActingDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ActingDomain)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HomeEnumerator","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "HomeEnumerator: system getter","filters" : [["IsAttributeStoringRep","Tester(HomeEnumerator)"]]},{"rank" : 11,"comment" : "HomeEnumerator","filters" : [["IsConjugacyClassGroupRep"]]},{"rank" : 11,"comment" : "HomeEnumerator","filters" : [["IsConjugacyClassGroupRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(HomeEnumerator)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(HomeEnumerator): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(HomeEnumerator): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(HomeEnumerator)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ActionKernelExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "ActionKernelExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(ActionKernelExternalSet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ActionKernelExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ActionKernelExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ActionKernelExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ActionKernelExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LinearActionBasis","type" : "GAP_Operation","filters" : [[["IsLinearActionHomomorphism"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "LinearActionBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(LinearActionBasis)"]]},{"rank" : 23,"comment" : "LinearActionBasis: projective with extra vector","filters" : [["IsProjectiveActionHomomorphism"]]},{"rank" : 23,"comment" : "LinearActionBasis: find basis in domain","filters" : [["IsLinearActionHomomorphism"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LinearActionBasis)","type" : "GAP_Operation","filters" : [[["IsLinearActionHomomorphism"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LinearActionBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LinearActionBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LinearActionBasis)","type" : "GAP_Operation","filters" : [[["IsLinearActionHomomorphism"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FunctionAction","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "FunctionAction: system getter","filters" : [["IsAttributeStoringRep","Tester(FunctionAction)"]]},{"rank" : 9,"comment" : "FunctionAction: ExternalSetByActorsRep","filters" : [["IsExternalSetByActorsRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FunctionAction)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FunctionAction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FunctionAction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FunctionAction)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StabilizerOfExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "StabilizerOfExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(StabilizerOfExternalSet)"]]},{"rank" : 21,"comment" : "StabilizerOfExternalSet","filters" : [["IsConjugacyClassSubgroupsRep"]]},{"rank" : 21,"comment" : "StabilizerOfExternalSet","filters" : [["IsConjugacyClassGroupRep"]]},{"rank" : 11,"comment" : "StabilizerOfExternalSet","filters" : [["IsExternalOrbit","IsExternalSetByPcgs"]]},{"rank" : 6,"comment" : "StabilizerOfExternalSet: stabilizer of the represenattive","filters" : [["IsExternalSet"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StabilizerOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StabilizerOfExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StabilizerOfExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StabilizerOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalRepresentativeOfExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "CanonicalRepresentativeOfExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalRepresentativeOfExternalSet)"]]},{"rank" : 11,"comment" : "CanonicalRepresentativeOfExternalSet: via `ActorOfExternalSet'","filters" : [["IsExternalOrbit","IsExternalSetByPcgs"]]},{"rank" : 8,"comment" : "CanonicalRepresentativeOfExternalSet: by CanonicalRepresentativeDeterminator","filters" : [["IsExternalSet","Tester(CanonicalRepresentativeDeterminatorOfExternalSet)"]]},{"rank" : 6,"comment" : "CanonicalRepresentativeOfExternalSet: smallest element","filters" : [["IsExternalSet"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalRepresentativeOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalRepresentativeOfExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalRepresentativeOfExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalRepresentativeOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalRepresentativeDeterminatorOfExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "CanonicalRepresentativeDeterminatorOfExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalRepresentativeDeterminatorOfExternalSet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalRepresentativeDeterminatorOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalRepresentativeDeterminatorOfExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalRepresentativeDeterminatorOfExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanEasilyDetermineCanonicalRepresentativeExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "CanEasilyDetermineCanonicalRepresentativeExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanEasilyDetermineCanonicalRepresentativeExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanEasilyDetermineCanonicalRepresentativeExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanEasilyDetermineCanonicalRepresentativeExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ActorOfExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "ActorOfExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(ActorOfExternalSet)"]]},{"rank" : 11,"comment" : "ActorOfExternalSet","filters" : [["IsConjugacyClassGroupRep"]]},{"rank" : 11,"comment" : "ActorOfExternalSet","filters" : [["IsExternalOrbit","IsExternalSetByPcgs"]]},{"rank" : 6,"comment" : "ActorOfExternalSet","filters" : [["IsExternalSet"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ActorOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ActorOfExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ActorOfExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ActorOfExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreOrbishProcessing","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 32,"comment" : "PreOrbishProcessing","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ActionHomomorphismAttr","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "ActionHomomorphismAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(ActionHomomorphismAttr)"]]},{"rank" : 6,"comment" : "ActionHomomorphismAttr: call OpHomConstructor","filters" : [["IsExternalSet"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ActionHomomorphismAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ActionHomomorphismAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ActionHomomorphismAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ActionHomomorphismAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SurjectiveActionHomomorphismAttr","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "SurjectiveActionHomomorphismAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(SurjectiveActionHomomorphismAttr)"]]},{"rank" : 6,"comment" : "SurjectiveActionHomomorphismAttr: call Ac.Hom.Constructor","filters" : [["IsExternalSet"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SurjectiveActionHomomorphismAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SurjectiveActionHomomorphismAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SurjectiveActionHomomorphismAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SurjectiveActionHomomorphismAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingExternalSet","type" : "GAP_Operation","filters" : [[["IsActionHomomorphism"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "UnderlyingExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingExternalSet)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingExternalSet)","type" : "GAP_Operation","filters" : [[["IsActionHomomorphism"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingExternalSet)","type" : "GAP_Operation","filters" : [[["IsActionHomomorphism"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SparseActionHomomorphismOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 40,"comment" : "SparseActionHomomorphismOp: no domain given","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 42,"comment" : "SparseActionHomomorphismOp: domain given","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "SortedSparseActionHomomorphismOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 40,"comment" : "SortedSparseActionHomomorphismOp: no domain given","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "ExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "ExternalSet: system getter","filters" : [["IsAttributeStoringRep","Tester(ExternalSet)"]]},{"rank" : 43,"comment" : "ExternalSet: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "ExternalSet: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "ExternalSet: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "ExternalSet: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "ExternalSet: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "ExternalSet: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "ExternalSet: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 42,"comment" : "ExternalSet: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "ExternalSet: G, D, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(ExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExternalSet): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExternalSet): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExternalSet)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedExternalSet","type" : "GAP_Operation","filters" : [[["IsExternalSet"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 39,"comment" : "RestrictedExternalSet: restrict the acting domain","filters" : [["IsExternalSet"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExternalSubsetOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 40,"comment" : "ExternalSubsetOp: G, start, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 46,"comment" : "ExternalSubsetOp: G, xset, start, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsExternalSet"],["IsList"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "ExternalSubsetOp: G, D, start, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "ExternalOrbitOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 38,"comment" : "ExternalOrbitOp: G, pnt, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 44,"comment" : "ExternalOrbitOp: G, xset, pnt, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsExternalSet"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "ExternalOrbitOp: G, D, pnt, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "OrbitOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 121,"comment" : "OrbitOp: G, H, gens, oprs, opr for AffineCrystGroups","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 121,"comment" : "OrbitOp: G, H, gens, oprs, opr for AffineCrystGroups","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 81,"comment" : "OrbitOp: G, int, gens, perms, act = `OnPoints'","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 59,"comment" : "OrbitOp: action via prime order pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 58,"comment" : "OrbitOp: G, pnt, [ 1gen ], [ 1act ], act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 38,"comment" : "OrbitOp: standard orbit algorithm:list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 61,"comment" : "OrbitOp: via prime order pcgs, with domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 59,"comment" : "OrbitOp: G, D, pnt, [ 1gen ], [ 1act ], act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "OrbitOp: with domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "Orbits","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "Orbits: system getter","filters" : [["IsAttributeStoringRep","Tester(Orbits)"]]},{"rank" : 43,"comment" : "Orbits: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "Orbits: group without domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "Orbits: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "Orbits: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "Orbits: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "Orbits: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "Orbits: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "Orbits: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 126,"comment" : "Orbits: permgroup on points","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"],["IsList","CategoryCollections(IsPerm)"],["IsFunction"]]},{"rank" : 42,"comment" : "Orbits: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "Orbits: for arbitrary domains","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(Orbits)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Orbits): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Orbits): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Orbits)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrbitsDomain","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "OrbitsDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(OrbitsDomain)"]]},{"rank" : 43,"comment" : "OrbitsDomain: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "OrbitsDomain: group without domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "OrbitsDomain: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "OrbitsDomain: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "OrbitsDomain: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "OrbitsDomain: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "OrbitsDomain: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "OrbitsDomain: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 126,"comment" : "OrbitsDomain: permgroup on points","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"],["IsList","CategoryCollections(IsPerm)"],["IsFunction"]]},{"rank" : 55,"comment" : "OrbitsDomain: empty domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 55,"comment" : "OrbitsDomain: empty domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "OrbitsDomain: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 41,"comment" : "OrbitsDomain: for quick position domains","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsQuickPositionList"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "OrbitsDomain: for arbitrary domains","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(OrbitsDomain)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrbitsDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrbitsDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrbitsDomain)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrbitLengthOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 38,"comment" : "OrbitLengthOp: compute orbit","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 39,"comment" : "OrbitLengthOp: compute orbit","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "OrbitLengths","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "OrbitLengths: system getter","filters" : [["IsAttributeStoringRep","Tester(OrbitLengths)"]]},{"rank" : 43,"comment" : "OrbitLengths: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "OrbitLengths: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "OrbitLengths: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "OrbitLengths: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "OrbitLengths: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "OrbitLengths: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "OrbitLengths: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 42,"comment" : "OrbitLengths: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "OrbitLengths: compute orbits","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(OrbitLengths)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrbitLengths): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrbitLengths): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrbitLengths)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrbitLengthsDomain","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "OrbitLengthsDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(OrbitLengthsDomain)"]]},{"rank" : 43,"comment" : "OrbitLengthsDomain: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "OrbitLengthsDomain: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "OrbitLengthsDomain: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "OrbitLengthsDomain: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "OrbitLengthsDomain: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "OrbitLengthsDomain: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "OrbitLengthsDomain: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 42,"comment" : "OrbitLengthsDomain: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "OrbitLengthsDomain: compute orbits","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(OrbitLengthsDomain)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrbitLengthsDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrbitLengthsDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrbitLengthsDomain)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrbitStabilizerOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 111,"comment" : "OrbitStabilizerOp: G, H, gens, oprs, opr for AffineCrystGroups","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 111,"comment" : "OrbitStabilizerOp: G, H, gens, oprs, opr for AffineCrystGroups","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 81,"comment" : "OrbitStabilizerOp: permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 59,"comment" : "OrbitStabilizerOp: G, pnt, pcgs, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 38,"comment" : "OrbitStabilizerOp: `OrbitStabilizerAlgorithm' without domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 61,"comment" : "OrbitStabilizerOp: G, D, pnt, pcgs, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "OrbitStabilizerOp: `OrbitStabilizerAlgorithm' with domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "ExternalOrbits","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "ExternalOrbits: system getter","filters" : [["IsAttributeStoringRep","Tester(ExternalOrbits)"]]},{"rank" : 43,"comment" : "ExternalOrbits: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "ExternalOrbits: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "ExternalOrbits: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "ExternalOrbits: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "ExternalOrbits: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "ExternalOrbits: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "ExternalOrbits: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 44,"comment" : "ExternalOrbits: G, xset, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsExternalSet"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "ExternalOrbits: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "ExternalOrbits: G, D, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(ExternalOrbits)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExternalOrbits): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExternalOrbits): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExternalOrbits)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExternalOrbitsStabilizers","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "ExternalOrbitsStabilizers: system getter","filters" : [["IsAttributeStoringRep","Tester(ExternalOrbitsStabilizers)"]]},{"rank" : 43,"comment" : "ExternalOrbitsStabilizers: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "ExternalOrbitsStabilizers: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "ExternalOrbitsStabilizers: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "ExternalOrbitsStabilizers: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "ExternalOrbitsStabilizers: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "ExternalOrbitsStabilizers: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "ExternalOrbitsStabilizers: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 44,"comment" : "ExternalOrbitsStabilizers: external set","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsExternalSet"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "ExternalOrbitsStabilizers: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "ExternalOrbitsStabilizers: arbitrary domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(ExternalOrbitsStabilizers)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExternalOrbitsStabilizers): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExternalOrbitsStabilizers): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExternalOrbitsStabilizers)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Transitivity","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]],[["IsClassFunction"]],[["IsOrdinaryTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "Transitivity: system getter","filters" : [["IsAttributeStoringRep","Tester(Transitivity)"]]},{"rank" : 59,"comment" : "Transitivity: for a permutation group with known size","filters" : [["Tester(Size)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "Transitivity: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "Transitivity: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 6,"comment" : "Transitivity: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "Transitivity: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "Transitivity: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]},{"rank" : 26,"comment" : "Transitivity: for an ordinary table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 45,"comment" : "Transitivity: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "Transitivity: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "Transitivity: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 92,"comment" : "Transitivity: permgroup on numbers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 75,"comment" : "Transitivity: G, [  ], gens, perms, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "Transitivity: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "Transitivity: of the image of an ophom","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(Transitivity)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]],[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Transitivity): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Transitivity): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Transitivity)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BlocksAttr","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "BlocksAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(BlocksAttr)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BlocksAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BlocksAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BlocksAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BlocksAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BlocksOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 40,"comment" : "BlocksOp: G, D, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 155,"comment" : "BlocksOp: integers, with seed","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"],["IsList","CategoryCollections(IsPerm)"],["IsFunction"]]},{"rank" : 143,"comment" : "BlocksOp: permgroup on integers","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList","CategoryCollections(IsPerm)"],["IsFunction"]]},{"rank" : 77,"comment" : "BlocksOp: G, [  ], seed, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "BlocksOp: via action homomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "MaximalBlocksAttr","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "MaximalBlocksAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalBlocksAttr)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalBlocksAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalBlocksAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalBlocksAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalBlocksAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalBlocksOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 40,"comment" : "MaximalBlocksOp: G, D, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 42,"comment" : "MaximalBlocksOp: G, D, seed, gens, acts, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "RepresentativesMinimalBlocksAttr","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "RepresentativesMinimalBlocksAttr: system getter","filters" : [["IsAttributeStoringRep","Tester(RepresentativesMinimalBlocksAttr)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RepresentativesMinimalBlocksAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RepresentativesMinimalBlocksAttr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RepresentativesMinimalBlocksAttr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RepresentativesMinimalBlocksAttr)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativesMinimalBlocksOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 126,"comment" : "RepresentativesMinimalBlocksOp: permgrp on points","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"],["IsList","CategoryCollections(IsPerm)"],["IsFunction"]]},{"rank" : 39,"comment" : "RepresentativesMinimalBlocksOp: general case: translate","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 129,"comment" : "RepresentativesMinimalBlocksOp: G, domain, noseed, gens, perms, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList","CategoryCollections(IsPerm)"],["IsFunction"]]}]}},{"name" : "Earns","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "Earns: system getter","filters" : [["IsAttributeStoringRep","Tester(Earns)"]]},{"rank" : 43,"comment" : "Earns: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "Earns: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "Earns: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "Earns: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "Earns: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "Earns: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "Earns: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 65,"comment" : "Earns: G, ints, gens, perms, act","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "Earns: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(Earns)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "Setter(Earns): never set fail","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]},{"rank" : 2,"comment" : "Setter(Earns): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Earns): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Earns)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTransitive","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]],[["IsClassFunction"]],[["IsCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "IsTransitive: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTransitive)"]]},{"rank" : 59,"comment" : "IsTransitive: for a permutation group (use shortcuts)","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "IsTransitive: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "IsTransitive: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 6,"comment" : "IsTransitive: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "IsTransitive: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "IsTransitive: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]},{"rank" : 26,"comment" : "IsTransitive: for an ordinary table and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 45,"comment" : "IsTransitive: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "IsTransitive: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "IsTransitive: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 42,"comment" : "IsTransitive: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "IsTransitive: compare with orbit of element","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(IsTransitive)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTransitive): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTransitive): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTransitive)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitive","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "IsPrimitive: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPrimitive)"]]},{"rank" : 43,"comment" : "IsPrimitive: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "IsPrimitive: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "IsPrimitive: for a character","filters" : [["IsClassFunction"]]},{"rank" : 6,"comment" : "IsPrimitive: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 95,"comment" : "IsPrimitive: for matrix group over field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 44,"comment" : "IsPrimitive: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "IsPrimitive: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "IsPrimitive: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "IsPrimitive: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "IsPrimitive: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 42,"comment" : "IsPrimitive: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "IsPrimitive: transitive and no blocks","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(IsPrimitive)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPrimitive): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPrimitive): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPrimitive)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitiveAffine","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "IsPrimitiveAffine: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPrimitiveAffine)"]]},{"rank" : 43,"comment" : "IsPrimitiveAffine: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "IsPrimitiveAffine: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "IsPrimitiveAffine: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "IsPrimitiveAffine: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "IsPrimitiveAffine: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "IsPrimitiveAffine: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "IsPrimitiveAffine: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 42,"comment" : "IsPrimitiveAffine: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "IsPrimitiveAffine: primitive and earns","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(IsPrimitiveAffine)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPrimitiveAffine): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPrimitiveAffine): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPrimitiveAffine)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSemiRegular","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "IsSemiRegular: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSemiRegular)"]]},{"rank" : 43,"comment" : "IsSemiRegular: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "IsSemiRegular: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "IsSemiRegular: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "IsSemiRegular: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "IsSemiRegular: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "IsSemiRegular: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "IsSemiRegular: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 126,"comment" : "IsSemiRegular: permgroup on numbers","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"],["IsList","CategoryCollections(IsPerm)"],["IsFunction"]]},{"rank" : 75,"comment" : "IsSemiRegular: G, D, gens, [  ], act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsFunction"]]},{"rank" : 75,"comment" : "IsSemiRegular: G, [  ], gens, perms, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "IsSemiRegular: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "IsSemiRegular: via ophom","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(IsSemiRegular)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSemiRegular): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSemiRegular): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSemiRegular)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRegular","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "IsRegular: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRegular)"]]},{"rank" : 59,"comment" : "IsRegular: permgroup with known size","filters" : [["Tester(Size)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "IsRegular: permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "IsRegular: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "IsRegular: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "IsRegular: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "IsRegular: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "IsRegular: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "IsRegular: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "IsRegular: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 42,"comment" : "IsRegular: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "IsRegular: transitive and semiregular","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(IsRegular)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRegular): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRegular): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRegular)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankAction","type" : "GAP_Operation","filters" : [[["IsExternalSet"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "RankAction: system getter","filters" : [["IsAttributeStoringRep","Tester(RankAction)"]]},{"rank" : 43,"comment" : "RankAction: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 6,"comment" : "RankAction: for an external set","filters" : [["IsExternalSet"]]}],"2args" : [{"rank" : 44,"comment" : "RankAction: for a permutation group and a domain or list of integers","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]},{"rank" : 32,"comment" : "RankAction: for a group and a domain or list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 45,"comment" : "RankAction: for permutation group, domain or list of integers, and function","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 33,"comment" : "RankAction: for a group, a domain or list, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsFunction"]]}],"4args" : [{"rank" : 36,"comment" : "RankAction: for a group, a domain or list, and two lists","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"]]}],"5args" : [{"rank" : 75,"comment" : "RankAction: G, [  ], gens, perms, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 67,"comment" : "RankAction: G, ints, gens, perms, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 42,"comment" : "RankAction: for a group, a domain, two lists, and a function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection","IsGeneralizedDomain"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "RankAction: via ophom","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsList"],["IsList"],["IsFunction"]]}],"6args" : []}},{"name" : "Setter(RankAction)","type" : "GAP_Operation","filters" : [[["IsExternalSet"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RankAction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RankAction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RankAction)","type" : "GAP_Operation","filters" : [[["IsExternalSet"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermutationOp","type" : "GAP_Operation","filters" : [[[],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 3,"comment" : "PermutationOp: object on list","filters" : [[],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermutationCycleOp","type" : "GAP_Operation","filters" : [[[],["IsList"],[],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 3,"comment" : "PermutationCycleOp: of object in list","filters" : [[],["IsList"],[],["IsFunction"]]}],"5args" : [],"6args" : []}},{"name" : "CycleOp","type" : "GAP_Operation","filters" : [[[],["IsList"],[],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 129,"comment" : "CycleOp: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"],["IsInt"]]},{"rank" : 128,"comment" : "CycleOp: for a permutation with memory and an integer","filters" : [["IsPerm","IsObjWithMemory"],["IsInt"]]},{"rank" : 27,"comment" : "CycleOp: perm, int","filters" : [["IsPerm","IsInternalRep"],["IsInt"]]}],"3args" : [{"rank" : 27,"comment" : "CycleOp: perm, int, act","filters" : [["IsPerm"],["IsInt"],["IsFunction"]]},{"rank" : 1,"comment" : "CycleOp","filters" : [[],[],["IsFunction"]]}],"4args" : [{"rank" : 3,"comment" : "CycleOp: of object in list","filters" : [[],["IsList"],[],["IsFunction"]]}],"5args" : [],"6args" : []}},{"name" : "CyclesOp","type" : "GAP_Operation","filters" : [[[],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 4,"comment" : "CyclesOp","filters" : [[],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CycleLengthOp","type" : "GAP_Operation","filters" : [[[],["IsList"],[],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 129,"comment" : "CycleLengthOp: straight line program perms","filters" : [["IsPerm","IsStraightLineProgElm"],["IsInt"]]},{"rank" : 128,"comment" : "CycleLengthOp: for a permutation with memory and an integer","filters" : [["IsPerm","IsObjWithMemory"],["IsInt"]]},{"rank" : 27,"comment" : "CycleLengthOp: perm, int","filters" : [["IsPerm","IsInternalRep"],["IsInt"]]}],"3args" : [{"rank" : 27,"comment" : "CycleLengthOp: perm, int, act","filters" : [["IsPerm"],["IsInt"],["IsFunction"]]},{"rank" : 1,"comment" : "CycleLengthOp","filters" : [[],[],["IsFunction"]]}],"4args" : [{"rank" : 3,"comment" : "CycleLengthOp","filters" : [[],["IsList"],[],["IsFunction"]]}],"5args" : [],"6args" : []}},{"name" : "CycleLengthsOp","type" : "GAP_Operation","filters" : [[[],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 3,"comment" : "CycleLengthsOp","filters" : [[],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CycleIndexOp","type" : "GAP_Operation","filters" : [[[],["IsListOrCollection"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 44,"comment" : "CycleIndexOp: finite group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],["IsFunction"]]},{"rank" : 7,"comment" : "CycleIndexOp: element","filters" : [["IsMultiplicativeElementWithInverse"],["IsListOrCollection"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativeActionOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],[],[],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 440,"comment" : "RepresentativeActionOp: TF Method on elements","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingFreeLiftSetup)"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"],["IsFunction"]]},{"rank" : 389,"comment" : "RepresentativeActionOp: nice group on elements","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"],["IsFunction"]]},{"rank" : 160,"comment" : "RepresentativeActionOp: G, d, e, opr for AffineCrystGroups","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsFunction"]]},{"rank" : 160,"comment" : "RepresentativeActionOp: G, d, e, opr for AffineCrystGroups","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsFunction"]]},{"rank" : 152,"comment" : "RepresentativeActionOp: for subgroups of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsFunction"]]},{"rank" : 130,"comment" : "RepresentativeActionOp: pc group on subgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsFunction"]]},{"rank" : 73,"comment" : "RepresentativeActionOp: for natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],[],[],["IsFunction"]]},{"rank" : 73,"comment" : "RepresentativeActionOp: natural alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],[],[],["IsFunction"]]},{"rank" : 73,"comment" : "RepresentativeActionOp: cycle structure comparison for solvable perm groups","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsPerm"],["IsPerm"],["IsFunction"]]},{"rank" : 69,"comment" : "RepresentativeActionOp: permgrp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[],["IsFunction"]]},{"rank" : 63,"comment" : "RepresentativeActionOp: for conjugation of elements in a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsFunction"]]},{"rank" : 54,"comment" : "RepresentativeActionOp: element conjugacy in pcgs computable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMultiplicativeElementWithInverse"],["IsMultiplicativeElementWithInverse"],["IsFunction"]]},{"rank" : 34,"comment" : "RepresentativeActionOp: trivial general cases","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[],["IsFunction"]]},{"rank" : 34,"comment" : "RepresentativeActionOp: orbit algorithm: trace transversal","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[],["IsFunction"]]}],"5args" : [{"rank" : 36,"comment" : "RepresentativeActionOp: ignore domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],[],[],["IsFunction"]]}],"6args" : []}},{"name" : "StabilizerFuncOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 271,"comment" : "StabilizerFuncOp: use normalizer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 107,"comment" : "StabilizerFuncOp: alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 107,"comment" : "StabilizerFuncOp: symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 103,"comment" : "StabilizerFuncOp: permutation group with generators list","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 64,"comment" : "StabilizerFuncOp: G (solv.), pnt, gens, gens, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 59,"comment" : "StabilizerFuncOp: G, pnt, pcgs, acts, act, calling `Pcgs_MutableOrbitStabilizerOp'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 43,"comment" : "StabilizerFuncOp: G (solv.), pnt, gens, gens, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 38,"comment" : "StabilizerFuncOp: `OrbitStabilizerAlgorithm' without domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsList"],["IsList"],["IsFunction"]]}],"6args" : [{"rank" : 273,"comment" : "StabilizerFuncOp: with domain, use normalizer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 112,"comment" : "StabilizerFuncOp: alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["IsCollection","IsGeneralizedDomain"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 112,"comment" : "StabilizerFuncOp: symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsCollection","IsGeneralizedDomain"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 103,"comment" : "StabilizerFuncOp: permutation group with domain","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 64,"comment" : "StabilizerFuncOp: G (solv.), D,pnt, gens, gens, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],[],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 61,"comment" : "StabilizerFuncOp: G, D, pnt, pcgs, acts, act, calling `Pcgs_MutableOrbitStabilizerOp'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],[],["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)"],["IsList"],["IsFunction"]]},{"rank" : 44,"comment" : "StabilizerFuncOp: G (solv.), D,pnt, gens, gens, act","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]},{"rank" : 39,"comment" : "StabilizerFuncOp: `OrbitStabilizerAlgorithm' with domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"],[],["IsList"],["IsList"],["IsFunction"]]}]}},{"name" : "OrbitStabilizerAlgorithm","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[],["IsList"],["IsList"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : [{"rank" : 57,"comment" : "OrbitStabilizerAlgorithm: for pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[],["IsPcgs"],["IsList"],["IsRecord"]]},{"rank" : 50,"comment" : "OrbitStabilizerAlgorithm: use stabilizer size","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanComputeSizeAnySubgroup"],[],[],["IsList"],["IsList"],["IsRecord"]]},{"rank" : 38,"comment" : "OrbitStabilizerAlgorithm: collect stabilizer generators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],[],["IsList"],["IsList"],["IsRecord"]]}]}},{"name" : "AbelianSubfactorAction","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 99,"comment" : "AbelianSubfactorAction: generic:use modulo pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DomainForAction","type" : "GAP_Operation","filters" : [[[],["IsListOrCollection"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 45,"comment" : "DomainForAction: matrix\/matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"],["IsList"],["IsFunction"]]},{"rank" : 29,"comment" : "DomainForAction: FFE vector\/matrix","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","CategoryCollections(IsFFE)"],["IsList"],["IsFunction"]]},{"rank" : 5,"comment" : "DomainForAction: vector\/permgrp","filters" : [["IsList"],["IsList"],["IsFunction"]]},{"rank" : 2,"comment" : "DomainForAction: default: fail","filters" : [[],["IsListOrCollection"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StabChainOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 87,"comment" : "StabChainOp: trivial group","filters" : [["IsTrivial","Tester(IsTrivial)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]},{"rank" : 87,"comment" : "StabChainOp: with base","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 75,"comment" : "StabChainOp: empty base","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 63,"comment" : "StabChainOp: alternating group","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"],["IsRecord"]]},{"rank" : 63,"comment" : "StabChainOp: symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsRecord"]]},{"rank" : 59,"comment" : "StabChainOp: group and option","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StabChainMutable","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "StabChainMutable: system getter","filters" : [["IsAttributeStoringRep","Tester(StabChainMutable)"]]},{"rank" : 33,"comment" : "StabChainMutable: call StabChainOp","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "StabChainMutable: for blocks homomorphism","filters" : [["IsBlocksHomomorphism"]]},{"rank" : 20,"comment" : "StabChainMutable: perm to perm mapping by images","filters" : [["IsPermGroupGeneralMappingByImages","IsToPermGroupGeneralMappingByImages"]]},{"rank" : 19,"comment" : "StabChainMutable: perm mapping by images","filters" : [["IsPermGroupGeneralMappingByImages"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StabChainMutable)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StabChainMutable): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StabChainMutable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StabChainMutable)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StabChainImmutable","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "StabChainImmutable: system getter","filters" : [["IsAttributeStoringRep","Tester(StabChainImmutable)"]]},{"rank" : 0,"comment" : "StabChainImmutable: use StabChainMutable","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StabChainImmutable)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StabChainImmutable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StabChainImmutable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StabChainImmutable)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StabChainOptions","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "StabChainOptions: system getter","filters" : [["IsAttributeStoringRep","Tester(StabChainOptions)"]]},{"rank" : 58,"comment" : "StabChainOptions","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "StabChainOptions: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StabChainOptions)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StabChainOptions): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StabChainOptions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StabChainOptions)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaseOfGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "BaseOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(BaseOfGroup)"]]},{"rank" : 58,"comment" : "BaseOfGroup: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "BaseOfGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BaseOfGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BaseOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BaseOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BaseOfGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalStabChain","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "MinimalStabChain: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimalStabChain)"]]},{"rank" : 388,"comment" : "MinimalStabChain: matrix group via niceo","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 58,"comment" : "MinimalStabChain: Perm","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -16,"comment" : "MinimalStabChain: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimalStabChain)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimalStabChain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimalStabChain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimalStabChain)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MembershipTestKnownBase","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 42,"comment" : "MembershipTestKnownBase","filters" : [["IsRecord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPerm"]]},{"rank" : 32,"comment" : "MembershipTestKnownBase: stabchain, base, word","filters" : [["IsRecord"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermOnEnumerator","type" : "GAP_Operation","filters" : [[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugacyClass","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "ConjugacyClass: class of element","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [{"rank" : 66,"comment" : "ConjugacyClass: class of element and centralizer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RationalClass","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "RationalClass","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DecomposedRationalClass","type" : "GAP_Operation","filters" : [[["IsRationalClassGroupRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "DecomposedRationalClass: system getter","filters" : [["IsAttributeStoringRep","Tester(DecomposedRationalClass)"]]},{"rank" : 11,"comment" : "DecomposedRationalClass: generic","filters" : [["IsRationalClassGroupRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DecomposedRationalClass)","type" : "GAP_Operation","filters" : [[["IsRationalClassGroupRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DecomposedRationalClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DecomposedRationalClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DecomposedRationalClass)","type" : "GAP_Operation","filters" : [[["IsRationalClassGroupRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StoredPermliftSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "StoredPermliftSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(StoredPermliftSeries)"]]},{"rank" : 33,"comment" : "StoredPermliftSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "StoredPermliftSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StoredPermliftSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StoredPermliftSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StoredPermliftSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StoredPermliftSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AscendingChainOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 116,"comment" : "AscendingChainOp: PermGroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "AscendingChainOp: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedAscendingChains","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ComputedAscendingChains: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedAscendingChains)"]]},{"rank" : 33,"comment" : "ComputedAscendingChains: init","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedAscendingChains: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedAscendingChains)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedAscendingChains): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedAscendingChains): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedAscendingChains)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalRightCosetElement","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 418,"comment" : "CanonicalRightCosetElement: finite matric group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 66,"comment" : "CanonicalRightCosetElement: Perm","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsPerm"]]},{"rank" : 53,"comment" : "CanonicalRightCosetElement: for AffineCrystGroupOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],[]]},{"rank" : 53,"comment" : "CanonicalRightCosetElement: for AffineCrystGroupOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],[]]},{"rank" : 46,"comment" : "CanonicalRightCosetElement: Pc","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]},{"rank" : 33,"comment" : "CanonicalRightCosetElement: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftActingGroup","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "LeftActingGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(LeftActingGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeftActingGroup)","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LeftActingGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeftActingGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeftActingGroup)","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightActingGroup","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "RightActingGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RightActingGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RightActingGroup)","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RightActingGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RightActingGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RightActingGroup)","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DoubleCoset","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 66,"comment" : "DoubleCoset: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [{"rank" : 85,"comment" : "DoubleCoset: with size","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "DoubleCosetsNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 99,"comment" : "DoubleCosetsNC: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DoubleCosetRepsAndSizes","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 138,"comment" : "DoubleCosetRepsAndSizes: Pc","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 99,"comment" : "DoubleCosetRepsAndSizes: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativesContainedRightCosets","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "RepresentativesContainedRightCosets: system getter","filters" : [["IsAttributeStoringRep","Tester(RepresentativesContainedRightCosets)"]]},{"rank" : 8,"comment" : "RepresentativesContainedRightCosets: generic","filters" : [["IsDoubleCoset"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RepresentativesContainedRightCosets)","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RepresentativesContainedRightCosets): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RepresentativesContainedRightCosets): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RepresentativesContainedRightCosets)","type" : "GAP_Operation","filters" : [[["IsDoubleCoset"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightCoset","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "RightCoset: use subgroup size","filters" : [["Tester(Size)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]},{"rank" : 33,"comment" : "RightCoset: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightCosetsNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 401,"comment" : "RightCosetsNC: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 116,"comment" : "RightCosetsNC: perm groups, use RightTransversal","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 106,"comment" : "RightCosetsNC: AffineCrystGroupOnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 106,"comment" : "RightCosetsNC: AffineCrystGroupOnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 92,"comment" : "RightCosetsNC: pc groups, use RightTransversal","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 66,"comment" : "RightCosetsNC: generic: orbit","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DoCheapActionImages","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 58,"comment" : "DoCheapActionImages: permutation","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "DoCheapActionImages: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FindActionKernel","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 400,"comment" : "FindActionKernel: Niceo","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 116,"comment" : "FindActionKernel: perm","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 75,"comment" : "FindActionKernel: generic for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "FindActionKernel: general case: can't do","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismsPool","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NaturalHomomorphismsPool: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalHomomorphismsPool)"]]},{"rank" : 33,"comment" : "NaturalHomomorphismsPool","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NaturalHomomorphismsPool: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalHomomorphismsPool)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalHomomorphismsPool): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalHomomorphismsPool): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalHomomorphismsPool)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorCosetAction","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 400,"comment" : "FactorCosetAction: by right transversal operation, Niceo","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 76,"comment" : "FactorCosetAction: for full fp group on subgroup","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 71,"comment" : "FactorCosetAction: subgrp in quotient Rep","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 70,"comment" : "FactorCosetAction: for subgroups of an fp group","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 66,"comment" : "FactorCosetAction: by right transversal operation","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [{"rank" : 433,"comment" : "FactorCosetAction: by right transversal operation, given kernel, Niceo","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 99,"comment" : "FactorCosetAction: by right transversal operation, given kernel","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbsolutIrreducibleModules","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 114,"comment" : "AbsolutIrreducibleModules: generic method for groups with pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsInt"]]},{"rank" : 107,"comment" : "AbsolutIrreducibleModules: generic method for groups and finite field","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IrreducibleModules","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 114,"comment" : "IrreducibleModules: generic method for groups with pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"],["IsInt"]]},{"rank" : 107,"comment" : "IrreducibleModules: generic method for groups and finite field","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RegularModule","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 85,"comment" : "RegularModule: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OCAddToFunctions2","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "OCAddToFunctions2: pc group","filters" : [["IsRecord"],["IsModuloPcgs"]]},{"rank" : 3,"comment" : "OCAddToFunctions2: generic","filters" : [["IsRecord"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OCAddRelations","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "OCAddRelations: pc group","filters" : [["IsRecord"],["IsModuloPcgs"]]},{"rank" : 3,"comment" : "OCAddRelations: perm group","filters" : [["IsRecord"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OCNormalRelations","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 48,"comment" : "OCNormalRelations: pc group","filters" : [["IsRecord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsListOrCollection"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OCAddSumMatrices","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "OCAddSumMatrices: pc group","filters" : [["IsRecord"],["IsPcgs"]]},{"rank" : 3,"comment" : "OCAddSumMatrices: perm group","filters" : [["IsRecord"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OCAddBigMatrices","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 3,"comment" : "OCAddBigMatrices: general","filters" : [["IsRecord"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OCCoprimeComplement","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OCAddComplement","type" : "GAP_Operation","filters" : [[["IsRecord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 48,"comment" : "OCAddComplement: pc group","filters" : [["IsRecord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsListOrCollection"]]},{"rank" : 35,"comment" : "OCAddComplement: generic","filters" : [["IsRecord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsListOrCollection"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComplementClassesRepresentativesSolvableNC","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 76,"comment" : "ComplementClassesRepresentativesSolvableNC: pc groups","filters" : [["CanEasilyComputePcgs"],["CanEasilyComputePcgs"]]},{"rank" : 67,"comment" : "ComplementClassesRepresentativesSolvableNC: using cohomology","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComplementClassesRepresentatives","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 96,"comment" : "ComplementClassesRepresentatives: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 66,"comment" : "ComplementClassesRepresentatives: solvable normal subgroup or factor group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComplementClassesRepresentatives: tell that the normal subgroup must be solvable","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TwoCocycles","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 46,"comment" : "TwoCocycles: generic method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TwoCoboundaries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 46,"comment" : "TwoCoboundaries: generic method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TwoCohomology","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 46,"comment" : "TwoCohomology: generic method for pc groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Extension","type" : "GAP_Operation","filters" : [[["CanEasilyComputePcgs"],[],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 45,"comment" : "Extension: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],[],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtensionNC","type" : "GAP_Operation","filters" : [[["CanEasilyComputePcgs"],[],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 45,"comment" : "ExtensionNC: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],[],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Extensions","type" : "GAP_Operation","filters" : [[["CanEasilyComputePcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "Extensions: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtensionRepresentatives","type" : "GAP_Operation","filters" : [[["CanEasilyComputePcgs"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 72,"comment" : "ExtensionRepresentatives: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],["IsRecord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SplitExtension","type" : "GAP_Operation","filters" : [[["CanEasilyComputePcgs"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "SplitExtension: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],[]]}],"3args" : [{"rank" : 76,"comment" : "SplitExtension: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],[],["CanEasilyComputePcgs"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TopExtensionsByAutomorphism","type" : "GAP_Operation","filters" : [[["CanEasilyComputePcgs"],[],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 56,"comment" : "TopExtensionsByAutomorphism: generic method for groups","filters" : [["CanEasilyComputePcgs"],[],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CyclicTopExtensions","type" : "GAP_Operation","filters" : [[["CanEasilyComputePcgs"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 56,"comment" : "CyclicTopExtensions: generic method for pc groups","filters" : [["CanEasilyComputePcgs"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SocleComplement","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SocleComplement: system getter","filters" : [["IsAttributeStoringRep","Tester(SocleComplement)"]]},{"rank" : 35,"comment" : "SocleComplement: for primitive solvable group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsPrimitiveSolvableGroup","Tester(IsPrimitiveSolvableGroup)"]]},{"rank" : 0,"comment" : "SocleComplement: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SocleComplement)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SocleComplement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SocleComplement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SocleComplement)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SocleDimensions","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SocleDimensions: system getter","filters" : [["IsAttributeStoringRep","Tester(SocleDimensions)"]]},{"rank" : 0,"comment" : "SocleDimensions: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SocleDimensions)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SocleDimensions): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SocleDimensions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SocleDimensions)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ModuleOfExtension","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ModuleOfExtension: system getter","filters" : [["IsAttributeStoringRep","Tester(ModuleOfExtension)"]]},{"rank" : 0,"comment" : "ModuleOfExtension: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ModuleOfExtension)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ModuleOfExtension): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ModuleOfExtension): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ModuleOfExtension)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OmegaAndLowerPCentralSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "OmegaAndLowerPCentralSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(OmegaAndLowerPCentralSeries)"]]},{"rank" : 46,"comment" : "OmegaAndLowerPCentralSeries: omega and lower central","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 33,"comment" : "OmegaAndLowerPCentralSeries: general case: warn that no method available","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "OmegaAndLowerPCentralSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OmegaAndLowerPCentralSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OmegaAndLowerPCentralSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OmegaAndLowerPCentralSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OmegaAndLowerPCentralSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SchurCover","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SchurCover: system getter","filters" : [["IsAttributeStoringRep","Tester(SchurCover)"]]},{"rank" : 35,"comment" : "SchurCover: of fp group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 33,"comment" : "SchurCover: general: Holt's algorithm","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SchurCover: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SchurCover)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SchurCover): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SchurCover): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SchurCover)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EpimorphismSchurCover","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "EpimorphismSchurCover: system getter","filters" : [["IsAttributeStoringRep","Tester(EpimorphismSchurCover)"]]},{"rank" : 63,"comment" : "EpimorphismSchurCover: Use copy of AtlasRep's 6-fold cover","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 62,"comment" : "EpimorphismSchurCover: Use library copy of double cover","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 62,"comment" : "EpimorphismSchurCover: Use library copy of double cover","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"]]},{"rank" : 48,"comment" : "EpimorphismSchurCover: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 34,"comment" : "EpimorphismSchurCover: generic, via fp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "EpimorphismSchurCover: Holt's algorithm","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "EpimorphismSchurCover: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 35,"comment" : "EpimorphismSchurCover: Holt's algorithm, primes","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EpimorphismSchurCover)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EpimorphismSchurCover): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EpimorphismSchurCover): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EpimorphismSchurCover)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbelianInvariantsMultiplier","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "AbelianInvariantsMultiplier: system getter","filters" : [["IsAttributeStoringRep","Tester(AbelianInvariantsMultiplier)"]]},{"rank" : 48,"comment" : "AbelianInvariantsMultiplier: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 34,"comment" : "AbelianInvariantsMultiplier: naive","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "AbelianInvariantsMultiplier: via Sylow Subgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "AbelianInvariantsMultiplier: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AbelianInvariantsMultiplier)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AbelianInvariantsMultiplier): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AbelianInvariantsMultiplier): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AbelianInvariantsMultiplier)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Epicentre","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Epicentre: system getter","filters" : [["IsAttributeStoringRep","Tester(Epicentre)"]]},{"rank" : 48,"comment" : "Epicentre: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 33,"comment" : "Epicentre: Naive Method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "Epicentre: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 66,"comment" : "Epicentre: Naive method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Epicentre)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Epicentre): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Epicentre): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Epicentre)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NonabelianExteriorSquare","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "NonabelianExteriorSquare: Naive method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EpimorphismNonabelianExteriorSquare","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "EpimorphismNonabelianExteriorSquare: Naive method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCentralFactor","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsCentralFactor: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCentralFactor)"]]},{"rank" : 33,"comment" : "IsCentralFactor: Naive method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsCentralFactor: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCentralFactor)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCentralFactor): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCentralFactor): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCentralFactor)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SchurCoverOfSymmetricGroup","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "SchurCoverOfSymmetricGroup: P=3, Sign=+1 by default","filters" : [["IsInt","IsPosRat"]]}],"2args" : [{"rank" : 37,"comment" : "SchurCoverOfSymmetricGroup: Sign=+1 by default","filters" : [["IsInt","IsPosRat"],["IsInt"]]}],"3args" : [{"rank" : 56,"comment" : "SchurCoverOfSymmetricGroup: Use explicit matrix reps for degrees 1,2,3","filters" : [["IsInt","IsPosRat"],["IsInt"],["IsInt"]]},{"rank" : 55,"comment" : "SchurCoverOfSymmetricGroup: Use Lukas Maas's inductive construction of a basic spin rep","filters" : [["IsInt","IsPosRat"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DoubleCoverOfAlternatingGroup","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "DoubleCoverOfAlternatingGroup: P=3 by default","filters" : [["IsInt","IsPosRat"]]}],"2args" : [{"rank" : 37,"comment" : "DoubleCoverOfAlternatingGroup: Use Lukas Maas's inductive construction of a basic spin rep","filters" : [["IsInt","IsPosRat"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugacyClassSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 86,"comment" : "ConjugacyClassSubgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 66,"comment" : "ConjugacyClassSubgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassElementLattice","type" : "GAP_Operation","filters" : [[["IsExternalOrbit"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "ClassElementLattice: for classes of subgroups","filters" : [["IsConjugacyClassSubgroupsRep"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Zuppos","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Zuppos: system getter","filters" : [["IsAttributeStoringRep","Tester(Zuppos)"]]},{"rank" : 33,"comment" : "Zuppos: group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "Zuppos: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 34,"comment" : "Zuppos: group with condition","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Zuppos)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Zuppos): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Zuppos): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Zuppos)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalSubgroupsLattice","type" : "GAP_Operation","filters" : [[["IsLatticeSubgroupsRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MaximalSubgroupsLattice: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalSubgroupsLattice)"]]},{"rank" : 3,"comment" : "MaximalSubgroupsLattice: cyclic extension","filters" : [["IsLatticeSubgroupsRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalSubgroupsLattice)","type" : "GAP_Operation","filters" : [[["IsLatticeSubgroupsRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalSubgroupsLattice): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalSubgroupsLattice): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalSubgroupsLattice)","type" : "GAP_Operation","filters" : [[["IsLatticeSubgroupsRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalSupergroupsLattice","type" : "GAP_Operation","filters" : [[["IsLatticeSubgroupsRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MinimalSupergroupsLattice: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimalSupergroupsLattice)"]]},{"rank" : 3,"comment" : "MinimalSupergroupsLattice: cyclic extension","filters" : [["IsLatticeSubgroupsRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimalSupergroupsLattice)","type" : "GAP_Operation","filters" : [[["IsLatticeSubgroupsRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimalSupergroupsLattice): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimalSupergroupsLattice): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimalSupergroupsLattice)","type" : "GAP_Operation","filters" : [[["IsLatticeSubgroupsRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TomDataAlmostSimpleRecognition","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "TomDataAlmostSimpleRecognition: system getter","filters" : [["IsAttributeStoringRep","Tester(TomDataAlmostSimpleRecognition)"]]},{"rank" : 62,"comment" : "TomDataAlmostSimpleRecognition: alt","filters" : [["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)"]]},{"rank" : 33,"comment" : "TomDataAlmostSimpleRecognition: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "TomDataAlmostSimpleRecognition: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TomDataAlmostSimpleRecognition)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TomDataAlmostSimpleRecognition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TomDataAlmostSimpleRecognition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TomDataAlmostSimpleRecognition)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubgroupsOrbitsAndNormalizers","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 61,"comment" : "SubgroupsOrbitsAndNormalizers: perm group on list","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsBool"]]},{"rank" : 49,"comment" : "SubgroupsOrbitsAndNormalizers: pc group on list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsList"],["IsBool"]]},{"rank" : 36,"comment" : "SubgroupsOrbitsAndNormalizers: generic on list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsBool"]]},{"rank" : 35,"comment" : "SubgroupsOrbitsAndNormalizers: generic on record with list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFrattiniFree","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsFrattiniFree: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFrattiniFree)"]]},{"rank" : 0,"comment" : "IsFrattiniFree: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFrattiniFree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFrattiniFree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFrattiniFree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFrattiniFree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LinesOfStraightLineProgram","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "LinesOfStraightLineProgram: system getter","filters" : [["IsAttributeStoringRep","Tester(LinesOfStraightLineProgram)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LinesOfStraightLineProgram)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LinesOfStraightLineProgram): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LinesOfStraightLineProgram): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LinesOfStraightLineProgram)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrInputsOfStraightLineProgram","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "NrInputsOfStraightLineProgram: system getter","filters" : [["IsAttributeStoringRep","Tester(NrInputsOfStraightLineProgram)"]]},{"rank" : 1,"comment" : "NrInputsOfStraightLineProgram: for a straight line program","filters" : [["IsStraightLineProgram"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrInputsOfStraightLineProgram)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrInputsOfStraightLineProgram): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrInputsOfStraightLineProgram): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrInputsOfStraightLineProgram)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ResultOfStraightLineProgram","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 6,"comment" : "ResultOfStraightLineProgram: for a straight line program with slot usage pattern, a list","filters" : [["IsStraightLineProgram","Tester(SlotUsagePattern)"],["IsHomogeneousList"]]},{"rank" : 5,"comment" : "ResultOfStraightLineProgram: for a straight line program, and a homogeneous list","filters" : [["IsStraightLineProgram"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StraightLineProgElmType","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "StraightLineProgElmType: system getter","filters" : [["IsAttributeStoringRep","Tester(StraightLineProgElmType)"]]},{"rank" : 1,"comment" : "StraightLineProgElmType: generic","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StraightLineProgElmType)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StraightLineProgElmType): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StraightLineProgElmType): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StraightLineProgElmType)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StretchImportantSLPElement","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 107,"comment" : "StretchImportantSLPElement: straight line program elements","filters" : [["IsStraightLineProgElm"]]},{"rank" : 5,"comment" : "StretchImportantSLPElement: arbitrary elements: do nothing","filters" : [["IsMultiplicativeElementWithInverse"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SlotUsagePattern","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "SlotUsagePattern: system getter","filters" : [["IsAttributeStoringRep","Tester(SlotUsagePattern)"]]},{"rank" : 1,"comment" : "SlotUsagePattern: for an slp","filters" : [["IsStraightLineProgram"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SlotUsagePattern)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SlotUsagePattern): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SlotUsagePattern): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SlotUsagePattern)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LargestNrSlots","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "LargestNrSlots: system getter","filters" : [["IsAttributeStoringRep","Tester(LargestNrSlots)"]]},{"rank" : 1,"comment" : "LargestNrSlots: for a straight line program","filters" : [["IsStraightLineProgram"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LargestNrSlots)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LargestNrSlots): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LargestNrSlots): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LargestNrSlots)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TypeOfObjWithMemory","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "TypeOfObjWithMemory: system getter","filters" : [["IsAttributeStoringRep","Tester(TypeOfObjWithMemory)"]]},{"rank" : 1,"comment" : "TypeOfObjWithMemory: generic","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TypeOfObjWithMemory)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TypeOfObjWithMemory): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TypeOfObjWithMemory): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TypeOfObjWithMemory)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StripMemory","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 107,"comment" : "StripMemory: for an object with memory","filters" : [["IsObjWithMemory"]]},{"rank" : 2,"comment" : "StripMemory: for a list","filters" : [["IsList"]]},{"rank" : 0,"comment" : "StripMemory: fallback for all objects","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ForgetMemory","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 107,"comment" : "ForgetMemory: nice error message for memory objects","filters" : [["IsObjWithMemory"]]},{"rank" : 4,"comment" : "ForgetMemory: for a mutable list","filters" : [["IsMutable","IsList"]]},{"rank" : 0,"comment" : "ForgetMemory: nice error message for all objects","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FpElmEqualityMethod","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FpElmEqualityMethod: system getter","filters" : [["IsAttributeStoringRep","Tester(FpElmEqualityMethod)"]]},{"rank" : 2,"comment" : "FpElmEqualityMethod: generic dispatcher","filters" : [["CategoryFamily(IsElementOfFpGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FpElmEqualityMethod)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FpElmEqualityMethod): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FpElmEqualityMethod): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FpElmEqualityMethod)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FpElmComparisonMethod","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FpElmComparisonMethod: system getter","filters" : [["IsAttributeStoringRep","Tester(FpElmComparisonMethod)"]]},{"rank" : 2,"comment" : "FpElmComparisonMethod: generic dispatcher","filters" : [["CategoryFamily(IsElementOfFpGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FpElmComparisonMethod)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FpElmComparisonMethod): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FpElmComparisonMethod): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FpElmComparisonMethod)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FpElementNFFunction","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FpElementNFFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(FpElementNFFunction)"]]},{"rank" : 2,"comment" : "FpElementNFFunction","filters" : [["CategoryFamily(IsElementOfFpGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FpElementNFFunction)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FpElementNFFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FpElementNFFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FpElementNFFunction)","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementOfFpGroup","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpGroup)"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "ElementOfFpGroup: for a family of free group elements, and an assoc. word","filters" : [["CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]},{"rank" : 9,"comment" : "ElementOfFpGroup: for a family of f.p. group elements, and an assoc. word","filters" : [["CategoryFamily(IsElementOfFpGroup)"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CosetTableInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CosetTableInWholeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(CosetTableInWholeGroup)"]]},{"rank" : 36,"comment" : "CosetTableInWholeGroup: ByQuoSubRep","filters" : [["IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 36,"comment" : "CosetTableInWholeGroup: from augmented table Mtc","filters" : [["IsSubgroupFpGroup","Tester(AugmentedCosetTableMtcInWholeGroup)"]]},{"rank" : 36,"comment" : "CosetTableInWholeGroup: from augmented table Rrs","filters" : [["IsSubgroupFpGroup","Tester(AugmentedCosetTableRrsInWholeGroup)"]]},{"rank" : 35,"comment" : "CosetTableInWholeGroup: for finitely presented groups","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "CosetTableInWholeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CosetTableInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CosetTableInWholeGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CosetTableInWholeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CosetTableInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TryCosetTableInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 35,"comment" : "TryCosetTableInWholeGroup: for finitely presented groups","filters" : [["IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CosetTableNormalClosureInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CosetTableNormalClosureInWholeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(CosetTableNormalClosureInWholeGroup)"]]},{"rank" : 35,"comment" : "CosetTableNormalClosureInWholeGroup: for finitely presented groups","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "CosetTableNormalClosureInWholeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CosetTableNormalClosureInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CosetTableNormalClosureInWholeGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CosetTableNormalClosureInWholeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CosetTableNormalClosureInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsSubgroupOfWholeGroupByQuotient","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "AsSubgroupOfWholeGroupByQuotient: system getter","filters" : [["IsAttributeStoringRep","Tester(AsSubgroupOfWholeGroupByQuotient)"]]},{"rank" : 36,"comment" : "AsSubgroupOfWholeGroupByQuotient: is already","filters" : [["IsSubgroupOfWholeGroupByQuotientRep"]]},{"rank" : 35,"comment" : "AsSubgroupOfWholeGroupByQuotient: create","filters" : [["IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsSubgroupOfWholeGroupByQuotient)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsSubgroupOfWholeGroupByQuotient): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsSubgroupOfWholeGroupByQuotient): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsSubgroupOfWholeGroupByQuotient)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LowIndexSubgroupsFpGroupIterator","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"],["IsInt","IsPosRat"]],[["IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"]],[["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsList"]],[["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 54,"comment" : "LowIndexSubgroupsFpGroupIterator: supply trivial subgroup","filters" : [["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 92,"comment" : "LowIndexSubgroupsFpGroupIterator: full f.p. group, subgroup of it","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : 91,"comment" : "LowIndexSubgroupsFpGroupIterator: full f.p. group, subgroup of it -- still the old code","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : 89,"comment" : "LowIndexSubgroupsFpGroupIterator: subgroups of f.p. group","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : 59,"comment" : "LowIndexSubgroupsFpGroupIterator: supply trivial subgroup, with exclusion list","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsList"]]}],"4args" : [{"rank" : 94,"comment" : "LowIndexSubgroupsFpGroupIterator: full f.p. group, subgroup of it, with exclusion list","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "LowIndexSubgroupsFpGroup","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 54,"comment" : "LowIndexSubgroupsFpGroup: supply trivial subgroup","filters" : [["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 92,"comment" : "LowIndexSubgroupsFpGroup: subgroups of full fp group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : 89,"comment" : "LowIndexSubgroupsFpGroup: subgroups of fp group","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : 59,"comment" : "LowIndexSubgroupsFpGroup: with exclusion list, supply trivial subgroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsList"]]}],"4args" : [{"rank" : 94,"comment" : "LowIndexSubgroupsFpGroup: subgroups of full fp group, with exclusion list","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsSubgroupFpGroup"],["IsInt","IsPosRat"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "FreeGeneratorsOfFpGroup","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "FreeGeneratorsOfFpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGeneratorsOfFpGroup)"]]},{"rank" : 45,"comment" : "FreeGeneratorsOfFpGroup: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsSubgroupFpGroup"]]},{"rank" : 36,"comment" : "FreeGeneratorsOfFpGroup: for a finitely presented group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGeneratorsOfFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGeneratorsOfFpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGeneratorsOfFpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGeneratorsOfFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGeneratorsOfWholeGroup","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 35,"comment" : "FreeGeneratorsOfWholeGroup: for a finitely presented group","filters" : [["IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelatorsOfFpGroup","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "RelatorsOfFpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RelatorsOfFpGroup)"]]},{"rank" : 45,"comment" : "RelatorsOfFpGroup: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsSubgroupFpGroup"]]},{"rank" : 36,"comment" : "RelatorsOfFpGroup: for finitely presented group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelatorsOfFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RelatorsOfFpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelatorsOfFpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelatorsOfFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGroupOfFpGroup","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "FreeGroupOfFpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGroupOfFpGroup)"]]},{"rank" : 45,"comment" : "FreeGroupOfFpGroup: for a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsGroupOfFamily","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsSubgroupFpGroup"]]},{"rank" : 36,"comment" : "FreeGroupOfFpGroup: for a finitely presented group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGroupOfFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGroupOfFpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGroupOfFpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGroupOfFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicesInvolutaryGenerators","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "IndicesInvolutaryGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(IndicesInvolutaryGenerators)"]]},{"rank" : 36,"comment" : "IndicesInvolutaryGenerators: for finitely presented group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndicesInvolutaryGenerators)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndicesInvolutaryGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndicesInvolutaryGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndicesInvolutaryGenerators)","type" : "GAP_Operation","filters" : [[["IsGroupOfFamily","IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StoredExcludedOrders","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "StoredExcludedOrders: system getter","filters" : [["IsAttributeStoringRep","Tester(StoredExcludedOrders)"]]},{"rank" : 36,"comment" : "StoredExcludedOrders: fp group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StoredExcludedOrders)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StoredExcludedOrders): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StoredExcludedOrders): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StoredExcludedOrders)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FPFaithHom","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "FPFaithHom: system getter","filters" : [["IsAttributeStoringRep","Tester(FPFaithHom)"]]},{"rank" : 1,"comment" : "FPFaithHom: try perm or pc hom","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FPFaithHom)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FPFaithHom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FPFaithHom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FPFaithHom)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentedCosetTableMtcInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "AugmentedCosetTableMtcInWholeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentedCosetTableMtcInWholeGroup)"]]},{"rank" : 35,"comment" : "AugmentedCosetTableMtcInWholeGroup: subgroup of fp group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "AugmentedCosetTableMtcInWholeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentedCosetTableMtcInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentedCosetTableMtcInWholeGroup): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentedCosetTableMtcInWholeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentedCosetTableMtcInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentedCosetTableRrsInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "AugmentedCosetTableRrsInWholeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentedCosetTableRrsInWholeGroup)"]]},{"rank" : 36,"comment" : "AugmentedCosetTableRrsInWholeGroup: use Mtc table","filters" : [["IsSubgroupFpGroup","Tester(AugmentedCosetTableMtcInWholeGroup)"]]},{"rank" : 35,"comment" : "AugmentedCosetTableRrsInWholeGroup: subgroup of fp group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "AugmentedCosetTableRrsInWholeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentedCosetTableRrsInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentedCosetTableRrsInWholeGroup): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentedCosetTableRrsInWholeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentedCosetTableRrsInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentedCosetTableNormalClosureInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "AugmentedCosetTableNormalClosureInWholeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentedCosetTableNormalClosureInWholeGroup)"]]},{"rank" : 35,"comment" : "AugmentedCosetTableNormalClosureInWholeGroup: subgroup of fp group","filters" : [["IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "AugmentedCosetTableNormalClosureInWholeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentedCosetTableNormalClosureInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentedCosetTableNormalClosureInWholeGroup): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentedCosetTableNormalClosureInWholeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentedCosetTableNormalClosureInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentedCosetTableNormalClosure","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "AugmentedCosetTableNormalClosure: for finitely presented groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CosetTableBySubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 70,"comment" : "CosetTableBySubgroup: use `CosetTableInWholeGroup","filters" : [["IsSubgroupFpGroup"],["IsSubgroupFpGroup"]]},{"rank" : 66,"comment" : "CosetTableBySubgroup: coset action","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimaryGeneratorWords","type" : "GAP_Operation","filters" : [[["IsPresentation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "PrimaryGeneratorWords: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimaryGeneratorWords)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimaryGeneratorWords)","type" : "GAP_Operation","filters" : [[["IsPresentation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimaryGeneratorWords): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimaryGeneratorWords): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimaryGeneratorWords)","type" : "GAP_Operation","filters" : [[["IsPresentation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TietzeOrigin","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "TietzeOrigin: system getter","filters" : [["IsAttributeStoringRep","Tester(TietzeOrigin)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TietzeOrigin)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TietzeOrigin): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TietzeOrigin): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TietzeOrigin)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TzOptions","type" : "GAP_Operation","filters" : [[["IsPresentation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "TzOptions: system getter","filters" : [["IsAttributeStoringRep","Tester(TzOptions)"]]},{"rank" : 2,"comment" : "TzOptions: set default values","filters" : [["IsPresentation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TzOptions)","type" : "GAP_Operation","filters" : [[["IsPresentation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TzOptions): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TzOptions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TzOptions)","type" : "GAP_Operation","filters" : [[["IsPresentation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsWordDecompHomomorphism","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IsWordDecompHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsWordDecompHomomorphism)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsWordDecompHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsWordDecompHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsWordDecompHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsWordDecompHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CosetTableFpHom","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "CosetTableFpHom: system getter","filters" : [["IsAttributeStoringRep","Tester(CosetTableFpHom)"]]},{"rank" : 29,"comment" : "CosetTableFpHom: for fp homomorphisms","filters" : [["IsGroupGeneralMappingByImages","IsFromFpGroupGeneralMappingByImages"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CosetTableFpHom)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CosetTableFpHom): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CosetTableFpHom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CosetTableFpHom)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismSimplifiedFpGroup","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "IsomorphismSimplifiedFpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismSimplifiedFpGroup)"]]},{"rank" : 35,"comment" : "IsomorphismSimplifiedFpGroup: using tietze transformations","filters" : [["IsSubgroupFpGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismSimplifiedFpGroup)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismSimplifiedFpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismSimplifiedFpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismSimplifiedFpGroup)","type" : "GAP_Operation","filters" : [[["IsSubgroupFpGroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EpimorphismFromFreeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "EpimorphismFromFreeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(EpimorphismFromFreeGroup)"]]},{"rank" : 34,"comment" : "EpimorphismFromFreeGroup: general","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "EpimorphismFromFreeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EpimorphismFromFreeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EpimorphismFromFreeGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EpimorphismFromFreeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EpimorphismFromFreeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceMonomorphism","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "NiceMonomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceMonomorphism)"]]},{"rank" : 1369,"comment" : "NiceMonomorphism: SeedFaithfulAction supersedes","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)","Tester(SeedFaithfulAction)"]]},{"rank" : 755,"comment" : "NiceMonomorphism: for subgroups that get the nice monomorphism by their parent","filters" : [["Tester(ParentAttr)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 391,"comment" : "NiceMonomorphism: falling back on GL","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 388,"comment" : "NiceMonomorphism: use NicomorphismOfGeneralMatrixGroup","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 381,"comment" : "NiceMonomorphism: for automorphism groups","filters" : [["IsGroupOfAutomorphismsFiniteGroup","Tester(IsGroupOfAutomorphismsFiniteGroup)"]]},{"rank" : 368,"comment" : "NiceMonomorphism: via IsomorphismAbelianGroupViaIndependentGenerators","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputeWithIndependentGensAbelianGroup","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 367,"comment" : "NiceMonomorphism: regular action","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 134,"comment" : "NiceMonomorphism: if a canonical nice monomorphism is already known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(CanonicalNiceMonomorphism)"]]},{"rank" : 46,"comment" : "NiceMonomorphism: for a (nonrational) cyclotomic matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceMonomorphism)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10056,"comment" : "Setter(NiceMonomorphism): set `IsNiceomorphism' property","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 2,"comment" : "Setter(NiceMonomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceMonomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceMonomorphism)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCanonicalNiceMonomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsCanonicalNiceMonomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCanonicalNiceMonomorphism)"]]},{"rank" : 0,"comment" : "IsCanonicalNiceMonomorphism: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCanonicalNiceMonomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCanonicalNiceMonomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCanonicalNiceMonomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCanonicalNiceMonomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalNiceMonomorphism","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "CanonicalNiceMonomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalNiceMonomorphism)"]]},{"rank" : 388,"comment" : "CanonicalNiceMonomorphism","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 34,"comment" : "CanonicalNiceMonomorphism: test canonicity of existing niceo","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(NiceMonomorphism)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalNiceMonomorphism)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalNiceMonomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalNiceMonomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalNiceMonomorphism)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceObject","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "NiceObject: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceObject)"]]},{"rank" : 367,"comment" : "NiceObject","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceObject)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NiceObject): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceObject): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceObject)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsHandledByNiceMonomorphism","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsHandledByNiceMonomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 46,"comment" : "IsHandledByNiceMonomorphism: for a cyclotomic matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsHandledByNiceMonomorphism)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsHandledByNiceMonomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsHandledByNiceMonomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsHandledByNiceMonomorphism)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupByNiceMonomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 50,"comment" : "GroupByNiceMonomorphism","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SeedFaithfulAction","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "SeedFaithfulAction: system getter","filters" : [["IsAttributeStoringRep","Tester(SeedFaithfulAction)"]]},{"rank" : 33,"comment" : "SeedFaithfulAction: default: fail","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SeedFaithfulAction: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SeedFaithfulAction)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SeedFaithfulAction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SeedFaithfulAction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SeedFaithfulAction)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AutomorphismGroup","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "AutomorphismGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AutomorphismGroup)"]]},{"rank" : 58,"comment" : "AutomorphismGroup: for finite p-groups","filters" : [["IsFinite","Tester(IsFinite)","IsPGroup","Tester(IsPGroup)","CanEasilyComputePcgs"]]},{"rank" : 50,"comment" : "AutomorphismGroup: for free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 42,"comment" : "AutomorphismGroup: for nilpotent Lie algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : 42,"comment" : "AutomorphismGroup: finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "AutomorphismGroup:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AutomorphismGroup)","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AutomorphismGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AutomorphismGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AutomorphismGroup)","type" : "GAP_Operation","filters" : [[["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupOfAutomorphisms","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsGroupOfAutomorphisms: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupOfAutomorphisms)"]]},{"rank" : 33,"comment" : "IsGroupOfAutomorphisms: test generators and one","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsGroupOfAutomorphisms: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupOfAutomorphisms)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupOfAutomorphisms): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupOfAutomorphisms): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupOfAutomorphisms)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupOfAutomorphismsFiniteGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsGroupOfAutomorphismsFiniteGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupOfAutomorphismsFiniteGroup)"]]},{"rank" : 33,"comment" : "IsGroupOfAutomorphismsFiniteGroup: default","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsGroupOfAutomorphismsFiniteGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupOfAutomorphismsFiniteGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupOfAutomorphismsFiniteGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupOfAutomorphismsFiniteGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupOfAutomorphismsFiniteGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AutomorphismDomain","type" : "GAP_Operation","filters" : [[["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "AutomorphismDomain: system getter","filters" : [["IsAttributeStoringRep","Tester(AutomorphismDomain)"]]},{"rank" : 35,"comment" : "AutomorphismDomain: use source of one","filters" : [["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"]]},{"rank" : 0,"comment" : "AutomorphismDomain: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AutomorphismDomain)","type" : "GAP_Operation","filters" : [[["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AutomorphismDomain): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AutomorphismDomain): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AutomorphismDomain)","type" : "GAP_Operation","filters" : [[["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAutomorphismGroup","type" : "GAP_Operation","filters" : [[["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20037,"comment" : "IsAutomorphismGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAutomorphismGroup)"]]},{"rank" : 0,"comment" : "IsAutomorphismGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAutomorphismGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAutomorphismGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAutomorphismGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAutomorphismGroup)","type" : "GAP_Operation","filters" : [[["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InnerAutomorphismsAutomorphismGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "InnerAutomorphismsAutomorphismGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(InnerAutomorphismsAutomorphismGroup)"]]},{"rank" : 46,"comment" : "InnerAutomorphismsAutomorphismGroup: for automorphism groups","filters" : [["IsFinite","Tester(IsFinite)","IsAutomorphismGroup","Tester(IsAutomorphismGroup)"]]},{"rank" : 0,"comment" : "InnerAutomorphismsAutomorphismGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InnerAutomorphismsAutomorphismGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InnerAutomorphismsAutomorphismGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InnerAutomorphismsAutomorphismGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InnerAutomorphismsAutomorphismGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GQuotients","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 81,"comment" : "GQuotients: whole fp group to finite group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsSubgroupFpGroup"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 78,"comment" : "GQuotients: subgroup of an fp group","filters" : [["IsSubgroupFpGroup"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 76,"comment" : "GQuotients: for groups which can compute element orders","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphicSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 85,"comment" : "IsomorphicSubgroups: for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DefaultFieldOfMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "DefaultFieldOfMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DefaultFieldOfMatrixGroup)"]]},{"rank" : 47,"comment" : "DefaultFieldOfMatrixGroup: alg elms","filters" : [["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)","CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))"]]},{"rank" : 46,"comment" : "DefaultFieldOfMatrixGroup: for a matrix group over an s.c. algebra","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))"]]},{"rank" : 46,"comment" : "DefaultFieldOfMatrixGroup: for matrix group over the cyclotomics","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "DefaultFieldOfMatrixGroup: for a matrix group over a ring Z\/nZ","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))"]]},{"rank" : 43,"comment" : "DefaultFieldOfMatrixGroup: for a matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "DefaultFieldOfMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DefaultFieldOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DefaultFieldOfMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DefaultFieldOfMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DefaultFieldOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DimensionOfMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "DimensionOfMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DimensionOfMatrixGroup)"]]},{"rank" : 60,"comment" : "DimensionOfMatrixGroup: for matrix group with dimension","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(Dimension)"]]},{"rank" : 47,"comment" : "DimensionOfMatrixGroup: from one","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","Tester(OneImmutable)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 44,"comment" : "DimensionOfMatrixGroup: for matrix group with dimension","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(DimensionOfMatrixGroup)"]]},{"rank" : 44,"comment" : "DimensionOfMatrixGroup: from generators","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "DimensionOfMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DimensionOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DimensionOfMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DimensionOfMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DimensionOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FieldOfMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "FieldOfMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FieldOfMatrixGroup)"]]},{"rank" : 46,"comment" : "FieldOfMatrixGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "FieldOfMatrixGroup: for a matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "FieldOfMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FieldOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FieldOfMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FieldOfMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FieldOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransposedMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "TransposedMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(TransposedMatrixGroup)"]]},{"rank" : 48,"comment" : "TransposedMatrixGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 43,"comment" : "TransposedMatrixGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "TransposedMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransposedMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransposedMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransposedMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransposedMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGeneralLinearGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsGeneralLinearGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGeneralLinearGroup)"]]},{"rank" : 43,"comment" : "IsGeneralLinearGroup: try natural","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 33,"comment" : "IsGeneralLinearGroup: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsGeneralLinearGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGeneralLinearGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGeneralLinearGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGeneralLinearGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGeneralLinearGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNaturalGL","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsNaturalGL: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNaturalGL)"]]},{"rank" : 391,"comment" : "IsNaturalGL: size comparison","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IsNaturalGL: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNaturalGL)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNaturalGL): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNaturalGL): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNaturalGL)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSpecialLinearGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSpecialLinearGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSpecialLinearGroup)"]]},{"rank" : 33,"comment" : "IsSpecialLinearGroup: generic method for finite groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsSpecialLinearGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSpecialLinearGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSpecialLinearGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSpecialLinearGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSpecialLinearGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNaturalSL","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsNaturalSL: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNaturalSL)"]]},{"rank" : 391,"comment" : "IsNaturalSL: size comparison","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IsNaturalSL: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNaturalSL)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNaturalSL): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNaturalSL): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNaturalSL)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubgroupSL","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsSubgroupSL: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSubgroupSL)"]]},{"rank" : 44,"comment" : "IsSubgroupSL: determinant test for generators","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IsSubgroupSL: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSubgroupSL)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSubgroupSL): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSubgroupSL): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSubgroupSL)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InvariantBilinearForm","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "InvariantBilinearForm: system getter","filters" : [["IsAttributeStoringRep","Tester(InvariantBilinearForm)"]]},{"rank" : 44,"comment" : "InvariantBilinearForm: for a matrix group with known `InvariantQuadraticForm'","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(InvariantQuadraticForm)"]]},{"rank" : -14,"comment" : "InvariantBilinearForm: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InvariantBilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InvariantBilinearForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InvariantBilinearForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InvariantBilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullSubgroupGLorSLRespectingBilinearForm","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsFullSubgroupGLorSLRespectingBilinearForm: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"]]},{"rank" : -14,"comment" : "IsFullSubgroupGLorSLRespectingBilinearForm: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullSubgroupGLorSLRespectingBilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullSubgroupGLorSLRespectingBilinearForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullSubgroupGLorSLRespectingBilinearForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InvariantSesquilinearForm","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "InvariantSesquilinearForm: system getter","filters" : [["IsAttributeStoringRep","Tester(InvariantSesquilinearForm)"]]},{"rank" : -14,"comment" : "InvariantSesquilinearForm: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InvariantSesquilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InvariantSesquilinearForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InvariantSesquilinearForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InvariantSesquilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullSubgroupGLorSLRespectingSesquilinearForm","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsFullSubgroupGLorSLRespectingSesquilinearForm: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]]},{"rank" : -14,"comment" : "IsFullSubgroupGLorSLRespectingSesquilinearForm: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullSubgroupGLorSLRespectingSesquilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullSubgroupGLorSLRespectingSesquilinearForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullSubgroupGLorSLRespectingSesquilinearForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InvariantQuadraticForm","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "InvariantQuadraticForm: system getter","filters" : [["IsAttributeStoringRep","Tester(InvariantQuadraticForm)"]]},{"rank" : -14,"comment" : "InvariantQuadraticForm: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InvariantQuadraticForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InvariantQuadraticForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InvariantQuadraticForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InvariantQuadraticForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullSubgroupGLorSLRespectingQuadraticForm","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsFullSubgroupGLorSLRespectingQuadraticForm: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"]]},{"rank" : -14,"comment" : "IsFullSubgroupGLorSLRespectingQuadraticForm: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullSubgroupGLorSLRespectingQuadraticForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullSubgroupGLorSLRespectingQuadraticForm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullSubgroupGLorSLRespectingQuadraticForm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FittingFreeLiftSetup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "FittingFreeLiftSetup: system getter","filters" : [["IsAttributeStoringRep","Tester(FittingFreeLiftSetup)"]]},{"rank" : 58,"comment" : "FittingFreeLiftSetup: permutation","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "FittingFreeLiftSetup: pc group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 0,"comment" : "FittingFreeLiftSetup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FittingFreeLiftSetup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FittingFreeLiftSetup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FittingFreeLiftSetup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FittingFreeLiftSetup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RecogDecompinfoHomomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "RecogDecompinfoHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(RecogDecompinfoHomomorphism)"]]},{"rank" : 0,"comment" : "RecogDecompinfoHomomorphism: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RecogDecompinfoHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RecogDecompinfoHomomorphism): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RecogDecompinfoHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RecogDecompinfoHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DirectFactorsFittingFreeSocle","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DirectFactorsFittingFreeSocle: system getter","filters" : [["IsAttributeStoringRep","Tester(DirectFactorsFittingFreeSocle)"]]},{"rank" : 42,"comment" : "DirectFactorsFittingFreeSocle: generic","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DirectFactorsFittingFreeSocle: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DirectFactorsFittingFreeSocle)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DirectFactorsFittingFreeSocle): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DirectFactorsFittingFreeSocle): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DirectFactorsFittingFreeSocle)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ChiefSeriesTF","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ChiefSeriesTF: system getter","filters" : [["IsAttributeStoringRep","Tester(ChiefSeriesTF)"]]},{"rank" : 43,"comment" : "ChiefSeriesTF: fitting free","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanComputeFittingFree"]]},{"rank" : 0,"comment" : "ChiefSeriesTF: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ChiefSeriesTF)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ChiefSeriesTF): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ChiefSeriesTF): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ChiefSeriesTF)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRationalMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "IsRationalMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRationalMatrixGroup)"]]},{"rank" : 46,"comment" : "IsRationalMatrixGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsRationalMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRationalMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRationalMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRationalMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRationalMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIntegerMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "IsIntegerMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIntegerMatrixGroup)"]]},{"rank" : 46,"comment" : "IsIntegerMatrixGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsIntegerMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIntegerMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIntegerMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIntegerMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIntegerMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ZClassRepsQClass","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "ZClassRepsQClass: system getter","filters" : [["IsAttributeStoringRep","Tester(ZClassRepsQClass)"]]},{"rank" : -30,"comment" : "ZClassRepsQClass: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ZClassRepsQClass)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ZClassRepsQClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ZClassRepsQClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ZClassRepsQClass)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerInGLnZ","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "NormalizerInGLnZ: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizerInGLnZ)"]]},{"rank" : 48,"comment" : "NormalizerInGLnZ: for PointGroups of space groups from the cryst. groups catalogue","filters" : [["IsPointGroup","Tester(IsPointGroup)"]]},{"rank" : -30,"comment" : "NormalizerInGLnZ: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizerInGLnZ)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizerInGLnZ): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizerInGLnZ): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizerInGLnZ)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralizerInGLnZ","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "CentralizerInGLnZ: system getter","filters" : [["IsAttributeStoringRep","Tester(CentralizerInGLnZ)"]]},{"rank" : -30,"comment" : "CentralizerInGLnZ: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CentralizerInGLnZ)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CentralizerInGLnZ): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CentralizerInGLnZ): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CentralizerInGLnZ)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBravaisGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "IsBravaisGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBravaisGroup)"]]},{"rank" : 46,"comment" : "IsBravaisGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsBravaisGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBravaisGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBravaisGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBravaisGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBravaisGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BravaisGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "BravaisGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(BravaisGroup)"]]},{"rank" : -30,"comment" : "BravaisGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BravaisGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BravaisGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BravaisGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BravaisGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BravaisSubgroups","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "BravaisSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(BravaisSubgroups)"]]},{"rank" : -30,"comment" : "BravaisSubgroups: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BravaisSubgroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BravaisSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BravaisSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BravaisSubgroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BravaisSupergroups","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "BravaisSupergroups: system getter","filters" : [["IsAttributeStoringRep","Tester(BravaisSupergroups)"]]},{"rank" : -30,"comment" : "BravaisSupergroups: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BravaisSupergroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BravaisSupergroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BravaisSupergroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BravaisSupergroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerInGLnZBravaisGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "NormalizerInGLnZBravaisGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizerInGLnZBravaisGroup)"]]},{"rank" : -30,"comment" : "NormalizerInGLnZBravaisGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizerInGLnZBravaisGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizerInGLnZBravaisGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizerInGLnZBravaisGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizerInGLnZBravaisGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InvariantLattice","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20048,"comment" : "InvariantLattice: system getter","filters" : [["IsAttributeStoringRep","Tester(InvariantLattice)"]]},{"rank" : 46,"comment" : "InvariantLattice: for rational matrix groups","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "InvariantLattice: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InvariantLattice)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InvariantLattice): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InvariantLattice): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InvariantLattice)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TrivialGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : -58,"comment" : "TrivialGroupCons: perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -60,"comment" : "TrivialGroupCons: pcp group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : -62,"comment" : "TrivialGroupCons: pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbelianGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -45,"comment" : "AbelianGroupCons: fp group","filters" : [["IsFinite","Tester(IsFinite)","IsGroupOfFamily","IsSubgroupFpGroup"],["IsList"]]},{"rank" : -48,"comment" : "AbelianGroupCons: pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsList"]]},{"rank" : -58,"comment" : "AbelianGroupCons: perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]},{"rank" : -62,"comment" : "AbelianGroupCons: pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlternatingGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -58,"comment" : "AlternatingGroupCons: perm group with domain","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]},{"rank" : -58,"comment" : "AlternatingGroupCons: perm group with degree","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]},{"rank" : -60,"comment" : "AlternatingGroupCons: pcp group with degree","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : -62,"comment" : "AlternatingGroupCons: pc group with degree","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt","IsPosRat"]]},{"rank" : -65,"comment" : "AlternatingGroupCons: regular perm group with domain","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsRegular","Tester(IsRegular)"],["IsDenseList"]]},{"rank" : -65,"comment" : "AlternatingGroupCons: regular perm group with degree","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsRegular","Tester(IsRegular)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CyclicGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -36,"comment" : "CyclicGroupCons: fp group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"],[]]},{"rank" : -48,"comment" : "CyclicGroupCons: pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInfinity"]]},{"rank" : -60,"comment" : "CyclicGroupCons: pcp group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : -62,"comment" : "CyclicGroupCons: pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt","IsPosRat"]]},{"rank" : -65,"comment" : "CyclicGroupCons: regular perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsRegular","Tester(IsRegular)"],["IsInt","IsPosRat"]]},{"rank" : -388,"comment" : "CyclicGroupCons: matrix group for default field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : -388,"comment" : "CyclicGroupCons: matrix group for given field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DihedralGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -45,"comment" : "DihedralGroupCons: fp group","filters" : [["IsFinite","Tester(IsFinite)","IsGroupOfFamily","IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : -48,"comment" : "DihedralGroupCons: pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInfinity"]]},{"rank" : -58,"comment" : "DihedralGroupCons: perm. group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : -60,"comment" : "DihedralGroupCons: pcp group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : -62,"comment" : "DihedralGroupCons: pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuaternionGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -45,"comment" : "QuaternionGroupCons: fp group","filters" : [["IsFinite","Tester(IsFinite)","IsGroupOfFamily","IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : -58,"comment" : "QuaternionGroupCons: perm. group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : -60,"comment" : "QuaternionGroupCons: pcp group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : -62,"comment" : "QuaternionGroupCons: pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt","IsPosRat"]]},{"rank" : -388,"comment" : "QuaternionGroupCons: matrix group for default field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : -388,"comment" : "QuaternionGroupCons: matrix group for given field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementaryAbelianGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -45,"comment" : "ElementaryAbelianGroupCons: fp group","filters" : [["IsFinite","Tester(IsFinite)","IsGroupOfFamily","IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : -58,"comment" : "ElementaryAbelianGroupCons: perm group","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : -60,"comment" : "ElementaryAbelianGroupCons: pcp group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : -62,"comment" : "ElementaryAbelianGroupCons: pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeAbelianGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -36,"comment" : "FreeAbelianGroupCons: fp group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"],["IsInt","IsPosRat"]]},{"rank" : -48,"comment" : "FreeAbelianGroupCons: pcp group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtraspecialGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -60,"comment" : "ExtraspecialGroupCons: pcp group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt"],[]]},{"rank" : -62,"comment" : "ExtraspecialGroupCons: pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MathieuGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -58,"comment" : "MathieuGroupCons: perm group with degree","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymmetricGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -58,"comment" : "SymmetricGroupCons: perm group with domain","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]},{"rank" : -58,"comment" : "SymmetricGroupCons: perm group with degree","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]},{"rank" : -60,"comment" : "SymmetricGroupCons: pcp group with degree","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]},{"rank" : -62,"comment" : "SymmetricGroupCons: pc group with degree","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsInt","IsPosRat"]]},{"rank" : -65,"comment" : "SymmetricGroupCons: regular perm group with domain","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsRegular","Tester(IsRegular)"],["IsDenseList"]]},{"rank" : -65,"comment" : "SymmetricGroupCons: regular perm group with degree","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsRegular","Tester(IsRegular)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneralLinearGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -43,"comment" : "GeneralLinearGroupCons: some generators for GL_n(Z)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsIntegers"]]},{"rank" : -134,"comment" : "GeneralLinearGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],[]]},{"rank" : -388,"comment" : "GeneralLinearGroupCons: natural GL for dimension and residue class ring","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsFinite","Tester(IsFinite)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : -388,"comment" : "GeneralLinearGroupCons: matrix group for dimension and finite field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneralOrthogonalGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : -152,"comment" : "GeneralOrthogonalGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"],[]]},{"rank" : -388,"comment" : "GeneralOrthogonalGroupCons: GO for dimension and residue class ring for prime powers","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsFinite","Tester(IsFinite)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : -388,"comment" : "GeneralOrthogonalGroupCons: matrix group for dimension and finite field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -388,"comment" : "GeneralOrthogonalGroupCons: matrix group for <e>, dimension, and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "GeneralUnitaryGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -134,"comment" : "GeneralUnitaryGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],[]]},{"rank" : -388,"comment" : "GeneralUnitaryGroupCons: matrix group for dimension and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpecialLinearGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -43,"comment" : "SpecialLinearGroupCons: some generators for SL_n(Z)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsIntegers"]]},{"rank" : -134,"comment" : "SpecialLinearGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],[]]},{"rank" : -388,"comment" : "SpecialLinearGroupCons: natural SL for dimension and residue class ring","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsFinite","Tester(IsFinite)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : -388,"comment" : "SpecialLinearGroupCons: matrix group for dimension and finite field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpecialOrthogonalGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : -152,"comment" : "SpecialOrthogonalGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"],[]]},{"rank" : -388,"comment" : "SpecialOrthogonalGroupCons: GO for dimension and residue class ring for prime powers","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsFinite","Tester(IsFinite)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : -388,"comment" : "SpecialOrthogonalGroupCons: matrix group for dimension and finite field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -388,"comment" : "SpecialOrthogonalGroupCons: matrix group for <e>, dimension, and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "SpecialUnitaryGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -134,"comment" : "SpecialUnitaryGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],[]]},{"rank" : -388,"comment" : "SpecialUnitaryGroupCons: matrix group for dimension and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymplecticGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -134,"comment" : "SymplecticGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],[]]},{"rank" : -388,"comment" : "SymplecticGroupCons: symplectic group for dimension and residue class ring for prime powers","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsFinite","Tester(IsFinite)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","CategoryCollections(IsZmodnZObjNonprime)"]]},{"rank" : -388,"comment" : "SymplecticGroupCons: matrix group for dimension and finite field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : -388,"comment" : "SymplecticGroupCons: matrix group for dimension and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OmegaCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -134,"comment" : "OmegaCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],[]]}],"4args" : [{"rank" : -388,"comment" : "OmegaCons: matrix group for <e>, dimension, and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "GeneralSemilinearGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -154,"comment" : "GeneralSemilinearGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : -388,"comment" : "GeneralSemilinearGroupCons: matrix group for dimension and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpecialSemilinearGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -154,"comment" : "SpecialSemilinearGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]},{"rank" : -388,"comment" : "SpecialSemilinearGroupCons: matrix group for dimension and finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectiveGeneralLinearGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -54,"comment" : "ProjectiveGeneralLinearGroupCons: action on lines","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectiveSpecialLinearGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -54,"comment" : "ProjectiveSpecialLinearGroupCons: action on lines","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectiveGeneralUnitaryGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -54,"comment" : "ProjectiveGeneralUnitaryGroupCons: action on lines","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectiveSpecialUnitaryGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -54,"comment" : "ProjectiveSpecialUnitaryGroupCons: action on lines","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectiveSymplecticGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -54,"comment" : "ProjectiveSymplecticGroupCons: action on lines","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectiveOmegaCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : -54,"comment" : "ProjectiveOmegaCons: action on lines","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"5args" : [],"6args" : []}},{"name" : "PerfGrpConst","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -35,"comment" : "PerfGrpConst: fp grp","filters" : [["IsSubgroupFpGroup"],["IsList"]]},{"rank" : -58,"comment" : "PerfGrpConst: perm grp","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PerfectIdentification","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "PerfectIdentification: system getter","filters" : [["IsAttributeStoringRep","Tester(PerfectIdentification)"]]},{"rank" : 33,"comment" : "PerfectIdentification: id. for perfect groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "PerfectIdentification: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PerfectIdentification)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PerfectIdentification): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PerfectIdentification): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PerfectIdentification)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SuzukiGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -58,"comment" : "SuzukiGroupCons: permutation group for finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : -388,"comment" : "SuzukiGroupCons: matrix group for finite field size","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReeGroupCons","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -43,"comment" : "ReeGroupCons: matrix","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : -116,"comment" : "ReeGroupCons: convert to permgroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DataAboutSimpleGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DataAboutSimpleGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DataAboutSimpleGroup)"]]},{"rank" : 33,"comment" : "DataAboutSimpleGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 1,"comment" : "DataAboutSimpleGroup","filters" : [["IsRecord"]]},{"rank" : 0,"comment" : "DataAboutSimpleGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DataAboutSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DataAboutSimpleGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DataAboutSimpleGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DataAboutSimpleGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImfRecord","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "ImfRecord: system getter","filters" : [["IsAttributeStoringRep","Tester(ImfRecord)"]]},{"rank" : 0,"comment" : "ImfRecord: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImfRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImfRecord): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImfRecord): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImfRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrderingsFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "OrderingsFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(OrderingsFamily)"]]},{"rank" : 1,"comment" : "OrderingsFamily: for a family","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrderingsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrderingsFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrderingsFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrderingsFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsWellFoundedOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsWellFoundedOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(IsWellFoundedOrdering)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsWellFoundedOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsWellFoundedOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsWellFoundedOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsWellFoundedOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTotalOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsTotalOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTotalOrdering)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTotalOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTotalOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTotalOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTotalOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FamilyForOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "FamilyForOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(FamilyForOrdering)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FamilyForOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FamilyForOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FamilyForOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FamilyForOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LessThanFunction","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "LessThanFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(LessThanFunction)"]]},{"rank" : 2,"comment" : "LessThanFunction: for an ordering which has a a LessThanOrEqualFunction","filters" : [["IsOrdering","Tester(LessThanOrEqualFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LessThanFunction)","type" : "GAP_Operation","filters" : [[["IsOrdering"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LessThanFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LessThanFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LessThanFunction)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LessThanOrEqualFunction","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "LessThanOrEqualFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(LessThanOrEqualFunction)"]]},{"rank" : 2,"comment" : "LessThanOrEqualFunction: for an ordering which has a a LessThanFunction","filters" : [["IsOrdering","Tester(LessThanFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LessThanOrEqualFunction)","type" : "GAP_Operation","filters" : [[["IsOrdering"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LessThanOrEqualFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LessThanOrEqualFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LessThanOrEqualFunction)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLessThanUnder","type" : "GAP_Operation","filters" : [[["IsOrdering"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 1,"comment" : "IsLessThanUnder: for an ordering ","filters" : [["IsOrdering"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLessThanOrEqualUnder","type" : "GAP_Operation","filters" : [[["IsOrdering"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 1,"comment" : "IsLessThanOrEqualUnder: for an ordering and two objects ","filters" : [["IsOrdering"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIncomparableUnder","type" : "GAP_Operation","filters" : [[["IsOrdering"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 1,"comment" : "IsIncomparableUnder: for an ordering","filters" : [["IsOrdering"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrderingByLessThanFunctionNC","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "OrderingByLessThanFunctionNC: for a family and a function","filters" : [["IsFamily"],["IsFunction"]]}],"3args" : [{"rank" : 4,"comment" : "OrderingByLessThanFunctionNC: for a family, a function, and a list of properties","filters" : [["IsFamily"],["IsFunction"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrderingByLessThanOrEqualFunctionNC","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "OrderingByLessThanOrEqualFunctionNC: for a family and a function","filters" : [["IsFamily"],["IsFunction"]]}],"3args" : [{"rank" : 4,"comment" : "OrderingByLessThanOrEqualFunctionNC: for a family, a function, and a list of properties","filters" : [["IsFamily"],["IsFunction"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsOrderingOnFamilyOfAssocWords","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsOrderingOnFamilyOfAssocWords: system getter","filters" : [["IsAttributeStoringRep","Tester(IsOrderingOnFamilyOfAssocWords)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsOrderingOnFamilyOfAssocWords)","type" : "GAP_Operation","filters" : [[["IsOrdering"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsOrderingOnFamilyOfAssocWords): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsOrderingOnFamilyOfAssocWords): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsOrderingOnFamilyOfAssocWords)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LetterRepWordsLessFunc","type" : "GAP_Operation","filters" : [[["IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "LetterRepWordsLessFunc: system getter","filters" : [["IsAttributeStoringRep","Tester(LetterRepWordsLessFunc)"]]},{"rank" : 0,"comment" : "LetterRepWordsLessFunc: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LetterRepWordsLessFunc)","type" : "GAP_Operation","filters" : [[["IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LetterRepWordsLessFunc): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LetterRepWordsLessFunc): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LetterRepWordsLessFunc)","type" : "GAP_Operation","filters" : [[["IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTranslationInvariantOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "IsTranslationInvariantOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTranslationInvariantOrdering)"]]},{"rank" : 0,"comment" : "IsTranslationInvariantOrdering: default method requiring categories and checking properties","filters" : [["IsOrdering"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTranslationInvariantOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTranslationInvariantOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTranslationInvariantOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTranslationInvariantOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrderingOnGenerators","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "OrderingOnGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(OrderingOnGenerators)"]]},{"rank" : 0,"comment" : "OrderingOnGenerators: default method requiring categories and checking properties","filters" : [["IsOrdering"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrderingOnGenerators)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrderingOnGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrderingOnGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrderingOnGenerators)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LexicographicOrdering","type" : "GAP_Operation","filters" : [[["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "LexicographicOrdering: for a free monoid","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"]]},{"rank" : 20,"comment" : "LexicographicOrdering: for a free semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 2,"comment" : "LexicographicOrdering: for a family of words of a free semigroup or free monoid","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"]]}],"2args" : [{"rank" : 41,"comment" : "LexicographicOrdering: for a free monoid and a list of generators","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 35,"comment" : "LexicographicOrdering: for a free semigroup and a list of generators","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 28,"comment" : "LexicographicOrdering: for a free monoid and a list","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList"]]},{"rank" : 22,"comment" : "LexicographicOrdering: for a free semigroup and a list","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList"]]},{"rank" : 17,"comment" : "LexicographicOrdering: for a family of words of a free semigroup or free monoid and a list of generators","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 4,"comment" : "LexicographicOrdering: for a family of words of a free semigroup or free monoid and a list","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ShortLexOrdering","type" : "GAP_Operation","filters" : [[["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "ShortLexOrdering: for a free monoid","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"]]},{"rank" : 20,"comment" : "ShortLexOrdering: for a free semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 2,"comment" : "ShortLexOrdering: for a family of words of a free semigroup or free  monoid","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"]]}],"2args" : [{"rank" : 41,"comment" : "ShortLexOrdering: for a free monoid and a list of generators in the required order ","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 35,"comment" : "ShortLexOrdering: for a free semigroup and a list of generators in the required order","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 28,"comment" : "ShortLexOrdering: for a free monoid and a list","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList"]]},{"rank" : 22,"comment" : "ShortLexOrdering: for a free semigroup and a list","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList"]]},{"rank" : 17,"comment" : "ShortLexOrdering: for a family of words of a free semigroup or free monoid and a list of generators","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 4,"comment" : "ShortLexOrdering: for a family of free words of a free semigroup or free  monoid and a list","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsShortLexOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "IsShortLexOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(IsShortLexOrdering)"]]},{"rank" : 0,"comment" : "IsShortLexOrdering: default method requiring categories and checking properties","filters" : [["IsOrdering"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsShortLexOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsShortLexOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsShortLexOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsShortLexOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WeightLexOrdering","type" : "GAP_Operation","filters" : [[["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 43,"comment" : "WeightLexOrdering: for a free monoid, a list of generators and a list of weights","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]},{"rank" : 37,"comment" : "WeightLexOrdering: for a free semigroup, a list of generators and a list of weights","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]},{"rank" : 30,"comment" : "WeightLexOrdering: for a free monoid, a list giving ordering on generators and a list of weights","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList"],["IsList"]]},{"rank" : 24,"comment" : "WeightLexOrdering: for a free semigroup, a list giving ordering on generators and a list of weights","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList"],["IsList"]]},{"rank" : 19,"comment" : "WeightLexOrdering: for a family of words of a free semigroup or free monoid, a list of generators and a list of weights","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]},{"rank" : 6,"comment" : "WeightLexOrdering: for a family of words of a free semigroup or free monoid, and two lists","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WeightOfGenerators","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "WeightOfGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(WeightOfGenerators)"]]},{"rank" : 0,"comment" : "WeightOfGenerators: default method requiring categories and checking properties","filters" : [["IsOrdering"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WeightOfGenerators)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WeightOfGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WeightOfGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WeightOfGenerators)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsWeightLexOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "IsWeightLexOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(IsWeightLexOrdering)"]]},{"rank" : 0,"comment" : "IsWeightLexOrdering: default method requiring categories and checking properties","filters" : [["IsOrdering"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsWeightLexOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsWeightLexOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsWeightLexOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsWeightLexOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BasicWreathProductOrdering","type" : "GAP_Operation","filters" : [[["CategoryFamily((IsWord and IsAssociativeElement))"],["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "BasicWreathProductOrdering: for a free monoid","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"]]},{"rank" : 20,"comment" : "BasicWreathProductOrdering: for a free semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 2,"comment" : "BasicWreathProductOrdering: for a family of words of a free semigroup or free monoid and a list","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"]]}],"2args" : [{"rank" : 41,"comment" : "BasicWreathProductOrdering: for a free monoid and a list of generators","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 35,"comment" : "BasicWreathProductOrdering: for a free semigroup and a list of generators","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 28,"comment" : "BasicWreathProductOrdering: for a free monoid and a list","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList"]]},{"rank" : 22,"comment" : "BasicWreathProductOrdering: for a free semigroup and a list","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList"]]},{"rank" : 17,"comment" : "BasicWreathProductOrdering: for a family of words of a free semigroup or free monoid and a list of generators","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"]]},{"rank" : 4,"comment" : "BasicWreathProductOrdering: for a family of words of a free semigroup or free monoid and a list","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBasicWreathProductOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsBasicWreathProductOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBasicWreathProductOrdering)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBasicWreathProductOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBasicWreathProductOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBasicWreathProductOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBasicWreathProductOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WreathProductOrdering","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "WreathProductOrdering: for a free monoid","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList"]]},{"rank" : 22,"comment" : "WreathProductOrdering: for a free semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList"]]},{"rank" : 4,"comment" : "WreathProductOrdering: for a family of words of a free semigroup or free monoid and a list","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList"]]}],"3args" : [{"rank" : 30,"comment" : "WreathProductOrdering: for a free monoid and a list","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList"],["IsList"]]},{"rank" : 30,"comment" : "WreathProductOrdering: for a free monoid and a list","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"],["IsList"],["IsList"]]},{"rank" : 24,"comment" : "WreathProductOrdering: for a free semigroup and a list","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"],["IsList"],["IsList"]]},{"rank" : 19,"comment" : "WreathProductOrdering: for a family of associative words, a list of generators and a list with the levels of the generators","filters" : [["CategoryFamily((IsWord and IsAssociativeElement))"],["IsList","CategoryCollections((IsWord and IsAssociativeElement))"],["IsList"]]},{"rank" : 6,"comment" : "WreathProductOrdering: for a family of words of a free semigroup or free monoid and a list","filters" : [["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsWreathProductOrdering","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsWreathProductOrdering: system getter","filters" : [["IsAttributeStoringRep","Tester(IsWreathProductOrdering)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsWreathProductOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsWreathProductOrdering): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsWreathProductOrdering): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsWreathProductOrdering)","type" : "GAP_Operation","filters" : [[["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LevelsOfGenerators","type" : "GAP_Operation","filters" : [[["IsOrdering","IsWreathProductOrdering","Tester(IsWreathProductOrdering)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "LevelsOfGenerators: system getter","filters" : [["IsAttributeStoringRep","Tester(LevelsOfGenerators)"]]},{"rank" : 0,"comment" : "LevelsOfGenerators: default method requiring categories and checking properties","filters" : [["IsOrdering"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LevelsOfGenerators)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsWreathProductOrdering","Tester(IsWreathProductOrdering)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LevelsOfGenerators): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LevelsOfGenerators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LevelsOfGenerators)","type" : "GAP_Operation","filters" : [[["IsOrdering","IsWreathProductOrdering","Tester(IsWreathProductOrdering)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Transformation","type" : "GAP_Operation","filters" : [[["IsList"]],[["IsList"],["IsList"]],[["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Transformation: for a list","filters" : [["IsList"]]}],"2args" : [{"rank" : 4,"comment" : "Transformation: for a list and list","filters" : [["IsList"],["IsList"]]},{"rank" : 3,"comment" : "Transformation: for a list and function","filters" : [["IsList"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformationListList","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 4,"comment" : "TransformationListList: for a list and list","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformationList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "TransformationList: for a list","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformationByImageAndKernel","type" : "GAP_Operation","filters" : [[["IsDenseList","CategoryCollections(IsCyclotomic)"],["IsDenseList","CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 58,"comment" : "TransformationByImageAndKernel: for a list of positive integers and a list of positive integers","filters" : [["IsDenseList","CategoryCollections(IsCyclotomic)"],["IsDenseList","CategoryCollections(IsCyclotomic)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumberTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsZeroCyc"]],[["IsTransformation"],["IsInt","IsPosRat"]],[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "NumberTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 28,"comment" : "NumberTransformation: for a transformation and zero","filters" : [["IsTransformation"],["IsZeroCyc"]]},{"rank" : 26,"comment" : "NumberTransformation: for a transformation and positive integer","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformationNumber","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "TransformationNumber: for a positive integer and positive integer","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LargestImageOfMovedPoint","type" : "GAP_Operation","filters" : [[["IsTransformation"]],[["CategoryCollections(IsTransformation)"]],[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "LargestImageOfMovedPoint: system getter","filters" : [["IsAttributeStoringRep","Tester(LargestImageOfMovedPoint)"]]},{"rank" : 23,"comment" : "LargestImageOfMovedPoint: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "LargestImageOfMovedPoint: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "LargestImageOfMovedPoint: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 13,"comment" : "LargestImageOfMovedPoint: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 7,"comment" : "LargestImageOfMovedPoint: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "LargestImageOfMovedPoint: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LargestImageOfMovedPoint)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]],[["CategoryCollections(IsTransformation)"],[]],[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LargestImageOfMovedPoint): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LargestImageOfMovedPoint): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LargestImageOfMovedPoint)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SmallestImageOfMovedPoint","type" : "GAP_Operation","filters" : [[["IsTransformation"]],[["CategoryCollections(IsTransformation)"]],[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "SmallestImageOfMovedPoint: system getter","filters" : [["IsAttributeStoringRep","Tester(SmallestImageOfMovedPoint)"]]},{"rank" : 23,"comment" : "SmallestImageOfMovedPoint: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "SmallestImageOfMovedPoint: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "SmallestImageOfMovedPoint: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 13,"comment" : "SmallestImageOfMovedPoint: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]},{"rank" : 7,"comment" : "SmallestImageOfMovedPoint: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "SmallestImageOfMovedPoint: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SmallestImageOfMovedPoint)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]],[["CategoryCollections(IsTransformation)"],[]],[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SmallestImageOfMovedPoint): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SmallestImageOfMovedPoint): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SmallestImageOfMovedPoint)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]],[["IsTransformation"],["IsInt","IsPosRat"]],[["IsTransformation"],["IsZeroCyc"]],[["IsTransformation"],["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "RankOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(RankOfTransformation)"]]},{"rank" : 7,"comment" : "RankOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 28,"comment" : "RankOfTransformation: for a transformation and zero","filters" : [["IsTransformation"],["IsZeroCyc"]]},{"rank" : 26,"comment" : "RankOfTransformation: for a transformation and pos int","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]},{"rank" : 10,"comment" : "RankOfTransformation: for a transformation and dense list","filters" : [["IsTransformation"],["IsDenseList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RankOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RankOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RankOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RankOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsBinaryRelation","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "AsBinaryRelation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsPermutation","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "AsPermutation: system getter","filters" : [["IsAttributeStoringRep","Tester(AsPermutation)"]]},{"rank" : 12,"comment" : "AsPermutation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 7,"comment" : "AsPermutation: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "AsPermutation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsPermutation)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsPermutation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsPermutation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsPermutation)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsTransformation","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]],[["IsAssociativeElement"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "AsTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(AsTransformation)"]]},{"rank" : 12,"comment" : "AsTransformation: for binary relations on points","filters" : [["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsBinaryRelationOnPointsRep"]]},{"rank" : 8,"comment" : "AsTransformation: for a permutation","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "AsTransformation: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "AsTransformation: for relation over [1..n]","filters" : [["IsGeneralMapping"]]},{"rank" : 7,"comment" : "AsTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 26,"comment" : "AsTransformation: for a partial perm and positive integer","filters" : [["IsPartialPerm"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "AsTransformation: for a permutation and positive integer","filters" : [["IsPerm"],["IsInt"]]},{"rank" : 25,"comment" : "AsTransformation: for a transformation and degree","filters" : [["IsTransformation"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsTransformation)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsTransformation)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermutationOfImage","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "PermutationOfImage: system getter","filters" : [["IsAttributeStoringRep","Tester(PermutationOfImage)"]]},{"rank" : 7,"comment" : "PermutationOfImage: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PermutationOfImage)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PermutationOfImage): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PermutationOfImage): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PermutationOfImage)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConstantTransformation","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "ConstantTransformation: for a pos int and pos int","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOfTransformationCollection","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsTransformation)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "DegreeOfTransformationCollection: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOfTransformationCollection)"]]},{"rank" : 13,"comment" : "DegreeOfTransformationCollection: for a transformation collection","filters" : [["CategoryCollections(IsTransformation)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOfTransformationCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsTransformation)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOfTransformationCollection): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOfTransformationCollection): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOfTransformationCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsTransformation)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FlatKernelOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]],[["IsTransformation"],["IsInt","IsPosRat"]],[["IsTransformation"],["IsZeroCyc"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "FlatKernelOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(FlatKernelOfTransformation)"]]},{"rank" : 7,"comment" : "FlatKernelOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 28,"comment" : "FlatKernelOfTransformation: for a transformation and zero","filters" : [["IsTransformation"],["IsZeroCyc"]]},{"rank" : 26,"comment" : "FlatKernelOfTransformation: for a transformation and pos int","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FlatKernelOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FlatKernelOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FlatKernelOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FlatKernelOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImageListOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsInt","IsPosRat"]],[["IsTransformation"],["IsZeroCyc"]],[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "ImageListOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 28,"comment" : "ImageListOfTransformation: for a transformation and zero","filters" : [["IsTransformation"],["IsZeroCyc"]]},{"rank" : 26,"comment" : "ImageListOfTransformation: for a transformation and pos int","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImageSetOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]],[["IsTransformation"],["IsInt","IsPosRat"]],[["IsTransformation"],["IsZeroCyc"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ImageSetOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(ImageSetOfTransformation)"]]},{"rank" : 7,"comment" : "ImageSetOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 28,"comment" : "ImageSetOfTransformation: for a transformation and zero","filters" : [["IsTransformation"],["IsZeroCyc"]]},{"rank" : 26,"comment" : "ImageSetOfTransformation: for a transformation and pos int","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImageSetOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImageSetOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImageSetOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImageSetOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndexPeriodOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IndexPeriodOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(IndexPeriodOfTransformation)"]]},{"rank" : 7,"comment" : "IndexPeriodOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndexPeriodOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndexPeriodOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndexPeriodOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndexPeriodOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInjectiveListTrans","type" : "GAP_Operation","filters" : [[["IsList"],["IsTransformation"]],[["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "IsInjectiveListTrans: for a list and trans","filters" : [["IsList"],["IsTransformation"]]},{"rank" : 4,"comment" : "IsInjectiveListTrans: for a list and list","filters" : [["IsList"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KernelOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]],[["IsTransformation"],["IsInt","IsPosRat"],["IsBool"]],[["IsTransformation"],["IsInt","IsPosRat"]],[["IsTransformation"],["IsZeroCyc"]],[["IsTransformation"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "KernelOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(KernelOfTransformation)"]]},{"rank" : 7,"comment" : "KernelOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 26,"comment" : "KernelOfTransformation: for a transformation and pos int","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]},{"rank" : 8,"comment" : "KernelOfTransformation: for a transformation and pos int","filters" : [["IsTransformation"],["IsBool"]]}],"3args" : [{"rank" : 27,"comment" : "KernelOfTransformation: for a transformation, positive integer and boolean","filters" : [["IsTransformation"],["IsInt","IsPosRat"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KernelOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KernelOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KernelOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KernelOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermLeftQuoTransformationNC","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 14,"comment" : "PermLeftQuoTransformationNC: for a transformation and transformation","filters" : [["IsTransformation"],["IsTransformation"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermLeftQuoTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 14,"comment" : "PermLeftQuoTransformation: for a transformation and transformation","filters" : [["IsTransformation"],["IsTransformation"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImagesOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "PreImagesOfTransformation: for a transformation and positive integer","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RandomTransformation","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"]],[["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "RandomTransformation: for a pos. int.","filters" : [["IsInt","IsPosRat"]]}],"2args" : [{"rank" : 38,"comment" : "RandomTransformation: for pos int and pos int","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedTransformationNC","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "RestrictedTransformationNC: for a transformation and list","filters" : [["IsTransformation"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "RestrictedTransformation: for transformation and list","filters" : [["IsTransformation"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SmallestIdempotentPower","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "SmallestIdempotentPower: system getter","filters" : [["IsAttributeStoringRep","Tester(SmallestIdempotentPower)"]]},{"rank" : 7,"comment" : "SmallestIdempotentPower: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "SmallestIdempotentPower: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SmallestIdempotentPower)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SmallestIdempotentPower): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SmallestIdempotentPower): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SmallestIdempotentPower)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TrimTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsInt","IsPosRat"]],[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "TrimTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 26,"comment" : "TrimTransformation: for a transformation and pos int","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Idempotent","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsCyclotomic)"],["CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "Idempotent: for a list of pos ints and list of pos ints","filters" : [["CategoryCollections(IsCyclotomic)"],["CategoryCollections(IsCyclotomic)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformationOp","type" : "GAP_Operation","filters" : [[[],["IsList"],["IsFunction"]],[[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]],[[],["IsList"]],[[],["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 5,"comment" : "TransformationOp: for an obj and domain","filters" : [[],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 2,"comment" : "TransformationOp: for an obj and list","filters" : [[],["IsList"]]}],"3args" : [{"rank" : 6,"comment" : "TransformationOp: for an obj, domain, and function","filters" : [[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]]},{"rank" : 3,"comment" : "TransformationOp: for object, list, function","filters" : [[],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformationOpNC","type" : "GAP_Operation","filters" : [[[],["IsList"],["IsFunction"]],[[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]],[[],["IsList"]],[[],["IsCollection","IsGeneralizedDomain"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 5,"comment" : "TransformationOpNC: for object and domain","filters" : [[],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 2,"comment" : "TransformationOpNC: for object and list","filters" : [[],["IsList"]]}],"3args" : [{"rank" : 6,"comment" : "TransformationOpNC: for object, domain, function","filters" : [[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]]},{"rank" : 3,"comment" : "TransformationOpNC: for object, list, function","filters" : [[],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "InverseOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComponentRepsOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ComponentRepsOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(ComponentRepsOfTransformation)"]]},{"rank" : 7,"comment" : "ComponentRepsOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComponentRepsOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComponentRepsOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComponentRepsOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComponentRepsOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrComponentsOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "NrComponentsOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(NrComponentsOfTransformation)"]]},{"rank" : 7,"comment" : "NrComponentsOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrComponentsOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrComponentsOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrComponentsOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrComponentsOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComponentsOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ComponentsOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(ComponentsOfTransformation)"]]},{"rank" : 7,"comment" : "ComponentsOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComponentsOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComponentsOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComponentsOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComponentsOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComponentTransformationInt","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "ComponentTransformationInt: for a transformation and positive integer","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CycleTransformationInt","type" : "GAP_Operation","filters" : [[["IsTransformation"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "CycleTransformationInt: for a transformation and positive integer","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CyclesOfTransformation","type" : "GAP_Operation","filters" : [[["IsTransformation"]],[["IsTransformation"],["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "CyclesOfTransformation: system getter","filters" : [["IsAttributeStoringRep","Tester(CyclesOfTransformation)"]]},{"rank" : 7,"comment" : "CyclesOfTransformation: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 9,"comment" : "CyclesOfTransformation: for a transformation and list","filters" : [["IsTransformation"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CyclesOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CyclesOfTransformation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CyclesOfTransformation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CyclesOfTransformation)","type" : "GAP_Operation","filters" : [[["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftOne","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "LeftOne: system getter","filters" : [["IsAttributeStoringRep","Tester(LeftOne)"]]},{"rank" : 7,"comment" : "LeftOne: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "LeftOne: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LeftOne)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LeftOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LeftOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LeftOne)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightOne","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "RightOne: system getter","filters" : [["IsAttributeStoringRep","Tester(RightOne)"]]},{"rank" : 7,"comment" : "RightOne: for a partial perm","filters" : [["IsPartialPerm"]]},{"rank" : 7,"comment" : "RightOne: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RightOne)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RightOne): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RightOne): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RightOne)","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OnKernelAntiAction","type" : "GAP_Operation","filters" : [[["IsList"],["IsTransformation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 11,"comment" : "OnKernelAntiAction: for a list and transformation","filters" : [["IsDenseList","IsHomogeneousList"],["IsTransformation"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DomainOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "DomainOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(DomainOfPartialPerm)"]]},{"rank" : 7,"comment" : "DomainOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DomainOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DomainOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DomainOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DomainOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImageListOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ImageListOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(ImageListOfPartialPerm)"]]},{"rank" : 7,"comment" : "ImageListOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImageListOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImageListOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImageListOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImageListOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImageSetOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ImageSetOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(ImageSetOfPartialPerm)"]]},{"rank" : 7,"comment" : "ImageSetOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImageSetOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImageSetOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImageSetOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImageSetOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndexPeriodOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IndexPeriodOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(IndexPeriodOfPartialPerm)"]]},{"rank" : 7,"comment" : "IndexPeriodOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IndexPeriodOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IndexPeriodOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IndexPeriodOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IndexPeriodOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComponentRepsOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ComponentRepsOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(ComponentRepsOfPartialPerm)"]]},{"rank" : 7,"comment" : "ComponentRepsOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComponentRepsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComponentRepsOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComponentRepsOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComponentRepsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrComponentsOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "NrComponentsOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(NrComponentsOfPartialPerm)"]]},{"rank" : 7,"comment" : "NrComponentsOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrComponentsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrComponentsOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrComponentsOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrComponentsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComponentsOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "ComponentsOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(ComponentsOfPartialPerm)"]]},{"rank" : 7,"comment" : "ComponentsOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComponentsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComponentsOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComponentsOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComponentsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FixedPointsOfPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "FixedPointsOfPartialPerm: system getter","filters" : [["IsAttributeStoringRep","Tester(FixedPointsOfPartialPerm)"]]},{"rank" : 23,"comment" : "FixedPointsOfPartialPerm: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "FixedPointsOfPartialPerm: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 7,"comment" : "FixedPointsOfPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FixedPointsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FixedPointsOfPartialPerm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FixedPointsOfPartialPerm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FixedPointsOfPartialPerm)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrFixedPoints","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]],[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "NrFixedPoints: system getter","filters" : [["IsAttributeStoringRep","Tester(NrFixedPoints)"]]},{"rank" : 23,"comment" : "NrFixedPoints: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "NrFixedPoints: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]},{"rank" : 7,"comment" : "NrFixedPoints: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrFixedPoints)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],[]],[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrFixedPoints): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrFixedPoints): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrFixedPoints)","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImagePartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "PreImagePartialPerm: for a partial perm and positive integer","filters" : [["IsPartialPerm"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComponentPartialPermInt","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "ComponentPartialPermInt: for a partial perm and positive integer","filters" : [["IsPartialPerm"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsPartialPerm","type" : "GAP_Operation","filters" : [[["IsAssociativeElement"],["IsList"]],[["IsAssociativeElement"]],[["IsAssociativeElement"],["IsInt","IsPosRat"]],[["IsAssociativeElement"],["IsZeroCyc"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 8,"comment" : "AsPartialPerm: for a perm","filters" : [["IsPerm"]]},{"rank" : 7,"comment" : "AsPartialPerm: for a transformation","filters" : [["IsTransformation"]]}],"2args" : [{"rank" : 29,"comment" : "AsPartialPerm: for a perm and zero","filters" : [["IsPerm"],["IsZeroCyc"]]},{"rank" : 27,"comment" : "AsPartialPerm: for a perm and pos int","filters" : [["IsPerm"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "AsPartialPerm: for a transformation and positive int","filters" : [["IsTransformation"],["IsInt","IsPosRat"]]},{"rank" : 10,"comment" : "AsPartialPerm: for a perm and a list","filters" : [["IsPerm"],["IsList"]]},{"rank" : 9,"comment" : "AsPartialPerm: for a transformation and list","filters" : [["IsTransformation"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],["IsList"]],[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "RestrictedPartialPerm: for a partial perm","filters" : [["IsPartialPerm"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermLeftQuoPartialPermNC","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 14,"comment" : "PermLeftQuoPartialPermNC: for a partial perm and partial perm","filters" : [["IsPartialPerm"],["IsPartialPerm"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermLeftQuoPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"],["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 14,"comment" : "PermLeftQuoPartialPerm: for a partial perm and partial perm","filters" : [["IsPartialPerm"],["IsPartialPerm"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TrimPartialPerm","type" : "GAP_Operation","filters" : [[["IsPartialPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "TrimPartialPerm: for a partial perm","filters" : [["IsPartialPerm"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PartialPermOp","type" : "GAP_Operation","filters" : [[[],["IsList"],["IsFunction"]],[[],["IsList"]],[[],["IsCollection","IsGeneralizedDomain"]],[[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 5,"comment" : "PartialPermOp: for an obj and domain","filters" : [[],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 2,"comment" : "PartialPermOp: for an obj and list","filters" : [[],["IsList"]]}],"3args" : [{"rank" : 6,"comment" : "PartialPermOp: for an obj, domain, and function","filters" : [[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]]},{"rank" : 3,"comment" : "PartialPermOp: for object, list, function","filters" : [[],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PartialPermOpNC","type" : "GAP_Operation","filters" : [[[],["IsList"],["IsFunction"]],[[],["IsList"]],[[],["IsCollection","IsGeneralizedDomain"]],[[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 5,"comment" : "PartialPermOpNC: for an obj and domain","filters" : [[],["IsCollection","IsGeneralizedDomain"]]},{"rank" : 2,"comment" : "PartialPermOpNC: for an obj and list","filters" : [[],["IsList"]]}],"3args" : [{"rank" : 6,"comment" : "PartialPermOpNC: for an obj, domain, and function","filters" : [[],["IsCollection","IsGeneralizedDomain"],["IsFunction"]]},{"rank" : 3,"comment" : "PartialPermOpNC: for object, list, function","filters" : [[],["IsList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOfPartialPermCollection","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "DegreeOfPartialPermCollection: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOfPartialPermCollection)"]]},{"rank" : 24,"comment" : "DegreeOfPartialPermCollection: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "DegreeOfPartialPermCollection: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOfPartialPermCollection): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOfPartialPermCollection): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CodegreeOfPartialPermCollection","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "CodegreeOfPartialPermCollection: system getter","filters" : [["IsAttributeStoringRep","Tester(CodegreeOfPartialPermCollection)"]]},{"rank" : 24,"comment" : "CodegreeOfPartialPermCollection: for a partial perm semigroup with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "CodegreeOfPartialPermCollection: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CodegreeOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CodegreeOfPartialPermCollection): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CodegreeOfPartialPermCollection): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CodegreeOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankOfPartialPermCollection","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "RankOfPartialPermCollection: system getter","filters" : [["IsAttributeStoringRep","Tester(RankOfPartialPermCollection)"]]},{"rank" : 24,"comment" : "RankOfPartialPermCollection: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "RankOfPartialPermCollection: for a partial perm collection","filters" : [["CategoryCollections(IsPartialPerm)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RankOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RankOfPartialPermCollection): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RankOfPartialPermCollection): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RankOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DomainOfPartialPermCollection","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "DomainOfPartialPermCollection: system getter","filters" : [["IsAttributeStoringRep","Tester(DomainOfPartialPermCollection)"]]},{"rank" : 23,"comment" : "DomainOfPartialPermCollection: for a partal perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "DomainOfPartialPermCollection: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DomainOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DomainOfPartialPermCollection): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DomainOfPartialPermCollection): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DomainOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImageOfPartialPermCollection","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "ImageOfPartialPermCollection: system getter","filters" : [["IsAttributeStoringRep","Tester(ImageOfPartialPermCollection)"]]},{"rank" : 23,"comment" : "ImageOfPartialPermCollection: for a partal perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "ImageOfPartialPermCollection: for a partial perm coll","filters" : [["CategoryCollections(IsPartialPerm)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImageOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImageOfPartialPermCollection): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImageOfPartialPermCollection): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImageOfPartialPermCollection)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformationRepresentation","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "TransformationRepresentation: system getter","filters" : [["IsAttributeStoringRep","Tester(TransformationRepresentation)"]]},{"rank" : 16,"comment" : "TransformationRepresentation: for an endo general mapping","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsTransformationRepOfEndo"]]},{"rank" : 13,"comment" : "TransformationRepresentation: for an endo general mapping","filters" : [["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]},{"rank" : 0,"comment" : "TransformationRepresentation: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransformationRepresentation)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransformationRepresentation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransformationRepresentation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransformationRepresentation)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FpSemigroupOfElementOfFpSemigroup","type" : "GAP_Operation","filters" : [[["IsElementOfFpSemigroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "FpSemigroupOfElementOfFpSemigroup: for an element of an fp semigroup","filters" : [["IsElementOfFpSemigroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementOfFpSemigroup","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpSemigroup)"],["IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 7,"comment" : "ElementOfFpSemigroup: for a family of f.p. semigroup elements, and an assoc. word","filters" : [["CategoryFamily(IsElementOfFpSemigroup)"],["IsAssociativeElement","IsWord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGeneratorsOfFpSemigroup","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "FreeGeneratorsOfFpSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGeneratorsOfFpSemigroup)"]]},{"rank" : 19,"comment" : "FreeGeneratorsOfFpSemigroup: for a finitely presented semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]},{"rank" : -5,"comment" : "FreeGeneratorsOfFpSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsElementOfFpSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGeneratorsOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGeneratorsOfFpSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGeneratorsOfFpSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGeneratorsOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeSemigroupOfFpSemigroup","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "FreeSemigroupOfFpSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeSemigroupOfFpSemigroup)"]]},{"rank" : 19,"comment" : "FreeSemigroupOfFpSemigroup: for a finitely presented semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]},{"rank" : -5,"comment" : "FreeSemigroupOfFpSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsElementOfFpSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeSemigroupOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeSemigroupOfFpSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeSemigroupOfFpSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeSemigroupOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelationsOfFpSemigroup","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "RelationsOfFpSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RelationsOfFpSemigroup)"]]},{"rank" : 20,"comment" : "RelationsOfFpSemigroup: method for a free semigroup","filters" : [["IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 19,"comment" : "RelationsOfFpSemigroup: for finitely presented semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]},{"rank" : -5,"comment" : "RelationsOfFpSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsElementOfFpSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelationsOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RelationsOfFpSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelationsOfFpSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelationsOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismFpSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismFpSemigroup)"]]},{"rank" : 36,"comment" : "IsomorphismFpSemigroup: for fp groups","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 24,"comment" : "IsomorphismFpSemigroup: for an fp monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]},{"rank" : 0,"comment" : "IsomorphismFpSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismFpSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismFpSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FpGrpMonSmgOfFpGrpMonSmgElement","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "FpGrpMonSmgOfFpGrpMonSmgElement: for an element of an fp group","filters" : [["IsElementOfFpGroup"]]},{"rank" : 6,"comment" : "FpGrpMonSmgOfFpGrpMonSmgElement: for an element of an fp monoid","filters" : [["IsElementOfFpMonoid"]]},{"rank" : 5,"comment" : "FpGrpMonSmgOfFpGrpMonSmgElement: for an element of an fp semigroup","filters" : [["IsElementOfFpSemigroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ElementOfFpMonoid","type" : "GAP_Operation","filters" : [[["CategoryFamily(IsElementOfFpMonoid)"],["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "ElementOfFpMonoid: for a family of f.p. monoid elements, and an assoc. word","filters" : [["CategoryFamily(IsElementOfFpMonoid)"],["IsMultiplicativeElementWithOne","IsAssociativeElement","IsWord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FpMonoidOfElementOfFpMonoid","type" : "GAP_Operation","filters" : [[["IsElementOfFpMonoid"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "FpMonoidOfElementOfFpMonoid: for an fp monoid element","filters" : [["IsElementOfFpMonoid"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGeneratorsOfFpMonoid","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "FreeGeneratorsOfFpMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGeneratorsOfFpMonoid)"]]},{"rank" : 24,"comment" : "FreeGeneratorsOfFpMonoid: for a finitely presented monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]},{"rank" : -4,"comment" : "FreeGeneratorsOfFpMonoid: default method requiring categories and checking properties","filters" : [["IsMagmaWithOne","CategoryCollections(IsElementOfFpMonoid)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGeneratorsOfFpMonoid)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGeneratorsOfFpMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGeneratorsOfFpMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGeneratorsOfFpMonoid)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeMonoidOfFpMonoid","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "FreeMonoidOfFpMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeMonoidOfFpMonoid)"]]},{"rank" : 24,"comment" : "FreeMonoidOfFpMonoid: for a finitely presented monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]},{"rank" : -4,"comment" : "FreeMonoidOfFpMonoid: default method requiring categories and checking properties","filters" : [["IsMagmaWithOne","CategoryCollections(IsElementOfFpMonoid)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeMonoidOfFpMonoid)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeMonoidOfFpMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeMonoidOfFpMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeMonoidOfFpMonoid)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelationsOfFpMonoid","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20026,"comment" : "RelationsOfFpMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(RelationsOfFpMonoid)"]]},{"rank" : 26,"comment" : "RelationsOfFpMonoid: method for a free monoid","filters" : [["IsFreeMonoid","Tester(IsFreeMonoid)"]]},{"rank" : 24,"comment" : "RelationsOfFpMonoid: for finitely presented monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]},{"rank" : -4,"comment" : "RelationsOfFpMonoid: default method requiring categories and checking properties","filters" : [["IsMagmaWithOne","CategoryCollections(IsElementOfFpMonoid)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelationsOfFpMonoid)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RelationsOfFpMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelationsOfFpMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelationsOfFpMonoid)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismFpMonoid","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "IsomorphismFpMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismFpMonoid)"]]},{"rank" : 36,"comment" : "IsomorphismFpMonoid: for an fp group","filters" : [["IsGroupOfFamily","IsSubgroupFpGroup"]]},{"rank" : 0,"comment" : "IsomorphismFpMonoid: default method requiring categories and checking properties","filters" : [["IsMagmaWithOne"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismFpMonoid)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismFpMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismFpMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismFpMonoid)","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedConfluentRewritingSystem","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "ReducedConfluentRewritingSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(ReducedConfluentRewritingSystem)"]]},{"rank" : 24,"comment" : "ReducedConfluentRewritingSystem: for an fp monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]},{"rank" : 19,"comment" : "ReducedConfluentRewritingSystem: for an fp semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]},{"rank" : 0,"comment" : "ReducedConfluentRewritingSystem: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [{"rank" : 25,"comment" : "ReducedConfluentRewritingSystem: for an fp monoid and an ordering on the underlying free monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],["IsOrdering"]]},{"rank" : 20,"comment" : "ReducedConfluentRewritingSystem: for an fp semigroup and an order on the underlying free semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],["IsFunction"]]},{"rank" : 20,"comment" : "ReducedConfluentRewritingSystem: for an fp semigroup and an ordering on the underlying free semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],["IsOrdering"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ReducedConfluentRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ReducedConfluentRewritingSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ReducedConfluentRewritingSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ReducedConfluentRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeMonoidOfRewritingSystem","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FreeMonoidOfRewritingSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeMonoidOfRewritingSystem)"]]},{"rank" : 4,"comment" : "FreeMonoidOfRewritingSystem: for a monoid rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeMonoidOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeMonoidOfRewritingSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeMonoidOfRewritingSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeMonoidOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FamilyForRewritingSystem","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FamilyForRewritingSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(FamilyForRewritingSystem)"]]},{"rank" : 5,"comment" : "FamilyForRewritingSystem: for a Knuth Bendix rewriting system","filters" : [["IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FamilyForRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FamilyForRewritingSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FamilyForRewritingSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FamilyForRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeSemigroupOfRewritingSystem","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FreeSemigroupOfRewritingSystem: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeSemigroupOfRewritingSystem)"]]},{"rank" : 4,"comment" : "FreeSemigroupOfRewritingSystem: for a semigroup rewriting system","filters" : [["IsRewritingSystem","IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeSemigroupOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeSemigroupOfRewritingSystem): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeSemigroupOfRewritingSystem): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeSemigroupOfRewritingSystem)","type" : "GAP_Operation","filters" : [[["IsRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KnuthBendixRewritingSystem","type" : "GAP_Operation","filters" : [[["IsFamily"],["IsOrdering"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 24,"comment" : "KnuthBendixRewritingSystem: for an fp monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"]]},{"rank" : 19,"comment" : "KnuthBendixRewritingSystem: for an fp semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]}],"2args" : [{"rank" : 25,"comment" : "KnuthBendixRewritingSystem: for an fp monoid and a function","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],["IsFunction"]]},{"rank" : 25,"comment" : "KnuthBendixRewritingSystem: for an fp monoid and an order on the family of words of the underlying free monoid","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpMonoid)"],["IsOrdering"]]},{"rank" : 20,"comment" : "KnuthBendixRewritingSystem: for an fp semigroup and a function","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],["IsFunction"]]},{"rank" : 20,"comment" : "KnuthBendixRewritingSystem: for an fp semigroup and an order on the family of words of the underlying free semigroup","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],["IsOrdering"]]},{"rank" : 3,"comment" : "KnuthBendixRewritingSystem: for a family of words of an fp monoid and on ordering on that family","filters" : [["CategoryFamily(IsElementOfFpMonoid)"],["IsOrdering"]]},{"rank" : 3,"comment" : "KnuthBendixRewritingSystem: for a family of words of an fp semigroup and on ordering on that family","filters" : [["CategoryFamily(IsElementOfFpSemigroup)"],["IsOrdering"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TzRules","type" : "GAP_Operation","filters" : [[["IsKnuthBendixRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20006,"comment" : "TzRules: system getter","filters" : [["IsAttributeStoringRep","Tester(TzRules)"]]},{"rank" : 5,"comment" : "TzRules: for a Knuth Bendix rewriting system","filters" : [["IsKnuthBendixRewritingSystem","IsKnuthBendixRewritingSystemRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TzRules)","type" : "GAP_Operation","filters" : [[["IsKnuthBendixRewritingSystem"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TzRules): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TzRules): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TzRules)","type" : "GAP_Operation","filters" : [[["IsKnuthBendixRewritingSystem"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CosetTableOfFpSemigroup","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "CosetTableOfFpSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(CosetTableOfFpSemigroup)"]]},{"rank" : 22,"comment" : "CosetTableOfFpSemigroup: for a right congruence on an fp semigroup","filters" : [["IsRightMagmaCongruence"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CosetTableOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CosetTableOfFpSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CosetTableOfFpSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CosetTableOfFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsRightMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdjoinedIdentityFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AdjoinedIdentityFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(AdjoinedIdentityFamily)"]]},{"rank" : 1,"comment" : "AdjoinedIdentityFamily","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdjoinedIdentityFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdjoinedIdentityFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdjoinedIdentityFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdjoinedIdentityFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingSemigroupFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "UnderlyingSemigroupFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingSemigroupFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingSemigroupFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingSemigroupFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingSemigroupFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingSemigroupFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AdjoinedIdentityDefaultType","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AdjoinedIdentityDefaultType: system getter","filters" : [["IsAttributeStoringRep","Tester(AdjoinedIdentityDefaultType)"]]},{"rank" : 1,"comment" : "AdjoinedIdentityDefaultType","filters" : [["IsFamily"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AdjoinedIdentityDefaultType)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AdjoinedIdentityDefaultType): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AdjoinedIdentityDefaultType): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AdjoinedIdentityDefaultType)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MonoidByAdjoiningIdentity","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "MonoidByAdjoiningIdentity: system getter","filters" : [["IsAttributeStoringRep","Tester(MonoidByAdjoiningIdentity)"]]},{"rank" : 17,"comment" : "MonoidByAdjoiningIdentity","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "MonoidByAdjoiningIdentity","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 14,"comment" : "MonoidByAdjoiningIdentity","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "MonoidByAdjoiningIdentity: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MonoidByAdjoiningIdentity)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MonoidByAdjoiningIdentity): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MonoidByAdjoiningIdentity): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MonoidByAdjoiningIdentity)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingSemigroupOfMonoidByAdjoiningIdentity","type" : "GAP_Operation","filters" : [[["IsMonoidByAdjoiningIdentity"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20021,"comment" : "UnderlyingSemigroupOfMonoidByAdjoiningIdentity: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)","type" : "GAP_Operation","filters" : [[["IsMonoidByAdjoiningIdentity"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingSemigroupOfMonoidByAdjoiningIdentity): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingSemigroupOfMonoidByAdjoiningIdentity): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)","type" : "GAP_Operation","filters" : [[["IsMonoidByAdjoiningIdentity"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MonoidByAdjoiningIdentityElt","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement","IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "MonoidByAdjoiningIdentityElt: system getter","filters" : [["IsAttributeStoringRep","Tester(MonoidByAdjoiningIdentityElt)"]]},{"rank" : 4,"comment" : "MonoidByAdjoiningIdentityElt","filters" : [["IsMultiplicativeElement","IsAssociativeElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MonoidByAdjoiningIdentityElt)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement","IsAssociativeElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MonoidByAdjoiningIdentityElt): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MonoidByAdjoiningIdentityElt): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MonoidByAdjoiningIdentityElt)","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement","IsAssociativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt","type" : "GAP_Operation","filters" : [[["IsMonoidByAdjoiningIdentityElt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)"]]},{"rank" : 6,"comment" : "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt","filters" : [["IsMonoidByAdjoiningIdentityElt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)","type" : "GAP_Operation","filters" : [[["IsMonoidByAdjoiningIdentityElt"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)","type" : "GAP_Operation","filters" : [[["IsMonoidByAdjoiningIdentityElt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFiniteSemigroupGreensRelation","type" : "GAP_Operation","filters" : [[["IsGreensRelation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IsFiniteSemigroupGreensRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFiniteSemigroupGreensRelation)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFiniteSemigroupGreensRelation)","type" : "GAP_Operation","filters" : [[["IsGreensRelation"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFiniteSemigroupGreensRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFiniteSemigroupGreensRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFiniteSemigroupGreensRelation)","type" : "GAP_Operation","filters" : [[["IsGreensRelation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensRRelation","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensRRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensRRelation)"]]},{"rank" : 20,"comment" : "GreensRRelation: for free semigroups","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 13,"comment" : "GreensRRelation: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GreensRRelation: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensRRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensRRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensRRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensRRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensLRelation","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensLRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensLRelation)"]]},{"rank" : 20,"comment" : "GreensLRelation: for free semigroups","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 13,"comment" : "GreensLRelation: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GreensLRelation: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensLRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensLRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensLRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensLRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensJRelation","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensJRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensJRelation)"]]},{"rank" : 20,"comment" : "GreensJRelation: for free semigroups","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 13,"comment" : "GreensJRelation: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GreensJRelation: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensJRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensJRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensJRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensJRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensDRelation","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensDRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensDRelation)"]]},{"rank" : 20,"comment" : "GreensDRelation: for free semigroups","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 13,"comment" : "GreensDRelation: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GreensDRelation: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensDRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensDRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensDRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensDRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensHRelation","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensHRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensHRelation)"]]},{"rank" : 20,"comment" : "GreensHRelation: for free semigroups","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","IsFreeSemigroup","Tester(IsFreeSemigroup)"]]},{"rank" : 13,"comment" : "GreensHRelation: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GreensHRelation: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensHRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensHRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensHRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensHRelation)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensRClassOfElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "GreensRClassOfElement: for a semigroup and object","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensLClassOfElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "GreensLClassOfElement: for a semigroup and object","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensDClassOfElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "GreensDClassOfElement: for a semigroup and object","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensJClassOfElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "GreensJClassOfElement: for a semigroup and object","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensHClassOfElement","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "GreensHClassOfElement: for a semigroup and object","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FroidurePinSimpleAlg","type" : "GAP_Operation","filters" : [[["IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "FroidurePinSimpleAlg: for a finite monoid","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FroidurePinExtendedAlg","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 13,"comment" : "FroidurePinExtendedAlg: for a finite semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AssociatedConcreteSemigroup","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "AssociatedConcreteSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AssociatedConcreteSemigroup)"]]},{"rank" : -5,"comment" : "AssociatedConcreteSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsElementOfFpSemigroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AssociatedConcreteSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AssociatedConcreteSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AssociatedConcreteSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AssociatedConcreteSemigroup)","type" : "GAP_Operation","filters" : [[["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AssociatedFpSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AssociatedFpSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AssociatedFpSemigroup)"]]},{"rank" : 0,"comment" : "AssociatedFpSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AssociatedFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AssociatedFpSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AssociatedFpSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AssociatedFpSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensRClasses","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]],[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensRClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensRClasses)"]]},{"rank" : 13,"comment" : "GreensRClasses: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 8,"comment" : "GreensRClasses: for a Green's D-class","filters" : [["IsGreensDClass"]]},{"rank" : 0,"comment" : "GreensRClasses: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensRClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]],[["IsGreensDClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensRClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensRClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensRClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensLClasses","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]],[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensLClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensLClasses)"]]},{"rank" : 13,"comment" : "GreensLClasses: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 8,"comment" : "GreensLClasses: for a Green's D-class","filters" : [["IsGreensDClass"]]},{"rank" : 0,"comment" : "GreensLClasses: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensLClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]],[["IsGreensDClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensLClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensLClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensLClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensJClasses","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensJClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensJClasses)"]]},{"rank" : 15,"comment" : "GreensJClasses: for a semigroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GreensJClasses: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensJClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensJClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensJClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensJClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensDClasses","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensDClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensDClasses)"]]},{"rank" : 13,"comment" : "GreensDClasses: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "GreensDClasses: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensDClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensDClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensDClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensDClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GreensHClasses","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]],[["IsGreensClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GreensHClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(GreensHClasses)"]]},{"rank" : 13,"comment" : "GreensHClasses: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 8,"comment" : "GreensHClasses: for a Green's Class","filters" : [["IsGreensLClass"]]},{"rank" : 8,"comment" : "GreensHClasses: for a Green's Class","filters" : [["IsGreensRClass"]]},{"rank" : 8,"comment" : "GreensHClasses: for a Green's Class","filters" : [["IsGreensDClass"]]},{"rank" : 0,"comment" : "GreensHClasses: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GreensHClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]],[["IsGreensClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GreensHClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GreensHClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GreensHClasses)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGreensLessThanOrEqual","type" : "GAP_Operation","filters" : [[["IsGreensClass"],["IsGreensClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 14,"comment" : "IsGreensLessThanOrEqual: for two Green's classes","filters" : [["IsGreensClass"],["IsGreensClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RClassOfHClass","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "RClassOfHClass: system getter","filters" : [["IsAttributeStoringRep","Tester(RClassOfHClass)"]]},{"rank" : 8,"comment" : "RClassOfHClass: for a Green's H-class","filters" : [["IsGreensHClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RClassOfHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RClassOfHClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RClassOfHClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RClassOfHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LClassOfHClass","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "LClassOfHClass: system getter","filters" : [["IsAttributeStoringRep","Tester(LClassOfHClass)"]]},{"rank" : 8,"comment" : "LClassOfHClass: for a Green's H-class","filters" : [["IsGreensHClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LClassOfHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LClassOfHClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LClassOfHClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LClassOfHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DClassOfHClass","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "DClassOfHClass: system getter","filters" : [["IsAttributeStoringRep","Tester(DClassOfHClass)"]]},{"rank" : 8,"comment" : "DClassOfHClass: for a Green's H-class","filters" : [["IsGreensHClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DClassOfHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DClassOfHClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DClassOfHClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DClassOfHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DClassOfLClass","type" : "GAP_Operation","filters" : [[["IsGreensLClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "DClassOfLClass: system getter","filters" : [["IsAttributeStoringRep","Tester(DClassOfLClass)"]]},{"rank" : 8,"comment" : "DClassOfLClass: for a Green's L-class","filters" : [["IsGreensLClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DClassOfLClass)","type" : "GAP_Operation","filters" : [[["IsGreensLClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DClassOfLClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DClassOfLClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DClassOfLClass)","type" : "GAP_Operation","filters" : [[["IsGreensLClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DClassOfRClass","type" : "GAP_Operation","filters" : [[["IsGreensRClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "DClassOfRClass: system getter","filters" : [["IsAttributeStoringRep","Tester(DClassOfRClass)"]]},{"rank" : 8,"comment" : "DClassOfRClass: for a Green's R-class","filters" : [["IsGreensRClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DClassOfRClass)","type" : "GAP_Operation","filters" : [[["IsGreensRClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DClassOfRClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DClassOfRClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DClassOfRClass)","type" : "GAP_Operation","filters" : [[["IsGreensRClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupHClassOfGreensDClass","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "GroupHClassOfGreensDClass: system getter","filters" : [["IsAttributeStoringRep","Tester(GroupHClassOfGreensDClass)"]]},{"rank" : 8,"comment" : "GroupHClassOfGreensDClass: for a Green's H-class","filters" : [["IsGreensDClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GroupHClassOfGreensDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GroupHClassOfGreensDClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GroupHClassOfGreensDClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GroupHClassOfGreensDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRegularDClass","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "IsRegularDClass: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRegularDClass)"]]},{"rank" : 8,"comment" : "IsRegularDClass: for a Green's D class","filters" : [["IsGreensDClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRegularDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRegularDClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRegularDClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRegularDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupHClass","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "IsGroupHClass: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupHClass)"]]},{"rank" : 8,"comment" : "IsGroupHClass: for Green's H-class","filters" : [["IsGreensHClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupHClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupHClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupHClass)","type" : "GAP_Operation","filters" : [[["IsGreensHClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EggBoxOfDClass","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "EggBoxOfDClass: system getter","filters" : [["IsAttributeStoringRep","Tester(EggBoxOfDClass)"]]},{"rank" : 8,"comment" : "EggBoxOfDClass: for a Green's D class","filters" : [["IsGreensDClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EggBoxOfDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EggBoxOfDClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EggBoxOfDClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EggBoxOfDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InternalRepGreensRelation","type" : "GAP_Operation","filters" : [[["IsGreensRelation"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "InternalRepGreensRelation: system getter","filters" : [["IsAttributeStoringRep","Tester(InternalRepGreensRelation)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InternalRepGreensRelation)","type" : "GAP_Operation","filters" : [[["IsGreensRelation"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InternalRepGreensRelation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InternalRepGreensRelation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InternalRepGreensRelation)","type" : "GAP_Operation","filters" : [[["IsGreensRelation"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CanonicalGreensClass","type" : "GAP_Operation","filters" : [[["IsGreensClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "CanonicalGreensClass: system getter","filters" : [["IsAttributeStoringRep","Tester(CanonicalGreensClass)"]]},{"rank" : 7,"comment" : "CanonicalGreensClass: for a Green's class","filters" : [["IsGreensClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CanonicalGreensClass)","type" : "GAP_Operation","filters" : [[["IsGreensClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CanonicalGreensClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CanonicalGreensClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CanonicalGreensClass)","type" : "GAP_Operation","filters" : [[["IsGreensClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DisplayEggBoxesOfSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "DisplayEggBoxesOfSemigroup: for finite semigroups","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemigroupHomomorphismByImagesNC","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 28,"comment" : "SemigroupHomomorphismByImagesNC: for a semigroup, semigroup, list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFpSemigpReducedElt","type" : "GAP_Operation","filters" : [[["IsElementOfFpSemigroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20008,"comment" : "IsFpSemigpReducedElt: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFpSemigpReducedElt)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFpSemigpReducedElt)","type" : "GAP_Operation","filters" : [[["IsElementOfFpSemigroup"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFpSemigpReducedElt): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFpSemigpReducedElt): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFpSemigpReducedElt)","type" : "GAP_Operation","filters" : [[["IsElementOfFpSemigroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFpMonoidReducedElt","type" : "GAP_Operation","filters" : [[["IsElementOfFpMonoid"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "IsFpMonoidReducedElt: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFpMonoidReducedElt)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFpMonoidReducedElt)","type" : "GAP_Operation","filters" : [[["IsElementOfFpMonoid"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFpMonoidReducedElt): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFpMonoidReducedElt): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFpMonoidReducedElt)","type" : "GAP_Operation","filters" : [[["IsElementOfFpMonoid"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFullTransformationSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsFullTransformationSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFullTransformationSemigroup)"]]},{"rank" : 21,"comment" : "IsFullTransformationSemigroup: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "IsFullTransformationSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsFullTransformationSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFullTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFullTransformationSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFullTransformationSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFullTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOfTransformationSemigroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "DegreeOfTransformationSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOfTransformationSemigroup)"]]},{"rank" : 47,"comment" : "DegreeOfTransformationSemigroup: for a transformation group with generators","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "DegreeOfTransformationSemigroup: for a transformation semigroup with generators","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -5,"comment" : "DegreeOfTransformationSemigroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsTransformation)","IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOfTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOfTransformationSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOfTransformationSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOfTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismTransformationSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismTransformationSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismTransformationSemigroup)"]]},{"rank" : 59,"comment" : "IsomorphismTransformationSemigroup: for a perm group with generators","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 21,"comment" : "IsomorphismTransformationSemigroup: for partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 21,"comment" : "IsomorphismTransformationSemigroup: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "IsomorphismTransformationSemigroup: for a semigroup of general mappings","filters" : [["CategoryCollections(IsGeneralMapping)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 19,"comment" : "IsomorphismTransformationSemigroup: <fp-semigroup>","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"]]},{"rank" : 15,"comment" : "IsomorphismTransformationSemigroup: for a semigroup with multiplicative neutral element and generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)"]]},{"rank" : 14,"comment" : "IsomorphismTransformationSemigroup: for a semigroup with multiplicative neutral element","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)"]]},{"rank" : 14,"comment" : "IsomorphismTransformationSemigroup: for a semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 13,"comment" : "IsomorphismTransformationSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismTransformationSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismTransformationSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismTransformationSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismTransformationMonoid","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismTransformationMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismTransformationMonoid)"]]},{"rank" : 59,"comment" : "IsomorphismTransformationMonoid: for a perm group with generators","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 21,"comment" : "IsomorphismTransformationMonoid: for partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 15,"comment" : "IsomorphismTransformationMonoid: for a semigroup with multiplicative neutral element and generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)"]]},{"rank" : 0,"comment" : "IsomorphismTransformationMonoid: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismTransformationMonoid)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismTransformationMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismTransformationMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismTransformationMonoid)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HomomorphismTransformationSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsRightMagmaCongruence"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 41,"comment" : "HomomorphismTransformationSemigroup: for an f.p. semigroup, and a right congruence","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsElementOfFpSemigroup)"],["IsRightMagmaCongruence"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AntiIsomorphismTransformationSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "AntiIsomorphismTransformationSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AntiIsomorphismTransformationSemigroup)"]]},{"rank" : 14,"comment" : "AntiIsomorphismTransformationSemigroup: for a semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "AntiIsomorphismTransformationSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AntiIsomorphismTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AntiIsomorphismTransformationSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AntiIsomorphismTransformationSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AntiIsomorphismTransformationSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RowOfReesMatrixSemigroupElement","type" : "GAP_Operation","filters" : [[["IsReesMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "RowOfReesMatrixSemigroupElement: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RowOfReesZeroMatrixSemigroupElement","type" : "GAP_Operation","filters" : [[["IsReesZeroMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "RowOfReesZeroMatrixSemigroupElement: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ColumnOfReesMatrixSemigroupElement","type" : "GAP_Operation","filters" : [[["IsReesMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "ColumnOfReesMatrixSemigroupElement: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ColumnOfReesZeroMatrixSemigroupElement","type" : "GAP_Operation","filters" : [[["IsReesZeroMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "ColumnOfReesZeroMatrixSemigroupElement: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingElementOfReesMatrixSemigroupElement","type" : "GAP_Operation","filters" : [[["IsReesMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "UnderlyingElementOfReesMatrixSemigroupElement: for a Rees matrix semigroup element","filters" : [["IsReesMatrixSemigroupElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingElementOfReesZeroMatrixSemigroupElement","type" : "GAP_Operation","filters" : [[["IsReesZeroMatrixSemigroupElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "UnderlyingElementOfReesZeroMatrixSemigroupElement: for a Rees 0-matrix semigroup element","filters" : [["IsReesZeroMatrixSemigroupElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsReesMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsReesMatrixSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsReesMatrixSemigroup)"]]},{"rank" : 18,"comment" : "IsReesMatrixSemigroup: for a Rees matrix subsemigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 13,"comment" : "IsReesMatrixSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsReesMatrixSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsReesMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsReesMatrixSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsReesMatrixSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsReesMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsReesZeroMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsReesZeroMatrixSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsReesZeroMatrixSemigroup)"]]},{"rank" : 18,"comment" : "IsReesZeroMatrixSemigroup: for a Rees 0-matrix subsemigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 13,"comment" : "IsReesZeroMatrixSemigroup: for a semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsReesZeroMatrixSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsReesZeroMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsReesZeroMatrixSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsReesZeroMatrixSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsReesZeroMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReesMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsRectangularTable","Tester(IsRectangularTable)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "ReesMatrixSemigroup: for a semigroup and a rectangular table","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsRectangularTable","Tester(IsRectangularTable)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReesZeroMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 16,"comment" : "ReesZeroMatrixSemigroup: for a semigroup and a dense list","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfReesMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 34,"comment" : "GeneratorsOfReesMatrixSemigroup: for a Rees matrix subsemigroup, rows, semigroup, columns","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "ReesMatrixSubsemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 34,"comment" : "ReesMatrixSubsemigroup: for a Rees matrix semigroup, rows, semigroup, columns","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "GeneratorsOfReesZeroMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 34,"comment" : "GeneratorsOfReesZeroMatrixSemigroup: for a Rees 0-matrix semigroup, rows, semigroup, columns","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "ReesZeroMatrixSubsemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 34,"comment" : "ReesZeroMatrixSubsemigroup: for a Rees 0-matrix semigroup, rows, semigroup, columns","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],["IsList"],["IsMagma","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "Setter(Matrix)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],[]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Matrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Matrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Matrix)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Rows","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "Rows: system getter","filters" : [["IsAttributeStoringRep","Tester(Rows)"]]},{"rank" : 18,"comment" : "Rows: for a Rees 0-matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 18,"comment" : "Rows: for a Rees matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : -5,"comment" : "Rows: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsReesMatrixSemigroupElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Rows)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],[]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Rows): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Rows): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Rows)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Columns","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "Columns: system getter","filters" : [["IsAttributeStoringRep","Tester(Columns)"]]},{"rank" : 18,"comment" : "Columns: for a Rees 0-matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 18,"comment" : "Columns: for a Rees matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : -5,"comment" : "Columns: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsReesMatrixSemigroupElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Columns)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],[]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Columns): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Columns): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Columns)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "UnderlyingSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingSemigroup)"]]},{"rank" : 18,"comment" : "UnderlyingSemigroup: for a Rees 0-matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 18,"comment" : "UnderlyingSemigroup: for a Rees matrix semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : -5,"comment" : "UnderlyingSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsReesMatrixSemigroupElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],[]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AssociatedReesMatrixSemigroupOfDClass","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20011,"comment" : "AssociatedReesMatrixSemigroupOfDClass: system getter","filters" : [["IsAttributeStoringRep","Tester(AssociatedReesMatrixSemigroupOfDClass)"]]},{"rank" : 8,"comment" : "AssociatedReesMatrixSemigroupOfDClass: for a Green's D-class of a semigroup","filters" : [["IsGreensDClass"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AssociatedReesMatrixSemigroupOfDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AssociatedReesMatrixSemigroupOfDClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AssociatedReesMatrixSemigroupOfDClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AssociatedReesMatrixSemigroupOfDClass)","type" : "GAP_Operation","filters" : [[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismReesMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]],[["IsGreensDClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismReesMatrixSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismReesMatrixSemigroup)"]]},{"rank" : 17,"comment" : "IsomorphismReesMatrixSemigroup: for a Rees matrix subsemigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : 13,"comment" : "IsomorphismReesMatrixSemigroup: for a finite simple","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 8,"comment" : "IsomorphismReesMatrixSemigroup: for a D-class","filters" : [["IsGreensDClass"]]},{"rank" : 0,"comment" : "IsomorphismReesMatrixSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismReesMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]],[["IsGreensDClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismReesMatrixSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismReesMatrixSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismReesMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismReesZeroMatrixSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismReesZeroMatrixSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismReesZeroMatrixSemigroup)"]]},{"rank" : 17,"comment" : "IsomorphismReesZeroMatrixSemigroup: for a Rees 0-matrix subsemigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 13,"comment" : "IsomorphismReesZeroMatrixSemigroup: for a finite 0-simple","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismReesZeroMatrixSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismReesZeroMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismReesZeroMatrixSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismReesZeroMatrixSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismReesZeroMatrixSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReesMatrixSemigroupOfFamily","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "ReesMatrixSemigroupOfFamily: system getter","filters" : [["IsAttributeStoringRep","Tester(ReesMatrixSemigroupOfFamily)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ReesMatrixSemigroupOfFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ReesMatrixSemigroupOfFamily): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ReesMatrixSemigroupOfFamily): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ReesMatrixSemigroupOfFamily)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TypeReesMatrixSemigroupElements","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "TypeReesMatrixSemigroupElements: system getter","filters" : [["IsAttributeStoringRep","Tester(TypeReesMatrixSemigroupElements)"]]},{"rank" : 17,"comment" : "TypeReesMatrixSemigroupElements: for a subsemigroup of Rees 0-matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]]},{"rank" : 17,"comment" : "TypeReesMatrixSemigroupElements: for a subsemigroup of Rees matrix semigroup","filters" : [["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]},{"rank" : -5,"comment" : "TypeReesMatrixSemigroupElements: default method requiring categories and checking properties","filters" : [["IsMagma","CategoryCollections(IsReesMatrixSemigroupElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TypeReesMatrixSemigroupElements)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"],[]],[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TypeReesMatrixSemigroupElements): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TypeReesMatrixSemigroupElements): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TypeReesMatrixSemigroupElements)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsReesMatrixSemigroupElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuotientSemigroupPreimage","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "QuotientSemigroupPreimage: system getter","filters" : [["IsAttributeStoringRep","Tester(QuotientSemigroupPreimage)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(QuotientSemigroupPreimage)","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(QuotientSemigroupPreimage): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(QuotientSemigroupPreimage): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(QuotientSemigroupPreimage)","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuotientSemigroupCongruence","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "QuotientSemigroupCongruence: system getter","filters" : [["IsAttributeStoringRep","Tester(QuotientSemigroupCongruence)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(QuotientSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(QuotientSemigroupCongruence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(QuotientSemigroupCongruence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(QuotientSemigroupCongruence)","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "QuotientSemigroupHomomorphism","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20017,"comment" : "QuotientSemigroupHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(QuotientSemigroupHomomorphism)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(QuotientSemigroupHomomorphism)","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(QuotientSemigroupHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(QuotientSemigroupHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(QuotientSemigroupHomomorphism)","type" : "GAP_Operation","filters" : [[["IsQuotientSemigroup"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOfPartialPermSemigroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "DegreeOfPartialPermSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOfPartialPermSemigroup)"]]},{"rank" : 24,"comment" : "DegreeOfPartialPermSemigroup: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -5,"comment" : "DegreeOfPartialPermSemigroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOfPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOfPartialPermSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOfPartialPermSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOfPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CodegreeOfPartialPermSemigroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "CodegreeOfPartialPermSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(CodegreeOfPartialPermSemigroup)"]]},{"rank" : 30,"comment" : "CodegreeOfPartialPermSemigroup: for an inverse partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)","IsInverseSemigroup","Tester(IsInverseSemigroup)"]]},{"rank" : 24,"comment" : "CodegreeOfPartialPermSemigroup: for a partial perm semigroup with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -5,"comment" : "CodegreeOfPartialPermSemigroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CodegreeOfPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CodegreeOfPartialPermSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CodegreeOfPartialPermSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CodegreeOfPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankOfPartialPermSemigroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "RankOfPartialPermSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RankOfPartialPermSemigroup)"]]},{"rank" : 49,"comment" : "RankOfPartialPermSemigroup: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 24,"comment" : "RankOfPartialPermSemigroup: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -5,"comment" : "RankOfPartialPermSemigroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RankOfPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RankOfPartialPermSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RankOfPartialPermSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RankOfPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSymmetricInverseSemigroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "IsSymmetricInverseSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSymmetricInverseSemigroup)"]]},{"rank" : 24,"comment" : "IsSymmetricInverseSemigroup: for a partial perm semigroup with generators","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -5,"comment" : "IsSymmetricInverseSemigroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSymmetricInverseSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSymmetricInverseSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSymmetricInverseSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSymmetricInverseSemigroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SymmetricInverseSemigroup","type" : "GAP_Operation","filters" : [[["IsInt"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "SymmetricInverseSemigroup: for a integer","filters" : [["IsInt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismPartialPermSemigroup","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismPartialPermSemigroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismPartialPermSemigroup)"]]},{"rank" : 58,"comment" : "IsomorphismPartialPermSemigroup: for a perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "IsomorphismPartialPermSemigroup: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsomorphismPartialPermSemigroup: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 14,"comment" : "IsomorphismPartialPermSemigroup: for a semigroup with generators","filters" : [["IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismPartialPermSemigroup: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismPartialPermSemigroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismPartialPermSemigroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismPartialPermSemigroup)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismPartialPermMonoid","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsomorphismPartialPermMonoid: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismPartialPermMonoid)"]]},{"rank" : 58,"comment" : "IsomorphismPartialPermMonoid: for a perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 27,"comment" : "IsomorphismPartialPermMonoid: for a partial perm monoid","filters" : [["CategoryCollections(IsPartialPerm)","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "IsomorphismPartialPermMonoid: for a partial perm semigroup","filters" : [["CategoryCollections(IsPartialPerm)","IsMagma","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsomorphismPartialPermMonoid: for a transformation semigroup","filters" : [["CategoryCollections(IsTransformation)","IsMagma","Tester(GeneratorsOfMagma)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 19,"comment" : "IsomorphismPartialPermMonoid: for a monoid with generators","filters" : [["IsMagmaWithOne","Tester(GeneratorsOfMagmaWithOne)","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsomorphismPartialPermMonoid: default method requiring categories and checking properties","filters" : [["IsMagma"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismPartialPermMonoid)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismPartialPermMonoid): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismPartialPermMonoid): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismPartialPermMonoid)","type" : "GAP_Operation","filters" : [[["IsMagma","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingGroup","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]],[["IsTableOfMarks"]],[["IsGroupRing","Tester(IsGroupRing)"]],[["IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "UnderlyingGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingGroup)"]]},{"rank" : 45,"comment" : "UnderlyingGroup: LAGUNA: for a Lie algebra of a group ring","filters" : [["IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 38,"comment" : "UnderlyingGroup","filters" : [["IsGroupRing","Tester(IsGroupRing)"]]},{"rank" : 31,"comment" : "UnderlyingGroup: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingGroup)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]],[["IsTableOfMarks"],[]],[["IsGroupRing","Tester(IsGroupRing)"],[]],[["IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingGroup)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdentificationOfConjugacyClasses","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IdentificationOfConjugacyClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(IdentificationOfConjugacyClasses)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdentificationOfConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdentificationOfConjugacyClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdentificationOfConjugacyClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdentificationOfConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CompatibleConjugacyClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsOrdinaryTable"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsOrdinaryTable"],["IsRecord"]],[["IsOrdinaryTable"]],[["IsOrdinaryTable"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "CompatibleConjugacyClasses: one argument version, call `CompatibleConjugacyClassesDefault'","filters" : [["IsOrdinaryTable"]]}],"2args" : [{"rank" : 23,"comment" : "CompatibleConjugacyClasses: two argument version, call `CompatibleConjugacyClassesDefault'","filters" : [["IsOrdinaryTable"],["IsRecord"]]}],"3args" : [{"rank" : 57,"comment" : "CompatibleConjugacyClasses: three argument version, call `CompatibleConjugacyClassesDefault'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsOrdinaryTable"]]}],"4args" : [{"rank" : 58,"comment" : "CompatibleConjugacyClasses: four argument version, call `CompatibleConjugacyClassesDefault'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsOrdinaryTable"],["IsRecord"]]}],"5args" : [],"6args" : []}},{"name" : "CharacterDegrees","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "CharacterDegrees: system getter","filters" : [["IsAttributeStoringRep","Tester(CharacterDegrees)"]]},{"rank" : 368,"comment" : "CharacterDegrees: handled by nice monomorphism: Attribute","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 33,"comment" : "CharacterDegrees: for a group (call the two-argument version)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 21,"comment" : "CharacterDegrees: for a character table","filters" : [["IsCharacterTable"]]},{"rank" : 0,"comment" : "CharacterDegrees: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 80,"comment" : "CharacterDegrees: for an abelian group, and an integer p (just strip off the p-part)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"],["IsInt"]]},{"rank" : 74,"comment" : "CharacterDegrees: for a solvable group and an integer (Conlon's algorithm)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsInt"]]},{"rank" : 54,"comment" : "CharacterDegrees: for a group, and zero","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsZeroCyc"]]},{"rank" : 52,"comment" : "CharacterDegrees: for a group, and positive integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CharacterDegrees)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CharacterDegrees): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CharacterDegrees): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CharacterDegrees)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Irr","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Irr: system getter","filters" : [["IsAttributeStoringRep","Tester(Irr)"]]},{"rank" : 33,"comment" : "Irr: for a group (call the two-argument version)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "Irr: for an ord. char. table with known group (delegate to the group)","filters" : [["IsOrdinaryTable","Tester(UnderlyingGroup)"]]},{"rank" : 22,"comment" : "Irr: for a <p>-solvable Brauer table (use the Fong-Swan Theorem)","filters" : [["IsBrauerTable"]]},{"rank" : 0,"comment" : "Irr: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 10054,"comment" : "Irr: partial method for a group, and zero","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsZeroCyc"]]},{"rank" : 389,"comment" : "Irr: via niceomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsZeroCyc"]]},{"rank" : 83,"comment" : "Irr: ordinary characters for natural symmetric group","filters" : [["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)"],["IsZeroCyc"]]},{"rank" : 59,"comment" : "Irr: for a supersolvable group with known `IrrBaumClausen'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSupersolvableGroup","Tester(IsSupersolvableGroup)","Tester(IrrBaumClausen)"],["IsZeroCyc"]]},{"rank" : 59,"comment" : "Irr: for a supersolvable group with known `IrrConlon'","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSupersolvableGroup","Tester(IsSupersolvableGroup)","Tester(IrrConlon)"],["IsZeroCyc"]]},{"rank" : 58,"comment" : "Irr: for a supersolvable group (Baum-Clausen algorithm)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSupersolvableGroup","Tester(IsSupersolvableGroup)"],["IsZeroCyc"]]},{"rank" : 58,"comment" : "Irr: for a supersolvable group (Conlon's algorithm)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSupersolvableGroup","Tester(IsSupersolvableGroup)"],["IsZeroCyc"]]},{"rank" : 54,"comment" : "Irr: Dixon\/Schneider","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsZeroCyc"]]},{"rank" : 52,"comment" : "Irr: for a group, and a prime","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Irr)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Irr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Irr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Irr)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LinearCharacters","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "LinearCharacters: system getter","filters" : [["IsAttributeStoringRep","Tester(LinearCharacters)"]]},{"rank" : 33,"comment" : "LinearCharacters: for a group (call the two-argument version)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "LinearCharacters: for a Brauer table","filters" : [["IsBrauerTable"]]},{"rank" : 22,"comment" : "LinearCharacters: for an ordinary table","filters" : [["IsOrdinaryTable"]]},{"rank" : 0,"comment" : "LinearCharacters: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 54,"comment" : "LinearCharacters: for a group, and zero","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsZeroCyc"]]},{"rank" : 52,"comment" : "LinearCharacters: for a group, and positive integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LinearCharacters)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LinearCharacters): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LinearCharacters): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LinearCharacters)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IBr","type" : "GAP_Operation","filters" : [[["IsBrauerTable"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "IBr: system getter","filters" : [["IsAttributeStoringRep","Tester(IBr)"]]},{"rank" : 22,"comment" : "IBr: for a Brauer table","filters" : [["IsBrauerTable"]]}],"2args" : [{"rank" : 52,"comment" : "IBr: for a group, and a prime integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IBr)","type" : "GAP_Operation","filters" : [[["IsBrauerTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IBr): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IBr): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IBr)","type" : "GAP_Operation","filters" : [[["IsBrauerTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrdinaryCharacterTable","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "OrdinaryCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(OrdinaryCharacterTable)"]]},{"rank" : 33,"comment" : "OrdinaryCharacterTable: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "OrdinaryCharacterTable: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrdinaryCharacterTable)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrdinaryCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrdinaryCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrdinaryCharacterTable)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAlmostSimpleCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsAlmostSimpleCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAlmostSimpleCharacterTable)"]]},{"rank" : 22,"comment" : "IsAlmostSimpleCharacterTable: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAlmostSimpleCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAlmostSimpleCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAlmostSimpleCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAlmostSimpleCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonomialCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsMonomialCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMonomialCharacterTable)"]]},{"rank" : 23,"comment" : "IsMonomialCharacterTable: for an ordinary character table with underlying group","filters" : [["IsOrdinaryTable","Tester(UnderlyingGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMonomialCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMonomialCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMonomialCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMonomialCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotentCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsNilpotentCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNilpotentCharacterTable)"]]},{"rank" : 22,"comment" : "IsNilpotentCharacterTable: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNilpotentCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNilpotentCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNilpotentCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNilpotentCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPerfectCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsPerfectCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPerfectCharacterTable)"]]},{"rank" : 22,"comment" : "IsPerfectCharacterTable: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPerfectCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPerfectCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPerfectCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPerfectCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSimpleCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsSimpleCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSimpleCharacterTable)"]]},{"rank" : 22,"comment" : "IsSimpleCharacterTable: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSimpleCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSimpleCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSimpleCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSimpleCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSolvableCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsSolvableCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSolvableCharacterTable)"]]},{"rank" : 22,"comment" : "IsSolvableCharacterTable: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSolvableCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSolvableCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSolvableCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSolvableCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSporadicSimpleCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsSporadicSimpleCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSporadicSimpleCharacterTable)"]]},{"rank" : 22,"comment" : "IsSporadicSimpleCharacterTable: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSporadicSimpleCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSporadicSimpleCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSporadicSimpleCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSporadicSimpleCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSupersolvableCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsSupersolvableCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSupersolvableCharacterTable)"]]},{"rank" : 22,"comment" : "IsSupersolvableCharacterTable: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSupersolvableCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSupersolvableCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSupersolvableCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSupersolvableCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrdersClassRepresentatives","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "OrdersClassRepresentatives: system getter","filters" : [["IsAttributeStoringRep","Tester(OrdersClassRepresentatives)"]]},{"rank" : 23,"comment" : "OrdersClassRepresentatives: for a character table with known group","filters" : [["IsNearlyCharacterTable","Tester(UnderlyingGroup)"]]},{"rank" : 22,"comment" : "OrdersClassRepresentatives: for a Brauer character table (delegate to the ordinary table)","filters" : [["IsBrauerTable"]]},{"rank" : 20,"comment" : "OrdersClassRepresentatives: for a character table, use known power maps","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrdersClassRepresentatives)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrdersClassRepresentatives): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrdersClassRepresentatives): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrdersClassRepresentatives)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SizesCentralizers","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "SizesCentralizers: system getter","filters" : [["IsAttributeStoringRep","Tester(SizesCentralizers)"]]},{"rank" : 22,"comment" : "SizesCentralizers: for a Brauer character table","filters" : [["IsBrauerTable"]]},{"rank" : 20,"comment" : "SizesCentralizers: for a character table","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SizesCentralizers)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SizesCentralizers): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SizesCentralizers): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SizesCentralizers)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SizesConjugacyClasses","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "SizesConjugacyClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(SizesConjugacyClasses)"]]},{"rank" : 22,"comment" : "SizesConjugacyClasses: for a Brauer character table","filters" : [["IsBrauerTable"]]},{"rank" : 20,"comment" : "SizesConjugacyClasses: for a character table ","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SizesConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SizesConjugacyClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SizesConjugacyClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SizesConjugacyClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AutomorphismsOfTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "AutomorphismsOfTable: system getter","filters" : [["IsAttributeStoringRep","Tester(AutomorphismsOfTable)"]]},{"rank" : 22,"comment" : "AutomorphismsOfTable: for a Brauer table in the case of good reduction","filters" : [["IsBrauerTable"]]},{"rank" : 21,"comment" : "AutomorphismsOfTable: for a character table","filters" : [["IsCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AutomorphismsOfTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AutomorphismsOfTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AutomorphismsOfTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AutomorphismsOfTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingCharacteristic","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "UnderlyingCharacteristic: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingCharacteristic)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingCharacteristic)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingCharacteristic): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingCharacteristic): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingCharacteristic)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassNames","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ClassNames: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassNames)"]]},{"rank" : 20,"comment" : "ClassNames","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [{"rank" : 25,"comment" : "ClassNames","filters" : [["IsNearlyCharacterTable"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassNames)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassNames): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassNames): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassNames)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterNames","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "CharacterNames: system getter","filters" : [["IsAttributeStoringRep","Tester(CharacterNames)"]]},{"rank" : 20,"comment" : "CharacterNames","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CharacterNames)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CharacterNames): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CharacterNames): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CharacterNames)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassParameters","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ClassParameters: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassParameters)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassParameters)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassParameters): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassParameters): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassParameters)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterParameters","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "CharacterParameters: system getter","filters" : [["IsAttributeStoringRep","Tester(CharacterParameters)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CharacterParameters)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CharacterParameters): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CharacterParameters): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CharacterParameters)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Identifier","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]],[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "Identifier: system getter","filters" : [["IsAttributeStoringRep","Tester(Identifier)"]]},{"rank" : 22,"comment" : "Identifier: for a Brauer table","filters" : [["IsBrauerTable"]]},{"rank" : 22,"comment" : "Identifier: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Identifier)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]],[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Identifier): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Identifier): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Identifier)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InverseClasses","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "InverseClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(InverseClasses)"]]},{"rank" : 55,"comment" : "InverseClasses: for a character table with known irreducibles","filters" : [["IsCharacterTable","Tester(Irr)"]]},{"rank" : 21,"comment" : "InverseClasses: for a character table","filters" : [["IsCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InverseClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InverseClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InverseClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InverseClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RealClasses","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "RealClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(RealClasses)"]]},{"rank" : 21,"comment" : "RealClasses: for a character table","filters" : [["IsCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RealClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RealClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RealClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RealClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassOrbit","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 40,"comment" : "ClassOrbit: for a character table, and a positive integer","filters" : [["IsCharacterTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassRoots","type" : "GAP_Operation","filters" : [[["IsCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "ClassRoots: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassRoots)"]]},{"rank" : 21,"comment" : "ClassRoots: for a character table","filters" : [["IsCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassRoots)","type" : "GAP_Operation","filters" : [[["IsCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassRoots): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassRoots): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassRoots)","type" : "GAP_Operation","filters" : [[["IsCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfNormalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfNormalSubgroups)"]]},{"rank" : 22,"comment" : "ClassPositionsOfNormalSubgroups: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfNormalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfNormalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfMaximalNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfMaximalNormalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfMaximalNormalSubgroups)"]]},{"rank" : 22,"comment" : "ClassPositionsOfMaximalNormalSubgroups: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfMaximalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfMaximalNormalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfMaximalNormalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfMaximalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfMinimalNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfMinimalNormalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfMinimalNormalSubgroups)"]]},{"rank" : 22,"comment" : "ClassPositionsOfMinimalNormalSubgroups: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfMinimalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfMinimalNormalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfMinimalNormalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfMinimalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfAgemo","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 41,"comment" : "ClassPositionsOfAgemo: for an ordinary table","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfCentre","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]],[["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfCentre: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfCentre)"]]},{"rank" : 22,"comment" : "ClassPositionsOfCentre: for an ordinary table","filters" : [["IsOrdinaryTable"]]},{"rank" : 4,"comment" : "ClassPositionsOfCentre: for a homogeneous list","filters" : [["IsHomogeneousList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfCentre)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]],[["IsHomogeneousList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfCentre): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfCentre): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfCentre)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfDirectProductDecompositions","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]],[["IsOrdinaryTable"],["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfDirectProductDecompositions: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfDirectProductDecompositions)"]]},{"rank" : 22,"comment" : "ClassPositionsOfDirectProductDecompositions: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [{"rank" : 51,"comment" : "ClassPositionsOfDirectProductDecompositions: for an ordinary table, and a list of positive integers","filters" : [["IsOrdinaryTable"],["IsList","CategoryCollections(IsCyclotomic)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfDirectProductDecompositions)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfDirectProductDecompositions): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfDirectProductDecompositions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfDirectProductDecompositions)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfDerivedSubgroup","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfDerivedSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfDerivedSubgroup)"]]},{"rank" : 22,"comment" : "ClassPositionsOfDerivedSubgroup: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfDerivedSubgroup)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfDerivedSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfDerivedSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfDerivedSubgroup)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfElementaryAbelianSeries","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfElementaryAbelianSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfElementaryAbelianSeries)"]]},{"rank" : 22,"comment" : "ClassPositionsOfElementaryAbelianSeries: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfElementaryAbelianSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfElementaryAbelianSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfElementaryAbelianSeries)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfFittingSubgroup","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfFittingSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfFittingSubgroup)"]]},{"rank" : 22,"comment" : "ClassPositionsOfFittingSubgroup: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfFittingSubgroup)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfFittingSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfFittingSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfFittingSubgroup)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfSolvableRadical","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfSolvableRadical: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfSolvableRadical)"]]},{"rank" : 22,"comment" : "ClassPositionsOfSolvableRadical: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfSolvableRadical)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfSolvableRadical): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfSolvableRadical): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfSolvableRadical)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfLowerCentralSeries","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfLowerCentralSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfLowerCentralSeries)"]]},{"rank" : 22,"comment" : "ClassPositionsOfLowerCentralSeries: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfLowerCentralSeries)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfLowerCentralSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfLowerCentralSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfLowerCentralSeries)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfUpperCentralSeries","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfUpperCentralSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfUpperCentralSeries)"]]},{"rank" : 22,"comment" : "ClassPositionsOfUpperCentralSeries: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfUpperCentralSeries)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfUpperCentralSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfUpperCentralSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfUpperCentralSeries)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfSolvableResiduum","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfSolvableResiduum: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfSolvableResiduum)"]]},{"rank" : 22,"comment" : "ClassPositionsOfSolvableResiduum: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfSolvableResiduum)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfSolvableResiduum): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfSolvableResiduum): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfSolvableResiduum)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfSupersolvableResiduum","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ClassPositionsOfSupersolvableResiduum: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfSupersolvableResiduum)"]]},{"rank" : 22,"comment" : "ClassPositionsOfSupersolvableResiduum: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfSupersolvableResiduum)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfSupersolvableResiduum): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfSupersolvableResiduum): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfSupersolvableResiduum)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfPCore","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 41,"comment" : "ClassPositionsOfPCore: for an ordinary table and a pos. integer","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfNormalClosure","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsHomogeneousList","CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "ClassPositionsOfNormalClosure: for an ordinary table","filters" : [["IsOrdinaryTable"],["IsHomogeneousList","CategoryCollections(IsCyclotomic)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimeBlocks","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 41,"comment" : "PrimeBlocks: for an ordinary table, and a positive integer","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PrimeBlocksOp","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 41,"comment" : "PrimeBlocksOp: for an ordinary table, and a positive integer","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedPrimeBlockss","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ComputedPrimeBlockss: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedPrimeBlockss)"]]},{"rank" : 22,"comment" : "ComputedPrimeBlockss: for an ordinary table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedPrimeBlockss)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedPrimeBlockss): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedPrimeBlockss): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedPrimeBlockss)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BlocksInfo","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "BlocksInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(BlocksInfo)"]]},{"rank" : 22,"comment" : "BlocksInfo: generic method for a Brauer character table","filters" : [["IsBrauerTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BlocksInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BlocksInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BlocksInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BlocksInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DecompositionMatrix","type" : "GAP_Operation","filters" : [[["IsBrauerTable"]],[["IsBrauerTable"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "DecompositionMatrix: system getter","filters" : [["IsAttributeStoringRep","Tester(DecompositionMatrix)"]]},{"rank" : 22,"comment" : "DecompositionMatrix: for a Brauer table","filters" : [["IsBrauerTable"]]}],"2args" : [{"rank" : 41,"comment" : "DecompositionMatrix: for a Brauer table, and a positive integer","filters" : [["IsBrauerTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DecompositionMatrix)","type" : "GAP_Operation","filters" : [[["IsBrauerTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DecompositionMatrix): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DecompositionMatrix): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DecompositionMatrix)","type" : "GAP_Operation","filters" : [[["IsBrauerTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPSolvableCharacterTable","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "IsPSolvableCharacterTable: for ord. char. table knowing `IsSolvableCharacterTable', and zero","filters" : [["IsOrdinaryTable","Tester(IsSolvableCharacterTable)"],["IsZeroCyc"]]},{"rank" : 43,"comment" : "IsPSolvableCharacterTable: for ord. char. table, and zero (call `IsPSolvableCharacterTableOp')","filters" : [["IsOrdinaryTable"],["IsZeroCyc"]]},{"rank" : 41,"comment" : "IsPSolvableCharacterTable: for ord.char.table, and pos.int. (call `IsPSolvableCharacterTableOp')","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPSolvableCharacterTableOp","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 40,"comment" : "IsPSolvableCharacterTableOp: for an ordinary character table, an an integer","filters" : [["IsOrdinaryTable"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedIsPSolvableCharacterTables","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ComputedIsPSolvableCharacterTables: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedIsPSolvableCharacterTables)"]]},{"rank" : 22,"comment" : "ComputedIsPSolvableCharacterTables: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedIsPSolvableCharacterTables)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedIsPSolvableCharacterTables): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedIsPSolvableCharacterTables): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedIsPSolvableCharacterTables)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Indicator","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsInt","IsPosRat"]],[["IsNearlyCharacterTable"],["IsList"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 40,"comment" : "Indicator: for a character table, and a positive integer","filters" : [["IsCharacterTable"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 44,"comment" : "Indicator: for a character table, a homogeneous list, and a positive integer","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IndicatorOp","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsList"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 45,"comment" : "IndicatorOp: for a Brauer character table and <n> = 2","filters" : [["IsBrauerTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]]},{"rank" : 45,"comment" : "IndicatorOp: for an ord. character table, a hom. list, and a pos. integer","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedIndicators","type" : "GAP_Operation","filters" : [[["IsCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "ComputedIndicators: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedIndicators)"]]},{"rank" : 21,"comment" : "ComputedIndicators: for a character table","filters" : [["IsCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedIndicators)","type" : "GAP_Operation","filters" : [[["IsCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedIndicators): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedIndicators): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedIndicators)","type" : "GAP_Operation","filters" : [[["IsCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterTable","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]],[["IsOrdinaryTable"],["IsInt"]],[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 134,"comment" : "CharacterTable: [ IsGroup and HasTableOfMarks ]","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(TableOfMarks)"]]},{"rank" : 33,"comment" : "CharacterTable: for a group (delegate to `OrdinaryCharacterTable')","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 5,"comment" : "CharacterTable: for a string","filters" : [["IsString"]]},{"rank" : 1,"comment" : "CharacterTable: [ IsTableOfMarks ]","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 51,"comment" : "CharacterTable: for a group, and a prime integer","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]},{"rank" : 41,"comment" : "CharacterTable: for an ordinary table, and a prime integer","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]},{"rank" : 5,"comment" : "CharacterTable: for a string and an object","filters" : [["IsString"],[]]}],"3args" : [{"rank" : 5,"comment" : "CharacterTable: for a string and two objects","filters" : [["IsString"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BrauerTable","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt","IsPosRat"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "BrauerTable: for a group, and a prime (delegate to the ord. table of the group)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 41,"comment" : "BrauerTable: for an ordinary table, and a prime","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BrauerTableOp","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsInt","IsPosRat"]],[["IsSpinSymTable"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10044,"comment" : "BrauerTableOp: [ IsOrdinaryTable and IsLibraryCharacterTableRep, IsPosInt ]","filters" : [["IsOrdinaryTable","IsLibraryCharacterTableRep"],["IsInt","IsPosRat"]]},{"rank" : 41,"comment" : "BrauerTableOp: for an ordinary character table created by SpinSymCharacterTableOfMaximalYoungSubgroup() and a positive rational prime","filters" : [["IsSpinSymTable"],["IsInt","IsPosRat"]]},{"rank" : 41,"comment" : "BrauerTableOp: for ordinary character table, and positive integer","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedBrauerTables","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "ComputedBrauerTables: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedBrauerTables)"]]},{"rank" : 22,"comment" : "ComputedBrauerTables: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedBrauerTables)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedBrauerTables): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedBrauerTables): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedBrauerTables)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DisplayOptions","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "DisplayOptions: system getter","filters" : [["IsAttributeStoringRep","Tester(DisplayOptions)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DisplayOptions)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DisplayOptions): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DisplayOptions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DisplayOptions)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterTableDirectProduct","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "CharacterTableDirectProduct: for two Brauer character tables","filters" : [["IsBrauerTable"],["IsBrauerTable"]]},{"rank" : 44,"comment" : "CharacterTableDirectProduct: for one ordinary and one Brauer character table","filters" : [["IsOrdinaryTable"],["IsBrauerTable"]]},{"rank" : 44,"comment" : "CharacterTableDirectProduct: for one Brauer table, and one ordinary character table","filters" : [["IsBrauerTable"],["IsOrdinaryTable"]]},{"rank" : 44,"comment" : "CharacterTableDirectProduct: for two ordinary character tables","filters" : [["IsOrdinaryTable"],["IsOrdinaryTable"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorsOfDirectProduct","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "FactorsOfDirectProduct: system getter","filters" : [["IsAttributeStoringRep","Tester(FactorsOfDirectProduct)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FactorsOfDirectProduct)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FactorsOfDirectProduct): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FactorsOfDirectProduct): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FactorsOfDirectProduct)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterTableFactorGroup","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "CharacterTableFactorGroup: for a Brauer table, and a list of class positions","filters" : [["IsBrauerTable"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 51,"comment" : "CharacterTableFactorGroup: for an ordinary table, and a list of class positions","filters" : [["IsOrdinaryTable"],["IsList","CategoryCollections(IsCyclotomic)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterTableIsoclinic","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsList","CategoryCollections(IsCyclotomic)"]],[["IsNearlyCharacterTable"],["IsInt","IsPosRat"]],[["IsNearlyCharacterTable"],["IsList","CategoryCollections(IsCyclotomic)"],["IsInt","IsPosRat"]],[["IsNearlyCharacterTable"],["IsList","CategoryCollections(IsCyclotomic)"],["IsList","CategoryCollections(IsCyclotomic)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "CharacterTableIsoclinic: system getter","filters" : [["IsAttributeStoringRep","Tester(CharacterTableIsoclinic)"]]},{"rank" : 22,"comment" : "CharacterTableIsoclinic: for a Brauer table","filters" : [["IsBrauerTable"]]},{"rank" : 22,"comment" : "CharacterTableIsoclinic: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [{"rank" : 51,"comment" : "CharacterTableIsoclinic: for a Brauer table and a list of classes","filters" : [["IsBrauerTable"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 51,"comment" : "CharacterTableIsoclinic: for an ordinary character table and a list of classes","filters" : [["IsOrdinaryTable"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 44,"comment" : "CharacterTableIsoclinic: for a Brauer table and an ordinary table","filters" : [["IsBrauerTable"],["IsOrdinaryTable"]]},{"rank" : 41,"comment" : "CharacterTableIsoclinic: for a Brauer table and a class pos.","filters" : [["IsBrauerTable"],["IsInt","IsPosRat"]]},{"rank" : 41,"comment" : "CharacterTableIsoclinic: for an ordinary character table and a class pos.","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 22,"comment" : "CharacterTableIsoclinic: for a Brauer table and two lists of class positions","filters" : [["IsBrauerTable"],[],[]]},{"rank" : 22,"comment" : "CharacterTableIsoclinic: for an ordinary character table and two lists of class positions","filters" : [["IsOrdinaryTable"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CharacterTableIsoclinic)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CharacterTableIsoclinic): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CharacterTableIsoclinic): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CharacterTableIsoclinic)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SourceOfIsoclinicTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "SourceOfIsoclinicTable: system getter","filters" : [["IsAttributeStoringRep","Tester(SourceOfIsoclinicTable)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SourceOfIsoclinicTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SourceOfIsoclinicTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SourceOfIsoclinicTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SourceOfIsoclinicTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterTableWithSortedCharacters","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "CharacterTableWithSortedCharacters: for a character table","filters" : [["IsCharacterTable"]]}],"2args" : [{"rank" : 30,"comment" : "CharacterTableWithSortedCharacters: for an ordinary character table, and a permutation","filters" : [["IsOrdinaryTable"],["IsPerm"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SortedCharacters","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsHomogeneousList"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 24,"comment" : "SortedCharacters: for a character table, and a homogeneous list","filters" : [["IsNearlyCharacterTable"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 29,"comment" : "SortedCharacters: for a character table, a homogeneous list, and a string","filters" : [["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacterTableWithSortedClasses","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsString"]],[["IsNearlyCharacterTable"],["IsPerm"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 21,"comment" : "CharacterTableWithSortedClasses: for a character table","filters" : [["IsCharacterTable"]]}],"2args" : [{"rank" : 30,"comment" : "CharacterTableWithSortedClasses: for an ordinary character table, and a permutation","filters" : [["IsOrdinaryTable"],["IsPerm"]]},{"rank" : 26,"comment" : "CharacterTableWithSortedClasses: for a character table, and string","filters" : [["IsCharacterTable"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPermutation","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ClassPermutation: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPermutation)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPermutation)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPermutation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPermutation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPermutation)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalSubgroupClassesInfo","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "NormalSubgroupClassesInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalSubgroupClassesInfo)"]]},{"rank" : 22,"comment" : "NormalSubgroupClassesInfo: default method, initialization","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalSubgroupClassesInfo)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalSubgroupClassesInfo): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalSubgroupClassesInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalSubgroupClassesInfo)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingCharacterTable","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "UnderlyingCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingCharacterTable)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingCharacterTable)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingCharacterTable)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ValuesOfClassFunction","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "ValuesOfClassFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(ValuesOfClassFunction)"]]},{"rank" : 3,"comment" : "ValuesOfClassFunction: for a dense list","filters" : [["IsDenseList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ValuesOfClassFunction)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ValuesOfClassFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ValuesOfClassFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ValuesOfClassFunction)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GlobalPartitionOfClasses","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "GlobalPartitionOfClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(GlobalPartitionOfClasses)"]]},{"rank" : 22,"comment" : "GlobalPartitionOfClasses: for an ordinary character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GlobalPartitionOfClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GlobalPartitionOfClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GlobalPartitionOfClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GlobalPartitionOfClasses)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CorrespondingPermutations","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsHomogeneousList"]],[["IsOrdinaryTable"],["IsClassFunction"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "CorrespondingPermutations: for character table and list of group elements","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 30,"comment" : "CorrespondingPermutations: for a char. table, a hom. list, and a list of group elements","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassFunction","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsDenseList"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "ClassFunction: for a group, and a dense list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]},{"rank" : 23,"comment" : "ClassFunction: for nearly character table, and dense list","filters" : [["IsNearlyCharacterTable"],["IsDenseList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "VirtualCharacter","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsDenseList"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "VirtualCharacter: for a group, and a dense list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]},{"rank" : 23,"comment" : "VirtualCharacter: for nearly character table, and dense list","filters" : [["IsNearlyCharacterTable"],["IsDenseList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Character","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsDenseList"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "Character: for a group, and a dense list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsDenseList"]]},{"rank" : 23,"comment" : "Character: for nearly character table, and dense list","filters" : [["IsNearlyCharacterTable"],["IsDenseList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TrivialCharacter","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "TrivialCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(TrivialCharacter)"]]},{"rank" : 33,"comment" : "TrivialCharacter: for a group (delegate to the table)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 20,"comment" : "TrivialCharacter: for a character table","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TrivialCharacter)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TrivialCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TrivialCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TrivialCharacter)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalCharacter","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "NaturalCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalCharacter)"]]},{"rank" : 58,"comment" : "NaturalCharacter: for a permutation group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 43,"comment" : "NaturalCharacter: for a matrix group in characteristic zero","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 7,"comment" : "NaturalCharacter: for a group general mapping","filters" : [["IsGeneralMapping"]]},{"rank" : 0,"comment" : "NaturalCharacter: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalCharacter)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalCharacter)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermutationCharacter","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection"],["IsFunction"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "PermutationCharacter: for two groups (use double cosets)","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [{"rank" : 36,"comment" : "PermutationCharacter: group action on domain","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsCollection"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCharacter)"]]},{"rank" : 33,"comment" : "IsCharacter: for a virtual character","filters" : [["IsClassFunction","IsVirtualCharacter","Tester(IsVirtualCharacter)"]]},{"rank" : 31,"comment" : "IsCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 26,"comment" : "IsCharacter: for a Brauer table, and a homogeneous list","filters" : [["IsBrauerTable"],["IsHomogeneousList"]]},{"rank" : 26,"comment" : "IsCharacter: for an ordinary character table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsVirtualCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsVirtualCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(IsVirtualCharacter)"]]},{"rank" : 31,"comment" : "IsVirtualCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 26,"comment" : "IsVirtualCharacter: for an ordinary character table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsVirtualCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsVirtualCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsVirtualCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsVirtualCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIrreducibleCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsIrreducibleCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIrreducibleCharacter)"]]},{"rank" : 31,"comment" : "IsIrreducibleCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 26,"comment" : "IsIrreducibleCharacter: for a Brauer table, and a homogeneous list","filters" : [["IsBrauerTable"],["IsHomogeneousList"]]},{"rank" : 26,"comment" : "IsIrreducibleCharacter: for an ordinary character table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIrreducibleCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIrreducibleCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIrreducibleCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIrreducibleCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MatScalarProducts","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"],["IsHomogeneousList"]],[["IsOrdinaryTable"],["IsHomogeneousList"],["IsHomogeneousList"]],[["IsHomogeneousList"]],[["IsOrdinaryTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "MatScalarProducts: for a homogeneous list","filters" : [["IsHomogeneousList"]]}],"2args" : [{"rank" : 26,"comment" : "MatScalarProducts: for an ordinary table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "MatScalarProducts: for two homogeneous lists","filters" : [["IsHomogeneousList"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 30,"comment" : "MatScalarProducts: for an ordinary table, and two homogeneous lists","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentreOfCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsOrdinaryTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "CentreOfCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(CentreOfCharacter)"]]},{"rank" : 31,"comment" : "CentreOfCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 26,"comment" : "CentreOfCharacter: for an ordinary table, and a homogeneous list ","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CentreOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CentreOfCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CentreOfCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CentreOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConstituentsOfCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "ConstituentsOfCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(ConstituentsOfCharacter)"]]},{"rank" : 35,"comment" : "ConstituentsOfCharacter: for a character","filters" : [["IsClassFunction","IsCharacter","Tester(IsCharacter)"]]},{"rank" : 31,"comment" : "ConstituentsOfCharacter","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 26,"comment" : "ConstituentsOfCharacter: for a Brauer table, and a homogeneous list","filters" : [["IsBrauerTable"],["IsHomogeneousList"]]},{"rank" : 26,"comment" : "ConstituentsOfCharacter: for an ordinary table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConstituentsOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConstituentsOfCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConstituentsOfCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConstituentsOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DegreeOfCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "DegreeOfCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(DegreeOfCharacter)"]]},{"rank" : 31,"comment" : "DegreeOfCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DegreeOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DegreeOfCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DegreeOfCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DegreeOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InertiaSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClassFunction"]],[["IsOrdinaryTable"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "InertiaSubgroup: for a group, and a class function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClassFunction"]]}],"3args" : [{"rank" : 59,"comment" : "InertiaSubgroup: for an ordinary table, a group, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KernelOfCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsOrdinaryTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "KernelOfCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(KernelOfCharacter)"]]},{"rank" : 31,"comment" : "KernelOfCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 26,"comment" : "KernelOfCharacter: for an ordinary table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KernelOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KernelOfCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KernelOfCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KernelOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassPositionsOfKernel","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "ClassPositionsOfKernel: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassPositionsOfKernel)"]]},{"rank" : 4,"comment" : "ClassPositionsOfKernel: for a homogeneous list","filters" : [["IsHomogeneousList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassPositionsOfKernel)","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassPositionsOfKernel): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassPositionsOfKernel): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassPositionsOfKernel)","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CycleStructureClass","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]],[["IsClassFunction"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 50,"comment" : "CycleStructureClass: for a class function, and a class position","filters" : [["IsClassFunction"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 45,"comment" : "CycleStructureClass: for an ordinary table, a list, and a class position","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "CentralCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(CentralCharacter)"]]},{"rank" : 31,"comment" : "CentralCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 26,"comment" : "CentralCharacter: for an ordinary table, and a homogeneous list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CentralCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CentralCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CentralCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CentralCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeterminantOfCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsCharacterTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "DeterminantOfCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(DeterminantOfCharacter)"]]},{"rank" : 31,"comment" : "DeterminantOfCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 25,"comment" : "DeterminantOfCharacter: for a nearly character table, and a class function","filters" : [["IsCharacterTable"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DeterminantOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DeterminantOfCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DeterminantOfCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DeterminantOfCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EigenvaluesChar","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsInt","IsPosRat"]],[["IsCharacterTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 50,"comment" : "EigenvaluesChar: for a class function and a positive integer","filters" : [["IsClassFunction"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 44,"comment" : "EigenvaluesChar: for a character table and a hom. list, and a pos.","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tensored","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "Tensored: method for two homogeneous lists","filters" : [["IsHomogeneousList"],["IsHomogeneousList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedClassFunction","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsClassFunction"],["IsGeneralMapping"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsGeneralMapping"]],[["IsClassFunction"],["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "RestrictedClassFunction: for a class function, and a group","filters" : [["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 51,"comment" : "RestrictedClassFunction: for class function and nearly character table","filters" : [["IsClassFunction"],["IsNearlyCharacterTable"]]},{"rank" : 38,"comment" : "RestrictedClassFunction: for a class function and a group homomorphism","filters" : [["IsClassFunction"],["IsGeneralMapping"]]}],"3args" : [{"rank" : 57,"comment" : "RestrictedClassFunction: for a character table, a homogeneous list, and a group","filters" : [["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 44,"comment" : "RestrictedClassFunction: for a character table, a homogeneous list, and a character table","filters" : [["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsNearlyCharacterTable"]]},{"rank" : 31,"comment" : "RestrictedClassFunction: for a character table, a homogeneous list, and a group homomorphism","filters" : [["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsGeneralMapping"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RestrictedClassFunctions","type" : "GAP_Operation","filters" : [[["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"],["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsList"],["IsGeneralMapping"]],[["IsNearlyCharacterTable"],["IsList"],["IsGeneralMapping"]],[["IsList"],["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsList"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "RestrictedClassFunctions: for list and group","filters" : [["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "RestrictedClassFunctions: for list and character table","filters" : [["IsList"],["IsCharacterTable"]]},{"rank" : 9,"comment" : "RestrictedClassFunctions: for list and group homomorphism","filters" : [["IsList"],["IsGeneralMapping"]]}],"3args" : [{"rank" : 56,"comment" : "RestrictedClassFunctions: for a character table, a list, and a group","filters" : [["IsCharacterTable"],["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 44,"comment" : "RestrictedClassFunctions: for a character table, a list, and a character table","filters" : [["IsCharacterTable"],["IsList"],["IsCharacterTable"]]},{"rank" : 30,"comment" : "RestrictedClassFunctions: for a character table, a list, and a group homomorphism","filters" : [["IsCharacterTable"],["IsList"],["IsGeneralMapping"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Restricted","type" : "GAP_Operation","filters" : [[[],[]],[[],[],[]],[[],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "Restricted","filters" : [["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 51,"comment" : "Restricted","filters" : [["IsClassFunction"],["IsNearlyCharacterTable"]]},{"rank" : 48,"comment" : "Restricted","filters" : [["IsClassFunction"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 37,"comment" : "Restricted","filters" : [["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "Restricted","filters" : [["IsList"],["IsList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 24,"comment" : "Restricted","filters" : [["IsHomogeneousList"],["IsNearlyCharacterTable"]]},{"rank" : 21,"comment" : "Restricted","filters" : [["IsHomogeneousList"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]}],"3args" : [{"rank" : 72,"comment" : "Restricted","filters" : [["IsCharacterTable"],["IsClassFunction"],["IsNearlyCharacterTable"]]},{"rank" : 69,"comment" : "Restricted","filters" : [["IsCharacterTable"],["IsClassFunction"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 58,"comment" : "Restricted","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 44,"comment" : "Restricted","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"],["IsHomogeneousList"]]}],"4args" : [{"rank" : 70,"comment" : "Restricted","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]}],"5args" : [],"6args" : []}},{"name" : "InducedClassFunction","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsClassFunction"],["IsGeneralMapping"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsGeneralMapping"]],[["IsClassFunction"],["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "InducedClassFunction: for a class function and a group","filters" : [["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 51,"comment" : "InducedClassFunction: for class function and nearly character table","filters" : [["IsClassFunction"],["IsNearlyCharacterTable"]]},{"rank" : 38,"comment" : "InducedClassFunction: for a class function and a group homomorphism","filters" : [["IsClassFunction"],["IsGeneralMapping"]]}],"3args" : [{"rank" : 58,"comment" : "InducedClassFunction: for a character table, a homogeneous list, and a group","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 45,"comment" : "InducedClassFunction: for character table, homogeneous list, and nearly character table","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsNearlyCharacterTable"]]},{"rank" : 32,"comment" : "InducedClassFunction: for a character table, a homogeneous list, and a group homomorphism","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsGeneralMapping"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InducedClassFunctions","type" : "GAP_Operation","filters" : [[["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsNearlyCharacterTable"],["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsList"],["IsGeneralMapping"]],[["IsNearlyCharacterTable"],["IsList"],["IsGeneralMapping"]],[["IsList"],["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsList"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "InducedClassFunctions: for list, and group","filters" : [["IsList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 23,"comment" : "InducedClassFunctions: for list, and group homomorphism","filters" : [["IsList"],["IsCharacterTable"]]},{"rank" : 9,"comment" : "InducedClassFunctions: for list, and group homomorphism","filters" : [["IsList"],["IsGeneralMapping"]]}],"3args" : [{"rank" : 58,"comment" : "InducedClassFunctions: for a character table, a homogeneous list, and a group","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 45,"comment" : "InducedClassFunctions: for character table, homogeneous list, and nearly character table","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsNearlyCharacterTable"]]},{"rank" : 32,"comment" : "InducedClassFunctions: for a character table, a homogeneous list, and a group homomorphism","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsGeneralMapping"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Induced","type" : "GAP_Operation","filters" : [[[],[]],[[],[],[]],[[],[],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 64,"comment" : "Induced","filters" : [["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 51,"comment" : "Induced","filters" : [["IsClassFunction"],["IsNearlyCharacterTable"]]},{"rank" : 48,"comment" : "Induced","filters" : [["IsClassFunction"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]},{"rank" : 37,"comment" : "Induced","filters" : [["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 25,"comment" : "Induced","filters" : [["IsHomogeneousList"],["IsCharacterTable"]]},{"rank" : 11,"comment" : "Induced","filters" : [["IsHomogeneousList"],["IsGeneralMapping"]]}],"3args" : [{"rank" : 58,"comment" : "Induced","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 45,"comment" : "Induced","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsNearlyCharacterTable"]]},{"rank" : 44,"comment" : "Induced: for two nearly character tables, and homog list","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"],["IsHomogeneousList"]]},{"rank" : 42,"comment" : "Induced","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]}],"4args" : [{"rank" : 73,"comment" : "Induced: for two nearly character tables and two homog. lists","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsHomogeneousList","CategoryCollections(IsCyclotomic)"]]},{"rank" : 49,"comment" : "Induced: for two nearly character tables, homog list, and string","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsString"]]}],"5args" : [],"6args" : []}},{"name" : "InducedCyclic","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]],[["IsOrdinaryTable"],["IsList"]],[["IsOrdinaryTable"],["IsList"],["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "InducedCyclic: for a character table","filters" : [["IsOrdinaryTable"]]}],"2args" : [{"rank" : 28,"comment" : "InducedCyclic: for a character table and a string","filters" : [["IsOrdinaryTable"],["IsString"]]},{"rank" : 26,"comment" : "InducedCyclic: for a character table and a hom. list","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 31,"comment" : "InducedCyclic: for a character table, a hom. list, and a string","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedClassFunctions","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"],["IsHomogeneousList"]],[["IsOrdinaryTable"],["IsHomogeneousList"],["IsHomogeneousList"]],[["IsHomogeneousList"]],[["IsOrdinaryTable"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "ReducedClassFunctions: for a list (of class functions)","filters" : [["IsHomogeneousList"]]}],"2args" : [{"rank" : 26,"comment" : "ReducedClassFunctions: for ordinary character table, and list of class functions","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"]]},{"rank" : 8,"comment" : "ReducedClassFunctions: for two lists (of class functions)","filters" : [["IsHomogeneousList"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 30,"comment" : "ReducedClassFunctions: for ordinary character table, and two lists (of class functions)","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ReducedCharacters","type" : "GAP_Operation","filters" : [[["IsHomogeneousList"],["IsHomogeneousList"]],[["IsOrdinaryTable"],["IsHomogeneousList"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 8,"comment" : "ReducedCharacters: for two lists (of characters)","filters" : [["IsHomogeneousList"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 30,"comment" : "ReducedCharacters: for ordinary character table, and two lists of characters","filters" : [["IsOrdinaryTable"],["IsHomogeneousList"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Symmetrizations","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsInt"]],[["IsNearlyCharacterTable"],["IsHomogeneousList"],["IsCharacterTable"]],[["IsHomogeneousList"],["IsInt"]],[["IsHomogeneousList"],["IsCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "Symmetrizations: for homogeneous list (of class functions) and character table","filters" : [["IsHomogeneousList"],["IsOrdinaryTable"]]},{"rank" : 23,"comment" : "Symmetrizations: for homogeneous list (of class functions) and positive integer","filters" : [["IsHomogeneousList"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 47,"comment" : "Symmetrizations: for char. table, homog. list (of class functions), and table of Sn","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsOrdinaryTable"]]},{"rank" : 44,"comment" : "Symmetrizations: for char. table, homog. list (of class functions), and pos. integer","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsInt","IsPosRat"]]},{"rank" : 26,"comment" : "Symmetrizations: for char. table, homog. list (of class functions), and record","filters" : [["IsCharacterTable"],["IsHomogeneousList"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BrauerCharacterValue","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20033,"comment" : "BrauerCharacterValue: system getter","filters" : [["IsAttributeStoringRep","Tester(BrauerCharacterValue)"]]},{"rank" : 30,"comment" : "BrauerCharacterValue: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BrauerCharacterValue)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BrauerCharacterValue): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BrauerCharacterValue): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BrauerCharacterValue)","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PowerMap","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsInt"]],[["IsNearlyCharacterTable"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "PowerMap: for a character table, and an integer","filters" : [["IsNearlyCharacterTable"],["IsInt"]]}],"3args" : [{"rank" : 56,"comment" : "PowerMap: for a character table, and two integers","filters" : [["IsNearlyCharacterTable"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PowerMapOp","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsInt"]],[["IsNearlyCharacterTable"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "PowerMapOp: for character table and zero","filters" : [["IsCharacterTable"],["IsZeroCyc"]]},{"rank" : 42,"comment" : "PowerMapOp: for ordinary table with group, and positive integer","filters" : [["IsOrdinaryTable","Tester(UnderlyingGroup)"],["IsInt","IsPosRat"]]},{"rank" : 41,"comment" : "PowerMapOp: for ordinary table, and positive integer","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]},{"rank" : 40,"comment" : "PowerMapOp: for Brauer table and integer","filters" : [["IsBrauerTable"],["IsInt"]]},{"rank" : 40,"comment" : "PowerMapOp: for character table and negative integer","filters" : [["IsCharacterTable"],["IsInt","IsNegRat"]]}],"3args" : [{"rank" : 59,"comment" : "PowerMapOp: for Brauer table, integer, positive integer","filters" : [["IsBrauerTable"],["IsInt"],["IsInt","IsPosRat"]]},{"rank" : 59,"comment" : "PowerMapOp: for ordinary table, integer, positive integer","filters" : [["IsOrdinaryTable"],["IsInt"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedPowerMaps","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ComputedPowerMaps: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedPowerMaps)"]]},{"rank" : 20,"comment" : "ComputedPowerMaps: for a nearly character table","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedPowerMaps)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedPowerMaps): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedPowerMaps): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedPowerMaps)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PossiblePowerMaps","type" : "GAP_Operation","filters" : [[["IsCharacterTable"],["IsInt"]],[["IsCharacterTable"],["IsInt"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 41,"comment" : "PossiblePowerMaps: for a Brauer character table and a prime","filters" : [["IsBrauerTable"],["IsInt","IsPosRat"]]},{"rank" : 41,"comment" : "PossiblePowerMaps: for an ordinary character table and a prime (add empty options record)","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 42,"comment" : "PossiblePowerMaps: for a Brauer character table, a prime, and a record","filters" : [["IsBrauerTable"],["IsInt","IsPosRat"],["IsRecord"]]},{"rank" : 42,"comment" : "PossiblePowerMaps: for an ordinary character table, a prime, and a record","filters" : [["IsOrdinaryTable"],["IsInt","IsPosRat"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FusionConjugacyClasses","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsGeneralMapping"]],[["IsGeneralMapping"],["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "FusionConjugacyClasses: for a group homomorphism","filters" : [["IsGeneralMapping"]]}],"2args" : [{"rank" : 66,"comment" : "FusionConjugacyClasses: for two groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 40,"comment" : "FusionConjugacyClasses: for two nearly character tables","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]}],"3args" : [{"rank" : 47,"comment" : "FusionConjugacyClasses: for a group homomorphism, and two nearly character tables","filters" : [["IsGeneralMapping"],["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FusionConjugacyClassesOp","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]],[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]],[["IsGeneralMapping"],["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "FusionConjugacyClassesOp: system getter","filters" : [["IsAttributeStoringRep","Tester(FusionConjugacyClassesOp)"]]},{"rank" : 7,"comment" : "FusionConjugacyClassesOp: for a group homomorphism","filters" : [["IsGeneralMapping"]]}],"2args" : [{"rank" : 46,"comment" : "FusionConjugacyClassesOp: for two ordinary tables with groups","filters" : [["IsOrdinaryTable","Tester(UnderlyingGroup)"],["IsOrdinaryTable","Tester(UnderlyingGroup)"]]},{"rank" : 44,"comment" : "FusionConjugacyClassesOp: for two Brauer tables","filters" : [["IsBrauerTable"],["IsBrauerTable"]]},{"rank" : 44,"comment" : "FusionConjugacyClassesOp: for two ordinary tables","filters" : [["IsOrdinaryTable"],["IsOrdinaryTable"]]}],"3args" : [{"rank" : 51,"comment" : "FusionConjugacyClassesOp: for a group homomorphism, and two character tables","filters" : [["IsGeneralMapping"],["IsOrdinaryTable"],["IsOrdinaryTable"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FusionConjugacyClassesOp)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FusionConjugacyClassesOp): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FusionConjugacyClassesOp): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FusionConjugacyClassesOp)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedClassFusions","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ComputedClassFusions: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedClassFusions)"]]},{"rank" : 20,"comment" : "ComputedClassFusions: for a nearly character table","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedClassFusions)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedClassFusions): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedClassFusions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedClassFusions)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NamesOfFusionSources","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "NamesOfFusionSources: system getter","filters" : [["IsAttributeStoringRep","Tester(NamesOfFusionSources)"]]},{"rank" : 20,"comment" : "NamesOfFusionSources: for a nearly character table","filters" : [["IsNearlyCharacterTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NamesOfFusionSources)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NamesOfFusionSources): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NamesOfFusionSources): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NamesOfFusionSources)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PossibleClassFusions","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]],[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "PossibleClassFusions: for two Brauer tables","filters" : [["IsBrauerTable"],["IsBrauerTable"]]},{"rank" : 40,"comment" : "PossibleClassFusions: for two ordinary character tables","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]}],"3args" : [{"rank" : 41,"comment" : "PossibleClassFusions: for two ordinary character tables, and a parameters record","filters" : [["IsNearlyCharacterTable"],["IsNearlyCharacterTable"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MatrixAutomorphisms","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]],[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsList"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "MatrixAutomorphisms: for a matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [{"rank" : 90,"comment" : "MatrixAutomorphisms: for matrix, list of maps, and subgroup","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsList"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TableAutomorphisms","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsList"]],[["IsNearlyCharacterTable"],["IsList"],["IsString"]],[["IsNearlyCharacterTable"],["IsList"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "TableAutomorphisms: for a character table and a list of characters","filters" : [["IsCharacterTable"],["IsList"]]}],"3args" : [{"rank" : 81,"comment" : "TableAutomorphisms: for a character table, a list of characters, and a perm. group","filters" : [["IsCharacterTable"],["IsList"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 28,"comment" : "TableAutomorphisms: for a character table, a list of characters, and a string","filters" : [["IsCharacterTable"],["IsList"],["IsString"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformingPermutations","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 60,"comment" : "TransformingPermutations: for two matrices","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransformingPermutationsCharacterTables","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 42,"comment" : "TransformingPermutationsCharacterTables: for two character tables","filters" : [["IsCharacterTable"],["IsCharacterTable"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BaumClausenInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "BaumClausenInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(BaumClausenInfo)"]]},{"rank" : 33,"comment" : "BaumClausenInfo: for a (solvable) group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "BaumClausenInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BaumClausenInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BaumClausenInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BaumClausenInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BaumClausenInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IrreducibleRepresentations","type" : "GAP_Operation","filters" : [[["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20044,"comment" : "IrreducibleRepresentations: system getter","filters" : [["IsAttributeStoringRep","Tester(IrreducibleRepresentations)"]]},{"rank" : 43,"comment" : "IrreducibleRepresentations: (abelian by supersolvable) finite group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 42,"comment" : "IrreducibleRepresentations: Dixon's method","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IrreducibleRepresentations: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 102,"comment" : "IrreducibleRepresentations: finite group, Cyclotomics","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 98,"comment" : "IrreducibleRepresentations: for a finite group over a finite field","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IrreducibleRepresentations)","type" : "GAP_Operation","filters" : [[["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IrreducibleRepresentations): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IrreducibleRepresentations): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IrreducibleRepresentations)","type" : "GAP_Operation","filters" : [[["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IrrBaumClausen","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IrrBaumClausen: system getter","filters" : [["IsAttributeStoringRep","Tester(IrrBaumClausen)"]]},{"rank" : 33,"comment" : "IrrBaumClausen: for a (solvable) group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IrrBaumClausen: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IrrBaumClausen)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IrrBaumClausen): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IrrBaumClausen): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IrrBaumClausen)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IrrConlon","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IrrConlon: system getter","filters" : [["IsAttributeStoringRep","Tester(IrrConlon)"]]},{"rank" : 33,"comment" : "IrrConlon: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IrrConlon: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IrrConlon)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IrrConlon): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IrrConlon): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IrrConlon)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Inequalities","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsList"]],[["IsOrdinaryTable"],["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 24,"comment" : "Inequalities","filters" : [["IsOrdinaryTable"],["IsList"]]}],"3args" : [{"rank" : 24,"comment" : "Inequalities","filters" : [["IsOrdinaryTable"],["IsList"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MolienSeriesInfo","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "MolienSeriesInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(MolienSeriesInfo)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MolienSeriesInfo)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MolienSeriesInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MolienSeriesInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MolienSeriesInfo)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Alpha","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Alpha: system getter","filters" : [["IsAttributeStoringRep","Tester(Alpha)"]]},{"rank" : 33,"comment" : "Alpha: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "Alpha: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Alpha)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Alpha): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Alpha): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Alpha)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Delta","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsUnionOfResidueClassesWithFixedRepresentatives"]],[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "Delta: system getter","filters" : [["IsAttributeStoringRep","Tester(Delta)"]]},{"rank" : 33,"comment" : "Delta: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 8,"comment" : "Delta: for unions of residue classes of Z with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesOfZWithFixedRepresentatives"]]},{"rank" : 8,"comment" : "Delta: for residue class unions of Z (ResClasses)","filters" : [["IsResidueClassUnionOfZ"]]},{"rank" : 0,"comment" : "Delta: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Delta)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsUnionOfResidueClassesWithFixedRepresentatives"],[]],[["IsResidueClassUnion"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Delta): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Delta): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Delta)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBergerCondition","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsBergerCondition: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBergerCondition)"]]},{"rank" : 33,"comment" : "IsBergerCondition: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "IsBergerCondition: for a class function","filters" : [["IsClassFunction"]]},{"rank" : 0,"comment" : "IsBergerCondition: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBergerCondition)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBergerCondition): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBergerCondition): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBergerCondition)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitiveCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsPrimitiveCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPrimitiveCharacter)"]]},{"rank" : 31,"comment" : "IsPrimitiveCharacter: for a class function","filters" : [["IsClassFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPrimitiveCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPrimitiveCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPrimitiveCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPrimitiveCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TestQuasiPrimitive","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "TestQuasiPrimitive: system getter","filters" : [["IsAttributeStoringRep","Tester(TestQuasiPrimitive)"]]},{"rank" : 35,"comment" : "TestQuasiPrimitive: for a character","filters" : [["IsCharacter","Tester(IsCharacter)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TestQuasiPrimitive)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TestQuasiPrimitive): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TestQuasiPrimitive): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TestQuasiPrimitive)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsQuasiPrimitive","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsQuasiPrimitive: system getter","filters" : [["IsAttributeStoringRep","Tester(IsQuasiPrimitive)"]]},{"rank" : 35,"comment" : "IsQuasiPrimitive: for a character","filters" : [["IsCharacter","Tester(IsCharacter)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsQuasiPrimitive)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsQuasiPrimitive): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsQuasiPrimitive): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsQuasiPrimitive)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsInducedFromNormalSubgroup","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsInducedFromNormalSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsInducedFromNormalSubgroup)"]]},{"rank" : 35,"comment" : "IsInducedFromNormalSubgroup: for a character","filters" : [["IsCharacter","Tester(IsCharacter)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsInducedFromNormalSubgroup)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsInducedFromNormalSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsInducedFromNormalSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsInducedFromNormalSubgroup)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonomialCharacter","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsMonomialCharacter: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMonomialCharacter)"]]},{"rank" : 31,"comment" : "IsMonomialCharacter: for a character","filters" : [["IsClassFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMonomialCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMonomialCharacter): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMonomialCharacter): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMonomialCharacter)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonomialNumber","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "IsMonomialNumber: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMonomialNumber)"]]},{"rank" : 19,"comment" : "IsMonomialNumber: for a positive integer","filters" : [["IsInt","IsPosRat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMonomialNumber)","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMonomialNumber): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMonomialNumber): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMonomialNumber)","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TestMonomialQuick","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "TestMonomialQuick: system getter","filters" : [["IsAttributeStoringRep","Tester(TestMonomialQuick)"]]},{"rank" : 33,"comment" : "TestMonomialQuick: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "TestMonomialQuick: for a character","filters" : [["IsClassFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TestMonomialQuick)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TestMonomialQuick): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TestMonomialQuick): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TestMonomialQuick)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TestMonomial","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsClassFunction"],["IsBool"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "TestMonomial: system getter","filters" : [["IsAttributeStoringRep","Tester(TestMonomial)"]]},{"rank" : 33,"comment" : "TestMonomial: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "TestMonomial: for a character","filters" : [["IsClassFunction"]]}],"2args" : [{"rank" : 34,"comment" : "TestMonomial: for a group, and a Boolean","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]},{"rank" : 32,"comment" : "TestMonomial: for a character, and a Boolean","filters" : [["IsClassFunction"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TestMonomial)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],[]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TestMonomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TestMonomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TestMonomial)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TestSubnormallyMonomial","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "TestSubnormallyMonomial: system getter","filters" : [["IsAttributeStoringRep","Tester(TestSubnormallyMonomial)"]]},{"rank" : 33,"comment" : "TestSubnormallyMonomial: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "TestSubnormallyMonomial: for a character","filters" : [["IsClassFunction"]]},{"rank" : 0,"comment" : "TestSubnormallyMonomial: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TestSubnormallyMonomial)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TestSubnormallyMonomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TestSubnormallyMonomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TestSubnormallyMonomial)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubnormallyMonomial","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsSubnormallyMonomial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSubnormallyMonomial)"]]},{"rank" : 33,"comment" : "IsSubnormallyMonomial: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "IsSubnormallyMonomial: for a character","filters" : [["IsClassFunction"]]},{"rank" : 0,"comment" : "IsSubnormallyMonomial: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSubnormallyMonomial)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSubnormallyMonomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSubnormallyMonomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSubnormallyMonomial)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TestRelativelySM","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsClassFunction"]],[["IsClassFunction"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "TestRelativelySM: system getter","filters" : [["IsAttributeStoringRep","Tester(TestRelativelySM)"]]},{"rank" : 33,"comment" : "TestRelativelySM: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "TestRelativelySM: for a character","filters" : [["IsClassFunction"]]},{"rank" : 0,"comment" : "TestRelativelySM: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 33,"comment" : "TestRelativelySM: for a group, and an object","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]},{"rank" : 31,"comment" : "TestRelativelySM: for a character, and an object","filters" : [["IsClassFunction"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TestRelativelySM)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsClassFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TestRelativelySM): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TestRelativelySM): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TestRelativelySM)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsRelativelySM","type" : "GAP_Operation","filters" : [[["IsClassFunction"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsRelativelySM: system getter","filters" : [["IsAttributeStoringRep","Tester(IsRelativelySM)"]]},{"rank" : 33,"comment" : "IsRelativelySM: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "IsRelativelySM: for a character","filters" : [["IsClassFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsRelativelySM)","type" : "GAP_Operation","filters" : [[["IsClassFunction"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsRelativelySM): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsRelativelySM): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsRelativelySM)","type" : "GAP_Operation","filters" : [[["IsClassFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMinimalNonmonomial","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IsMinimalNonmonomial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMinimalNonmonomial)"]]},{"rank" : 33,"comment" : "IsMinimalNonmonomial: for a (solvable) group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsMinimalNonmonomial: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMinimalNonmonomial)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMinimalNonmonomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMinimalNonmonomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMinimalNonmonomial)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DixonRecord","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "DixonRecord: system getter","filters" : [["IsAttributeStoringRep","Tester(DixonRecord)"]]},{"rank" : 33,"comment" : "DixonRecord: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DixonRecord: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DixonRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DixonRecord): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DixonRecord): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DixonRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DxPreparation","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 59,"comment" : "DxPreparation: perm","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]},{"rank" : 47,"comment" : "DxPreparation: pc group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsRecord"]]},{"rank" : 42,"comment" : "DxPreparation: abelian","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)"],["IsRecord"]]},{"rank" : 34,"comment" : "DxPreparation: generic","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IrrDixonSchneider","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "IrrDixonSchneider: system getter","filters" : [["IsAttributeStoringRep","Tester(IrrDixonSchneider)"]]},{"rank" : 33,"comment" : "IrrDixonSchneider: Dixon\/Schneider","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IrrDixonSchneider: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 34,"comment" : "IrrDixonSchneider: Dixon\/Schneider","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IrrDixonSchneider)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IrrDixonSchneider): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IrrDixonSchneider): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IrrDixonSchneider)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TableOfMarks","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsString"]],[["IsTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20035,"comment" : "TableOfMarks: system getter","filters" : [["IsAttributeStoringRep","Tester(TableOfMarks)"]]},{"rank" : 134,"comment" : "TableOfMarks: [ IsGroup and HasOrdinaryCharacterTable ]","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(OrdinaryCharacterTable)"]]},{"rank" : 44,"comment" : "TableOfMarks: for a group with lattice","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(LatticeSubgroups)"]]},{"rank" : 43,"comment" : "TableOfMarks: for a cyclic group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCyclic","Tester(IsCyclic)"]]},{"rank" : 35,"comment" : "TableOfMarks: for solvable groups (call `LatticeSubgroups' and use the lattice)","filters" : [["IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 33,"comment" : "TableOfMarks: cyclic extension method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 25,"comment" : "TableOfMarks: [ IsOrdinaryTable and IsLibraryCharacterTableRep ]","filters" : [["IsOrdinaryTable","IsLibraryCharacterTableRep"]]},{"rank" : 23,"comment" : "TableOfMarks: [ IsCharacterTable and HasUnderlyingGroup ]","filters" : [["IsCharacterTable","Tester(UnderlyingGroup)"]]},{"rank" : 6,"comment" : "TableOfMarks: for a matrix or a lower triangular matrix","filters" : [["IsTable"]]},{"rank" : 5,"comment" : "TableOfMarks: for a string (dispatch to `TableOfMarksFromLibrary')","filters" : [["IsString"]]},{"rank" : 0,"comment" : "TableOfMarks: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TableOfMarks)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsString"],[]],[["IsTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TableOfMarks): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TableOfMarks): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TableOfMarks)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SortedTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsPerm"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 9,"comment" : "SortedTom","filters" : [["IsTableOfMarks"],["IsPerm"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermutationTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "PermutationTom: system getter","filters" : [["IsAttributeStoringRep","Tester(PermutationTom)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PermutationTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PermutationTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PermutationTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PermutationTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MarksTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MarksTom: system getter","filters" : [["IsAttributeStoringRep","Tester(MarksTom)"]]},{"rank" : 3,"comment" : "MarksTom: for a table of marks with known `NrSubsTom' and `OrdersTom'","filters" : [["IsTableOfMarks","Tester(NrSubsTom)","Tester(OrdersTom)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MarksTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MarksTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MarksTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MarksTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "SubsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(SubsTom)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SubsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SubsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SubsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SubsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrSubsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "NrSubsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(NrSubsTom)"]]},{"rank" : 1,"comment" : "NrSubsTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrSubsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrSubsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrSubsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrSubsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrdersTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "OrdersTom: system getter","filters" : [["IsAttributeStoringRep","Tester(OrdersTom)"]]},{"rank" : 1,"comment" : "OrdersTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrdersTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrdersTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrdersTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrdersTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LengthsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "LengthsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(LengthsTom)"]]},{"rank" : 1,"comment" : "LengthsTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LengthsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LengthsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LengthsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LengthsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassTypesTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "ClassTypesTom: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassTypesTom)"]]},{"rank" : 1,"comment" : "ClassTypesTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassTypesTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassTypesTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassTypesTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassTypesTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ClassNamesTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "ClassNamesTom: system getter","filters" : [["IsAttributeStoringRep","Tester(ClassNamesTom)"]]},{"rank" : 1,"comment" : "ClassNamesTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ClassNamesTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ClassNamesTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ClassNamesTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ClassNamesTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FusionsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "FusionsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(FusionsTom)"]]},{"rank" : 1,"comment" : "FusionsTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FusionsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FusionsTom): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FusionsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FusionsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdempotentsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IdempotentsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(IdempotentsTom)"]]},{"rank" : 1,"comment" : "IdempotentsTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdempotentsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdempotentsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdempotentsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdempotentsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdempotentsTomInfo","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IdempotentsTomInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(IdempotentsTomInfo)"]]},{"rank" : 1,"comment" : "IdempotentsTomInfo: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdempotentsTomInfo)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdempotentsTomInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdempotentsTomInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdempotentsTomInfo)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MatTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MatTom: system getter","filters" : [["IsAttributeStoringRep","Tester(MatTom)"]]},{"rank" : 1,"comment" : "MatTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MatTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MatTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MatTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MatTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MoebiusTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MoebiusTom: system getter","filters" : [["IsAttributeStoringRep","Tester(MoebiusTom)"]]},{"rank" : 1,"comment" : "MoebiusTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MoebiusTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MoebiusTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MoebiusTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MoebiusTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WeightsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "WeightsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(WeightsTom)"]]},{"rank" : 1,"comment" : "WeightsTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WeightsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WeightsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WeightsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WeightsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAbelianTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]],[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsAbelianTom: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAbelianTom)"]]},{"rank" : 1,"comment" : "IsAbelianTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 1021,"comment" : "IsAbelianTom: for a table of marks with known der. subgroups, and a positive integer","filters" : [["IsTableOfMarks","Tester(DerivedSubgroupsTomUnique)"],["IsInt","IsPosRat"]]},{"rank" : 30,"comment" : "IsAbelianTom: for a table of marks and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]},{"rank" : 21,"comment" : "IsAbelianTom: for a table of marks with generators, and a positive integer","filters" : [["IsTableOfMarks","IsTableOfMarksWithGens"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAbelianTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAbelianTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAbelianTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAbelianTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCyclicTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]],[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsCyclicTom: system getter","filters" : [["IsAttributeStoringRep","Tester(IsCyclicTom)"]]},{"rank" : 1,"comment" : "IsCyclicTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 20,"comment" : "IsCyclicTom: for a table of marks and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsCyclicTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsCyclicTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsCyclicTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsCyclicTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotentTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]],[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsNilpotentTom: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNilpotentTom)"]]},{"rank" : 1,"comment" : "IsNilpotentTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 20,"comment" : "IsNilpotentTom: for a table of marks and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNilpotentTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNilpotentTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNilpotentTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNilpotentTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPerfectTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]],[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsPerfectTom: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPerfectTom)"]]},{"rank" : 1,"comment" : "IsPerfectTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 21,"comment" : "IsPerfectTom: for a table of marks with known der. subgroups, and a positive integer","filters" : [["IsTableOfMarks","Tester(DerivedSubgroupsTomUnique)"],["IsInt","IsPosRat"]]},{"rank" : 20,"comment" : "IsPerfectTom: for a table of marks and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPerfectTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPerfectTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPerfectTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPerfectTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSolvableTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]],[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "IsSolvableTom: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSolvableTom)"]]},{"rank" : 1,"comment" : "IsSolvableTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 20,"comment" : "IsSolvableTom: for a table of marks and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSolvableTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSolvableTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSolvableTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSolvableTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DerivedSubgroupTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "DerivedSubgroupTom: for a table of marks, and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DerivedSubgroupsTomPossible","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "DerivedSubgroupsTomPossible: system getter","filters" : [["IsAttributeStoringRep","Tester(DerivedSubgroupsTomPossible)"]]},{"rank" : 1,"comment" : "DerivedSubgroupsTomPossible: for a table of marks (initialize with empty list)","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DerivedSubgroupsTomPossible)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DerivedSubgroupsTomPossible): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DerivedSubgroupsTomPossible): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DerivedSubgroupsTomPossible)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DerivedSubgroupsTomUnique","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "DerivedSubgroupsTomUnique: system getter","filters" : [["IsAttributeStoringRep","Tester(DerivedSubgroupsTomUnique)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DerivedSubgroupsTomUnique)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DerivedSubgroupsTomUnique): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DerivedSubgroupsTomUnique): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DerivedSubgroupsTomUnique)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "NormalizerTom: for a table of marks, and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizersTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "NormalizersTom: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizersTom)"]]},{"rank" : 1,"comment" : "NormalizersTom: all normalizers of a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizersTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizersTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizersTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizersTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ContainedTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 39,"comment" : "ContainedTom","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ContainingTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 39,"comment" : "ContainingTom","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CyclicExtensionsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]],[["IsTableOfMarks"],["IsInt","IsPosRat"]],[["IsTableOfMarks"],["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "CyclicExtensionsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(CyclicExtensionsTom)"]]},{"rank" : 1,"comment" : "CyclicExtensionsTom: for a table of marks (classes for all prime div. of the group order)","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 20,"comment" : "CyclicExtensionsTom: for a table of marks, and a prime","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]},{"rank" : 3,"comment" : "CyclicExtensionsTom: for a table of marks, and a list (of primes)","filters" : [["IsTableOfMarks"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CyclicExtensionsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CyclicExtensionsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CyclicExtensionsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CyclicExtensionsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedCyclicExtensionsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "ComputedCyclicExtensionsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedCyclicExtensionsTom)"]]},{"rank" : 1,"comment" : "ComputedCyclicExtensionsTom","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedCyclicExtensionsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedCyclicExtensionsTom): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedCyclicExtensionsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedCyclicExtensionsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CyclicExtensionsTomOp","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"]],[["IsTableOfMarks"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "CyclicExtensionsTomOp: for one prime","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]},{"rank" : 3,"comment" : "CyclicExtensionsTomOp: for a table of marks, and a list (of primes)","filters" : [["IsTableOfMarks"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DecomposedFixedPointVector","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 3,"comment" : "DecomposedFixedPointVector","filters" : [["IsTableOfMarks"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EulerianFunctionByTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"]],[["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "EulerianFunctionByTom","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 39,"comment" : "EulerianFunctionByTom","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntersectionsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 39,"comment" : "IntersectionsTom","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorGroupTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "FactorGroupTom: for a table of marks, and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalSubgroupsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]],[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "MaximalSubgroupsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalSubgroupsTom)"]]},{"rank" : 1,"comment" : "MaximalSubgroupsTom: for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 20,"comment" : "MaximalSubgroupsTom: for a table of marks, and a positive integer","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalSubgroupsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalSubgroupsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalSubgroupsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalSubgroupsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalSupergroupsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "MinimalSupergroupsTom: for a table of marks","filters" : [["IsTableOfMarks"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GeneratorsSubgroupsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "GeneratorsSubgroupsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(GeneratorsSubgroupsTom)"]]},{"rank" : 1,"comment" : "GeneratorsSubgroupsTom: default method for a table of marks","filters" : [["IsTableOfMarks"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GeneratorsSubgroupsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GeneratorsSubgroupsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GeneratorsSubgroupsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GeneratorsSubgroupsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StraightLineProgramsTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "StraightLineProgramsTom: system getter","filters" : [["IsAttributeStoringRep","Tester(StraightLineProgramsTom)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StraightLineProgramsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StraightLineProgramsTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StraightLineProgramsTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StraightLineProgramsTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativeTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "RepresentativeTom: for a table of marks with stored `StraightLineProgramsTom' value","filters" : [["IsTableOfMarks","Tester(StraightLineProgramsTom)"],["IsInt","IsPosRat"]]},{"rank" : 22,"comment" : "RepresentativeTom: for a table of marks with stored `GeneratorsSubgroupsTom' value","filters" : [["IsTableOfMarks","Tester(GeneratorsSubgroupsTom)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativeTomByGenerators","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","Tester(StraightLineProgramsTom)"],["IsInt","IsPosRat"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 26,"comment" : "RepresentativeTomByGenerators","filters" : [["IsTableOfMarks","Tester(StraightLineProgramsTom)"],["IsInt","IsPosRat"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativeTomByGeneratorsNC","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","Tester(StraightLineProgramsTom)"],["IsInt","IsPosRat"],["IsHomogeneousList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 26,"comment" : "RepresentativeTomByGeneratorsNC","filters" : [["IsTableOfMarks","Tester(StraightLineProgramsTom)"],["IsInt","IsPosRat"],["IsHomogeneousList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FusionCharTableTom","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 30,"comment" : "FusionCharTableTom: [ IsOrdinaryTable and IsLibraryCharacterTableRep and HasFusionToTom, IsTableOfMarks and IsLibTomRep ]","filters" : [["IsOrdinaryTable","IsLibraryCharacterTableRep","Tester(FusionToTom)"],["IsTableOfMarks","IsLibTomRep"]]},{"rank" : 23,"comment" : "FusionCharTableTom: for ordinary character table and table of marks","filters" : [["IsOrdinaryTable"],["IsTableOfMarks"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PossibleFusionsCharTableTom","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],["IsTableOfMarks"]],[["IsOrdinaryTable"],["IsTableOfMarks"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "PossibleFusionsCharTableTom: for ordinary character table and table of marks","filters" : [["IsOrdinaryTable"],["IsTableOfMarks"]]}],"3args" : [{"rank" : 24,"comment" : "PossibleFusionsCharTableTom: for ordinary character table, table of marks, and record","filters" : [["IsOrdinaryTable"],["IsTableOfMarks"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PermCharsTom","type" : "GAP_Operation","filters" : [[["IsList"],["IsTableOfMarks"]],[["IsOrdinaryTable"],["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "PermCharsTom: for character table and table of marks","filters" : [["IsOrdinaryTable"],["IsTableOfMarks"]]},{"rank" : 3,"comment" : "PermCharsTom: for explicit fusion map and table of marks","filters" : [["IsList"],["IsTableOfMarks"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TableOfMarksCyclic","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "TableOfMarksCyclic: for a positive integer","filters" : [["IsInt","IsPosRat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TableOfMarksDihedral","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 19,"comment" : "TableOfMarksDihedral: for a positive integer","filters" : [["IsInt","IsPosRat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TableOfMarksFrobenius","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "TableOfMarksFrobenius: tom of a Frobenius group","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MagmaInputString","type" : "GAP_Operation","filters" : [[[],["IsString"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "MagmaInputString: perm group","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ShrinkCoeffs","type" : "GAP_Operation","filters" : [[["IsMutable","IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 26,"comment" : "ShrinkCoeffs: 8 bit vector","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","Is8BitVectorRep"]]},{"rank" : 23,"comment" : "ShrinkCoeffs: for GF2 vector","filters" : [["IsMutable","IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject","IsGF2VectorRep"]]},{"rank" : 4,"comment" : "ShrinkCoeffs: call `ShrinkRowVector'","filters" : [["IsMutable","IsList"]]},{"rank" : 2,"comment" : "ShrinkCoeffs: error if immutable","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TeXObj","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LaTeXObj","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "LaTeXObj: matrix","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 17,"comment" : "LaTeXObj: rational","filters" : [["IsRat"]]},{"rank" : 17,"comment" : "LaTeXObj: for an internal FFE","filters" : [["IsFFE","IsInternalRep"]]},{"rank" : 14,"comment" : "LaTeXObj: polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 9,"comment" : "LaTeXObj: for an element of an f.p. group (default repres.)","filters" : [["IsPackedElementDefaultRep","IsElementOfFpGroup"]]},{"rank" : 6,"comment" : "LaTeXObj: assoc word in letter rep","filters" : [["IsAssociativeElement","IsWord","IsLetterAssocWordRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PositionFirstComponent","type" : "GAP_Operation","filters" : [[["IsList"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "PositionFirstComponent: for dense plain list","filters" : [["IsDenseList","IsPlistRep","IsSortedList","Tester(IsSortedList)"],[]]},{"rank" : 8,"comment" : "PositionFirstComponent: for sorted list","filters" : [["IsSSortedList","Tester(IS_SSORT_LIST)"],[]]},{"rank" : 3,"comment" : "PositionFirstComponent: for dense list","filters" : [["IsDenseList"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UChar","type" : "GAP_Operation","filters" : [[[]],[[],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 18,"comment" : "UChar","filters" : [["IsInt"]]},{"rank" : 1,"comment" : "UChar","filters" : [["IsChar"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Unicode","type" : "GAP_Operation","filters" : [[[]],[[],[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Unicode","filters" : [["IsStringRep"]]},{"rank" : 2,"comment" : "Unicode","filters" : [["IsList"]]}],"2args" : [{"rank" : 10,"comment" : "Unicode","filters" : [["IsString"],["IsString"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Encode","type" : "GAP_Operation","filters" : [[["IsUnicodeString"]],[["IsUnicodeString"],["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "Encode","filters" : [["IsUnicodeString"]]}],"2args" : [{"rank" : 12,"comment" : "Encode","filters" : [["IsUnicodeString"],["IsString"]]}],"3args" : [{"rank" : 12,"comment" : "Encode","filters" : [["IsUnicodeString"],["IsString"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProcessID","type" : "GAP_Operation","filters" : [[["IsFile"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "ProcessID: system getter","filters" : [["IsAttributeStoringRep","Tester(ProcessID)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ProcessID)","type" : "GAP_Operation","filters" : [[["IsFile"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ProcessID): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ProcessID): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ProcessID)","type" : "GAP_Operation","filters" : [[["IsFile"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IO_Pickle","type" : "GAP_Operation","filters" : [[["IsFile"],[]],[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 0,"comment" : "IO_Pickle: for an object, pickle to string method","filters" : [[]]}],"2args" : [{"rank" : 59,"comment" : "IO_Pickle: for a permutation group","filters" : [["IsFile"],["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 57,"comment" : "IO_Pickle: for a finite field","filters" : [["IsFile"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 44,"comment" : "IO_Pickle: for a matrix group","filters" : [["IsFile"],["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 21,"comment" : "IO_Pickle: for a univariate Laurent polynomial","filters" : [["IsFile"],["IsLaurentPolynomial","Tester(IsLaurentPolynomial)","IsLaurentPolynomialDefaultRep"]]},{"rank" : 21,"comment" : "IO_Pickle: for a string","filters" : [["IsFile"],["IsList","IsStringRep"]]},{"rank" : 19,"comment" : "IO_Pickle: for a univariate rational function","filters" : [["IsFile"],["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsUnivariateRationalFunctionDefaultRep"]]},{"rank" : 19,"comment" : "IO_Pickle: for an integer","filters" : [["IsFile"],["IsInt"]]},{"rank" : 18,"comment" : "IO_Pickle: for rational functions","filters" : [["IsFile"],["IsPolynomialFunction","IsPolynomialDefaultRep"]]},{"rank" : 17,"comment" : "IO_Pickle: for rational functions","filters" : [["IsFile"],["IsPolynomialFunction","IsRationalFunctionDefaultRep"]]},{"rank" : 16,"comment" : "IO_Pickle: for a cyclotomic","filters" : [["IsFile"],["IsCyclotomic"]]},{"rank" : 16,"comment" : "IO_Pickle: for a finite field element","filters" : [["IsFile"],["IsFFE"]]},{"rank" : 14,"comment" : "IO_Pickle: for a float","filters" : [["IsFile"],["IsFloat"]]},{"rank" : 11,"comment" : "IO_Pickle: for a weak pointer object","filters" : [["IsFile"],["IsList","IsWeakPointerObject"]]},{"rank" : 9,"comment" : "IO_Pickle: for a permutation","filters" : [["IsFile"],["IsPerm"]]},{"rank" : 8,"comment" : "IO_Pickle: for a partial perm","filters" : [["IsFile"],["IsPartialPerm"]]},{"rank" : 8,"comment" : "IO_Pickle: for a transformation","filters" : [["IsFile"],["IsTransformation"]]},{"rank" : 4,"comment" : "IO_Pickle: for a real random source","filters" : [["IsFile"],["IsRealRandomSource"]]},{"rank" : 4,"comment" : "IO_Pickle: for a Mersenne twister random source","filters" : [["IsFile"],["IsRandomSource","IsMersenneTwister"]]},{"rank" : 4,"comment" : "IO_Pickle: for a GAP random source","filters" : [["IsFile"],["IsRandomSource","IsGAPRandomSource"]]},{"rank" : 4,"comment" : "IO_Pickle: for the global random source","filters" : [["IsFile"],["IsRandomSource","IsGlobalRandomSource"]]},{"rank" : 3,"comment" : "IO_Pickle: for an operation","filters" : [["IsFile"],["IsFunction","IsOperation"]]},{"rank" : 3,"comment" : "IO_Pickle: IO_Results are forbidden","filters" : [["IsFile"],["IO_Result"]]},{"rank" : 3,"comment" : "IO_Pickle: for a list","filters" : [["IsFile"],["IsList"]]},{"rank" : 2,"comment" : "IO_Pickle: for a function","filters" : [["IsFile"],["IsFunction"]]},{"rank" : 2,"comment" : "IO_Pickle: for a straight line program","filters" : [["IsFile"],["IsStraightLineProgram"]]},{"rank" : 2,"comment" : "IO_Pickle: for a record","filters" : [["IsFile"],["IsRecord"]]},{"rank" : 2,"comment" : "IO_Pickle: for a character","filters" : [["IsFile"],["IsChar"]]},{"rank" : 2,"comment" : "IO_Pickle: for a boolean","filters" : [["IsFile"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IO_Unpickle","type" : "GAP_Operation","filters" : [[["IsFile"]],[["IsStringRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "IO_Unpickle: for a string, unpickle from string method","filters" : [["IsStringRep"]]},{"rank" : 1,"comment" : "IO_Unpickle: for a file","filters" : [["IsFile"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BackgroundJobByFork","type" : "GAP_Operation","filters" : [[["IsFunction"],[]],[["IsFunction"],[],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 1,"comment" : "BackgroundJobByFork: for a function and a list","filters" : [["IsFunction"],[]]}],"3args" : [{"rank" : 2,"comment" : "BackgroundJobByFork: for a function, a list and a record","filters" : [["IsFunction"],[],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIdle","type" : "GAP_Operation","filters" : [[["IsBackgroundJob"]],[["IsWorkerFarmByFork"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "IsIdle: for a worker farm by fork","filters" : [["IsWorkerFarmByFork"]]},{"rank" : 4,"comment" : "IsIdle: for a background job by fork","filters" : [["IsBackgroundJobByFork"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasTerminated","type" : "GAP_Operation","filters" : [[["IsBackgroundJob"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "HasTerminated: for a background job by fork","filters" : [["IsBackgroundJobByFork"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WaitUntilIdle","type" : "GAP_Operation","filters" : [[["IsBackgroundJob"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "WaitUntilIdle: for a background job by fork","filters" : [["IsBackgroundJobByFork"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Kill","type" : "GAP_Operation","filters" : [[["IsBackgroundJob"]],[["IsWorkerFarmByFork"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "Kill: for a worker farm by fork","filters" : [["IsWorkerFarmByFork"]]},{"rank" : 4,"comment" : "Kill: for a background job by fork","filters" : [["IsBackgroundJobByFork"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Pickup","type" : "GAP_Operation","filters" : [[["IsBackgroundJob"]],[["IsWorkerFarmByFork"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 4,"comment" : "Pickup: for a worker farm by fork","filters" : [["IsWorkerFarmByFork"]]},{"rank" : 4,"comment" : "Pickup: for a background job by fork","filters" : [["IsBackgroundJobByFork"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Submit","type" : "GAP_Operation","filters" : [[["IsBackgroundJob"],[]],[["IsWorkerFarmByFork"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 6,"comment" : "Submit: for a worker farm by fork","filters" : [["IsWorkerFarmByFork"],["IsList"]]},{"rank" : 4,"comment" : "Submit: for a background job by fork and an object","filters" : [["IsBackgroundJobByFork"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParTakeFirstResultByFork","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]],[["IsList"],["IsList"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 4,"comment" : "ParTakeFirstResultByFork: for two lists","filters" : [["IsList"],["IsList"]]}],"3args" : [{"rank" : 5,"comment" : "ParTakeFirstResultByFork: for two lists and a record","filters" : [["IsList"],["IsList"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParDoByFork","type" : "GAP_Operation","filters" : [[["IsList"],["IsList"]],[["IsList"],["IsList"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 4,"comment" : "ParDoByFork: for two lists","filters" : [["IsList"],["IsList"]]}],"3args" : [{"rank" : 5,"comment" : "ParDoByFork: for two lists and a record","filters" : [["IsList"],["IsList"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParMapReduceByFork","type" : "GAP_Operation","filters" : [[["IsList"],["IsFunction"],["IsFunction"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 5,"comment" : "ParMapReduceByFork: for a list, two functions and a record","filters" : [["IsList"],["IsFunction"],["IsFunction"],["IsRecord"]]}],"5args" : [],"6args" : []}},{"name" : "ParListByFork","type" : "GAP_Operation","filters" : [[["IsList"],["IsFunction"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 4,"comment" : "ParListByFork: for a list, two functions and a record","filters" : [["IsList"],["IsFunction"],["IsRecord"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ParWorkerFarmByFork","type" : "GAP_Operation","filters" : [[["IsFunction"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "ParWorkerFarmByFork: for a function and a record","filters" : [["IsFunction"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DoQueues","type" : "GAP_Operation","filters" : [[["IsWorkerFarmByFork"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 5,"comment" : "DoQueues: for a worker farm by fork","filters" : [["IsWorkerFarmByFork"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IOHub","type" : "GAP_Operation","filters" : [[]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CloseConnection","type" : "GAP_Operation","filters" : [[["IsIOHub"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 22,"comment" : "CloseConnection: for an IO hub and a positive integer","filters" : [["IsIOHub"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ShutdownServingSocket","type" : "GAP_Operation","filters" : [[["IsIOHub"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "ShutdownServingSocket: for an IO hub","filters" : [["IsIOHub"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Shutdown","type" : "GAP_Operation","filters" : [[["IsIOHub"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "Shutdown: for an IO hub","filters" : [["IsIOHub"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AttachServingSocket","type" : "GAP_Operation","filters" : [[["IsIOHub"],["IsStringRep"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 24,"comment" : "AttachServingSocket: for an address and a port","filters" : [["IsIOHub"],["IsStringRep"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewConnection","type" : "GAP_Operation","filters" : [[["IsIOHub"],["IsInt"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 39,"comment" : "NewConnection: for an IO hub and two integers","filters" : [["IsIOHub"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AcceptNewConnection","type" : "GAP_Operation","filters" : [[["IsIOHub"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "AcceptNewConnection: for an IO hub","filters" : [["IsIOHub"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetInput","type" : "GAP_Operation","filters" : [[["IsIOHub"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "GetInput: for an IO hub and an integer","filters" : [["IsIOHub"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubmitOutput","type" : "GAP_Operation","filters" : [[["IsIOHub"],["IsInt","IsPosRat"],["IsStringRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 24,"comment" : "SubmitOutput: for an IO hub, a positive integers and an obj","filters" : [["IsIOHub"],["IsInt","IsPosRat"],["IsStringRep"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OutputQueue","type" : "GAP_Operation","filters" : [[["IsIOHub"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "OutputQueue: for an IO hub","filters" : [["IsIOHub"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InputQueue","type" : "GAP_Operation","filters" : [[["IsIOHub"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "InputQueue: for an IO hub","filters" : [["IsIOHub"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DoIO","type" : "GAP_Operation","filters" : [[["IsIOHub"],["IsBool"]],[["IsIOHub"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "DoIO: for an IO hub","filters" : [["IsIOHub"]]}],"2args" : [{"rank" : 4,"comment" : "DoIO: for an IO hub and a boolean","filters" : [["IsIOHub"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NewTCPConnection","type" : "GAP_Operation","filters" : [[["IsIOHub"],["IsStringRep"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 24,"comment" : "NewTCPConnection: for an IO hub, an address and a port","filters" : [["IsIOHub"],["IsStringRep"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StoreLenIn8Bytes","type" : "GAP_Operation","filters" : [[["IsStringRep"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "StoreLenIn8Bytes: for a string and a len","filters" : [["IsStringRep"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetLenFrom8Bytes","type" : "GAP_Operation","filters" : [[["IsStringRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "GetLenFrom8Bytes: for a string","filters" : [["IsStringRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RootsFloatOp","type" : "GAP_Operation","filters" : [[["IsList"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ValueInterval","type" : "GAP_Operation","filters" : [[["IsFloatRationalFunction"],["IsFloat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoKernel","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "CoKernel","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Degree","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 43,"comment" : "Degree: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "Degree","filters" : [["IsClassFunction"]]},{"rank" : 13,"comment" : "Degree","filters" : [["IsRationalFunction"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DerivedSeries","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 36,"comment" : "DerivedSeries","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 33,"comment" : "DerivedSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Determinant","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 31,"comment" : "Determinant","filters" : [["IsClassFunction"]]},{"rank" : 30,"comment" : "Determinant","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIrreducible","type" : "GAP_Operation","filters" : [[[]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 43,"comment" : "IsIrreducible: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "IsIrreducible","filters" : [["IsClassFunction"]]},{"rank" : 8,"comment" : "IsIrreducible","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"2args" : [{"rank" : 95,"comment" : "IsIrreducible: for matrix group and field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 41,"comment" : "IsIrreducible: polynomial","filters" : [["IsPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMonomial","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "IsMonomial","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 31,"comment" : "IsMonomial","filters" : [["IsClassFunction"]]},{"rank" : 30,"comment" : "IsMonomial","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 22,"comment" : "IsMonomial","filters" : [["IsOrdinaryTable"]]},{"rank" : 19,"comment" : "IsMonomial","filters" : [["IsInt","IsPosRat"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotent","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 36,"comment" : "IsNilpotent","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 33,"comment" : "IsNilpotent","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsNilpotent","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSimple","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 36,"comment" : "IsSimple","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 33,"comment" : "IsSimple","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsSimple","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAlmostSimple","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "IsAlmostSimple","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsAlmostSimple","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSolvable","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 36,"comment" : "IsSolvable","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 33,"comment" : "IsSolvable","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsSolvable","filters" : [["IsOrdinaryTable"]]},{"rank" : 14,"comment" : "IsSolvable: rational polynomials","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSporadicSimple","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "IsSporadicSimple","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsSporadicSimple","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSupersolvable","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "IsSupersolvable","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsSupersolvable","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPerfect","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 33,"comment" : "IsPerfect","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 22,"comment" : "IsPerfect","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Kernel","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 31,"comment" : "Kernel","filters" : [["IsClassFunction"]]},{"rank" : 7,"comment" : "Kernel","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LowerCentralSeries","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 36,"comment" : "LowerCentralSeries","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 33,"comment" : "LowerCentralSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Rank","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 48,"comment" : "Rank: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 33,"comment" : "Rank","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 30,"comment" : "Rank","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UpperCentralSeries","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 36,"comment" : "UpperCentralSeries","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 33,"comment" : "UpperCentralSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IdGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IdGroup)"]]},{"rank" : 33,"comment" : "IdGroup: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IdGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Gap3CatalogueIdGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "Gap3CatalogueIdGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(Gap3CatalogueIdGroup)"]]},{"rank" : 33,"comment" : "Gap3CatalogueIdGroup: for permgroups or pcgroups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "Gap3CatalogueIdGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Gap3CatalogueIdGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Gap3CatalogueIdGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Gap3CatalogueIdGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Gap3CatalogueIdGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FrattinifactorSize","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "FrattinifactorSize: system getter","filters" : [["IsAttributeStoringRep","Tester(FrattinifactorSize)"]]},{"rank" : 33,"comment" : "FrattinifactorSize: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "FrattinifactorSize: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FrattinifactorSize)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FrattinifactorSize): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FrattinifactorSize): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FrattinifactorSize)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FrattinifactorId","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "FrattinifactorId: system getter","filters" : [["IsAttributeStoringRep","Tester(FrattinifactorId)"]]},{"rank" : 33,"comment" : "FrattinifactorId: generic method for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "FrattinifactorId: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FrattinifactorId)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FrattinifactorId): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FrattinifactorId): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FrattinifactorId)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GaloisType","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "GaloisType: system getter","filters" : [["IsAttributeStoringRep","Tester(GaloisType)"]]},{"rank" : 20,"comment" : "GaloisType: for polynomials","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","Tester(GaloisGroupOnRoots)"]]},{"rank" : 19,"comment" : "GaloisType: for polynomials","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]}],"2args" : [{"rank" : 21,"comment" : "GaloisType: for polynomials and list","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GaloisType)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GaloisType): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GaloisType): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GaloisType)","type" : "GAP_Operation","filters" : [[["IsRationalFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SimsNo","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20061,"comment" : "SimsNo: system getter","filters" : [["IsAttributeStoringRep","Tester(SimsNo)"]]},{"rank" : 58,"comment" : "SimsNo: via `PrimitiveIdentification'","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -17,"comment" : "SimsNo: default method requiring categories and checking properties","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SimsNo)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SimsNo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SimsNo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SimsNo)","type" : "GAP_Operation","filters" : [[["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalBlockDimension","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "MinimalBlockDimension: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimalBlockDimension)"]]},{"rank" : 43,"comment" : "MinimalBlockDimension: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "MinimalBlockDimension: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [{"rank" : 95,"comment" : "MinimalBlockDimension: for matrix group and field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimalBlockDimension)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimalBlockDimension): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimalBlockDimension): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimalBlockDimension)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitiveMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsPrimitiveMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPrimitiveMatrixGroup)"]]},{"rank" : 43,"comment" : "IsPrimitiveMatrixGroup: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IsPrimitiveMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [{"rank" : 95,"comment" : "IsPrimitiveMatrixGroup: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPrimitiveMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPrimitiveMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPrimitiveMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [{"rank" : 95,"comment" : "Setter(IsPrimitiveMatrixGroup): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPrimitiveMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 95,"comment" : "Tester(IsPrimitiveMatrixGroup): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PGAutomorphism","type" : "GAP_Operation","filters" : [[["IsPGroup","Tester(IsPGroup)"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 45,"comment" : "PGAutomorphism: for p-groups","filters" : [["IsPGroup","Tester(IsPGroup)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PGMult","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "PGMult","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 44,"comment" : "PGMult","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PGInverse","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "PGInverse","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 22,"comment" : "PGInverse","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PGPower","type" : "GAP_Operation","filters" : [[["IsInt"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 40,"comment" : "PGPower","filters" : [["IsInt"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]},{"rank" : 40,"comment" : "PGPower","filters" : [["IsInt"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsPGAutomorphismRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PGMultList","type" : "GAP_Operation","filters" : [[["IsList"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "PGMultList","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IrrFacsAlgExtPol","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "IrrFacsAlgExtPol: system getter","filters" : [["IsAttributeStoringRep","Tester(IrrFacsAlgExtPol)"]]},{"rank" : 14,"comment" : "IrrFacsAlgExtPol","filters" : [["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 0,"comment" : "IrrFacsAlgExtPol: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IrrFacsAlgExtPol)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IrrFacsAlgExtPol): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IrrFacsAlgExtPol): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IrrFacsAlgExtPol)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentsOfUnits","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 56,"comment" : "ExponentsOfUnits: for number fields","filters" : [["IsNumberField","Tester(IsNumberField)"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitiveElementOfNumberField","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 54,"comment" : "IsPrimitiveElementOfNumberField: for number field and algebraic element","filters" : [["IsNumberField","Tester(IsNumberField)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelationLattice","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],["IsCollection"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 58,"comment" : "RelationLattice: for matrix fields","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"],["IsCollection"]]},{"rank" : 57,"comment" : "RelationLattice: for fields by polynomial","filters" : [["IsNumberField","Tester(IsNumberField)","IsAlgebraicExtension"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUnitGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsUnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsUnitGroup)"]]},{"rank" : 0,"comment" : "IsUnitGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsUnitGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsUnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsUnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsUnitGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUnitGroupIsomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "IsUnitGroupIsomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsUnitGroupIsomorphism)"]]},{"rank" : 0,"comment" : "IsUnitGroupIsomorphism: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsUnitGroupIsomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsUnitGroupIsomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsUnitGroupIsomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsUnitGroupIsomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNumberFieldByMatrices","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20057,"comment" : "IsNumberFieldByMatrices: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 0,"comment" : "IsNumberFieldByMatrices: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNumberFieldByMatrices)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNumberFieldByMatrices): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNumberFieldByMatrices): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNumberFieldByMatrices)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMultGroupByFieldElemsIsomorphism","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "IsMultGroupByFieldElemsIsomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMultGroupByFieldElemsIsomorphism)"]]},{"rank" : 0,"comment" : "IsMultGroupByFieldElemsIsomorphism: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMultGroupByFieldElemsIsomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMultGroupByFieldElemsIsomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMultGroupByFieldElemsIsomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMultGroupByFieldElemsIsomorphism)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntegerDefiningPolynomial","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20057,"comment" : "IntegerDefiningPolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(IntegerDefiningPolynomial)"]]},{"rank" : 56,"comment" : "IntegerDefiningPolynomial: for matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 55,"comment" : "IntegerDefiningPolynomial: for algebraic extension","filters" : [["IsNumberField","Tester(IsNumberField)","IsAlgebraicExtension"]]},{"rank" : 0,"comment" : "IntegerDefiningPolynomial: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IntegerDefiningPolynomial)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IntegerDefiningPolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IntegerDefiningPolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IntegerDefiningPolynomial)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IntegerPrimitiveElement","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20057,"comment" : "IntegerPrimitiveElement: system getter","filters" : [["IsAttributeStoringRep","Tester(IntegerPrimitiveElement)"]]},{"rank" : 69,"comment" : "IntegerPrimitiveElement: for the rationals","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 56,"comment" : "IntegerPrimitiveElement: for matrix field","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]]},{"rank" : 55,"comment" : "IntegerPrimitiveElement: for algebraic extension","filters" : [["IsNumberField","Tester(IsNumberField)","IsAlgebraicExtension"]]},{"rank" : 0,"comment" : "IntegerPrimitiveElement: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IntegerPrimitiveElement)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IntegerPrimitiveElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IntegerPrimitiveElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IntegerPrimitiveElement)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EquationOrderBasis","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20057,"comment" : "EquationOrderBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(EquationOrderBasis)"]]},{"rank" : 84,"comment" : "EquationOrderBasis: for the rationals","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 54,"comment" : "EquationOrderBasis: for number field","filters" : [["IsNumberField","Tester(IsNumberField)"]]},{"rank" : 0,"comment" : "EquationOrderBasis: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [{"rank" : 54,"comment" : "EquationOrderBasis: for number field and primitive element","filters" : [["IsNumberField","Tester(IsNumberField)"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EquationOrderBasis)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EquationOrderBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EquationOrderBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EquationOrderBasis)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalOrderBasis","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20057,"comment" : "MaximalOrderBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(MaximalOrderBasis)"]]},{"rank" : 84,"comment" : "MaximalOrderBasis: for the rationals","filters" : [["IsNonTrivial","Tester(IsNonTrivial)","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing","IsPrimeField","Tester(IsPrimeField)"]]},{"rank" : 54,"comment" : "MaximalOrderBasis: for number field","filters" : [["IsNumberField","Tester(IsNumberField)"]]},{"rank" : 0,"comment" : "MaximalOrderBasis: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MaximalOrderBasis)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MaximalOrderBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MaximalOrderBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MaximalOrderBasis)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnitGroup","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20057,"comment" : "UnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(UnitGroup)"]]},{"rank" : 54,"comment" : "UnitGroup: for number field","filters" : [["IsNumberField","Tester(IsNumberField)"]]},{"rank" : 0,"comment" : "UnitGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnitGroup)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnitGroup)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FieldOfUnitGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "FieldOfUnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FieldOfUnitGroup)"]]},{"rank" : 0,"comment" : "FieldOfUnitGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FieldOfUnitGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FieldOfUnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FieldOfUnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FieldOfUnitGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsWeightedCollector","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "IsWeightedCollector: system getter","filters" : [["IsAttributeStoringRep","Tester(IsWeightedCollector)"]]},{"rank" : 14,"comment" : "IsWeightedCollector: from-the-left collector","filters" : [["IsMutable","IsPolycyclicCollector","IsFromTheLeftCollectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsWeightedCollector)","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsWeightedCollector): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsWeightedCollector): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsWeightedCollector)","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPolynomialCollector","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsPolynomialCollector: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPolynomialCollector)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPolynomialCollector)","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPolynomialCollector): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPolynomialCollector): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPolynomialCollector)","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UseLibraryCollector","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "UseLibraryCollector: system getter","filters" : [["IsAttributeStoringRep","Tester(UseLibraryCollector)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UseLibraryCollector)","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UseLibraryCollector): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UseLibraryCollector): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UseLibraryCollector)","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FromTheLeftCollector","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 49,"comment" : "FromTheLeftCollector: for free groups","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 18,"comment" : "FromTheLeftCollector: for positive integer","filters" : [["IsInt"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExponentsByObj","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "ExponentsByObj: from-the-left collector, gen-exp-list","filters" : [["IsFromTheLeftCollectorRep"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetPower","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "GetPower: from-the-left collector","filters" : [["IsFromTheLeftCollectorRep"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GetConjugate","type" : "GAP_Operation","filters" : [[["IsPolycyclicCollector"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 49,"comment" : "GetConjugate: from the left collector","filters" : [["IsFromTheLeftCollectorRep"],["IsInt"],["IsInt"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPolycyclicPresentation","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsPolycyclicPresentation: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPolycyclicPresentation)"]]},{"rank" : 13,"comment" : "IsPolycyclicPresentation: FromTheLeftCollector","filters" : [["IsFromTheLeftCollectorRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPolycyclicPresentation)","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPolycyclicPresentation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPolycyclicPresentation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPolycyclicPresentation)","type" : "GAP_Operation","filters" : [[["IsFromTheLeftCollectorRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Exponents","type" : "GAP_Operation","filters" : [[["IsPcpElementRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Exponents: for pcp elements","filters" : [["IsPcpElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NameTag","type" : "GAP_Operation","filters" : [[["IsPcpElementRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "NameTag: for pcp elements","filters" : [["IsPcpElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GenExpList","type" : "GAP_Operation","filters" : [[["IsPcpElementRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "GenExpList: for pcp elements","filters" : [["IsPcpElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Depth","type" : "GAP_Operation","filters" : [[["IsPcpElementRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "Depth: for pcp elements","filters" : [["IsPcpElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeadingExponent","type" : "GAP_Operation","filters" : [[["IsPcpElementRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 2,"comment" : "LeadingExponent: for pcp elements","filters" : [["IsPcpElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TailOfElm","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "TailOfElm: system getter","filters" : [["IsAttributeStoringRep","Tester(TailOfElm)"]]},{"rank" : 8,"comment" : "TailOfElm: for pcp elements","filters" : [["IsPcpElement","IsPcpElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TailOfElm)","type" : "GAP_Operation","filters" : [[["IsPcpElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TailOfElm): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TailOfElm): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TailOfElm)","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelativeOrderPcp","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "RelativeOrderPcp: system getter","filters" : [["IsAttributeStoringRep","Tester(RelativeOrderPcp)"]]},{"rank" : 6,"comment" : "RelativeOrderPcp","filters" : [["IsPcpElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelativeOrderPcp)","type" : "GAP_Operation","filters" : [[["IsPcpElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RelativeOrderPcp): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelativeOrderPcp): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelativeOrderPcp)","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RelativeIndex","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "RelativeIndex: system getter","filters" : [["IsAttributeStoringRep","Tester(RelativeIndex)"]]},{"rank" : 6,"comment" : "RelativeIndex","filters" : [["IsPcpElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RelativeIndex)","type" : "GAP_Operation","filters" : [[["IsPcpElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RelativeIndex): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RelativeIndex): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RelativeIndex)","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FactorOrder","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "FactorOrder: system getter","filters" : [["IsAttributeStoringRep","Tester(FactorOrder)"]]},{"rank" : 6,"comment" : "FactorOrder","filters" : [["IsPcpElement"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FactorOrder)","type" : "GAP_Operation","filters" : [[["IsPcpElement"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FactorOrder): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FactorOrder): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FactorOrder)","type" : "GAP_Operation","filters" : [[["IsPcpElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Igs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "Igs: system getter","filters" : [["IsAttributeStoringRep","Tester(Igs)"]]},{"rank" : 46,"comment" : "Igs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 2,"comment" : "Igs","filters" : [["IsList"]]},{"rank" : -9,"comment" : "Igs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Igs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Igs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Igs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Igs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Ngs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "Ngs: system getter","filters" : [["IsAttributeStoringRep","Tester(Ngs)"]]},{"rank" : 46,"comment" : "Ngs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 2,"comment" : "Ngs","filters" : [["IsList"]]},{"rank" : -9,"comment" : "Ngs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Ngs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Ngs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Ngs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Ngs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Cgs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "Cgs: system getter","filters" : [["IsAttributeStoringRep","Tester(Cgs)"]]},{"rank" : 46,"comment" : "Cgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 2,"comment" : "Cgs","filters" : [["IsList"]]},{"rank" : -9,"comment" : "Cgs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Cgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Cgs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Cgs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Cgs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Collector","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "Collector: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 2,"comment" : "Collector: for pcp elements","filters" : [["IsPcpElementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "EfaSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "EfaSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(EfaSeries)"]]},{"rank" : 48,"comment" : "EfaSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : -9,"comment" : "EfaSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(EfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(EfaSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(EfaSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(EfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcpsOfEfaSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "PcpsOfEfaSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(PcpsOfEfaSeries)"]]},{"rank" : 48,"comment" : "PcpsOfEfaSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : -9,"comment" : "PcpsOfEfaSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcpsOfEfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcpsOfEfaSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcpsOfEfaSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcpsOfEfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismPcpGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsomorphismPcpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismPcpGroup)"]]},{"rank" : 10048,"comment" : "IsomorphismPcpGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 104,"comment" : "IsomorphismPcpGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","CanEasilyComputeWithIndependentGensAbelianGroup"]]},{"rank" : 60,"comment" : "IsomorphismPcpGroup","filters" : [["CategoryCollections(IsPerm)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 51,"comment" : "IsomorphismPcpGroup: for AffineCrystGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 48,"comment" : "IsomorphismPcpGroup: for rational matrix groups (Polenta)","filters" : [["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)"]]},{"rank" : 48,"comment" : "IsomorphismPcpGroup: for PointGroup","filters" : [["IsPointGroup","Tester(IsPointGroup)"]]},{"rank" : 46,"comment" : "IsomorphismPcpGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "IsomorphismPcpGroup: for matrix groups over a finite field (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "IsomorphismPcpGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]]},{"rank" : 44,"comment" : "IsomorphismPcpGroup: for ac groups","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(AlmostCrystallographicInfo)"]]},{"rank" : 0,"comment" : "IsomorphismPcpGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [{"rank" : 64,"comment" : "IsomorphismPcpGroup: for matrix groups (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]},{"rank" : 58,"comment" : "IsomorphismPcpGroup: for matrix fields","filters" : [["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"],["IsCollection"]]},{"rank" : 57,"comment" : "IsomorphismPcpGroup: for fields def. by polynomial","filters" : [["IsNumberField","Tester(IsNumberField)","IsAlgebraicExtension"],["IsCollection"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismPcpGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismPcpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismPcpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismPcpGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcpGroupByEfaSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "PcpGroupByEfaSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(PcpGroupByEfaSeries)"]]},{"rank" : 48,"comment" : "PcpGroupByEfaSeries","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "PcpGroupByEfaSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcpGroupByEfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcpGroupByEfaSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcpGroupByEfaSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcpGroupByEfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SplitExtensionByAutomorphisms","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 98,"comment" : "SplitExtensionByAutomorphisms: for a PcpGroup, a PcpGroup, and a list of automorphisms","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnitriangularMatrixRepresentation","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 54,"comment" : "UnitriangularMatrixRepresentation: for torsion free fin. gen. nilpotent pcp-groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsNilpotentGroup","Tester(IsNilpotentGroup)","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsHomomorphismIntoMatrixGroup","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IsHomomorphismIntoMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsHomomorphismIntoMatrixGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsHomomorphismIntoMatrixGroup)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsHomomorphismIntoMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsHomomorphismIntoMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsHomomorphismIntoMatrixGroup)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SemiSimpleEfaSeries","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "SemiSimpleEfaSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(SemiSimpleEfaSeries)"]]},{"rank" : 48,"comment" : "SemiSimpleEfaSeries: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : -9,"comment" : "SemiSimpleEfaSeries: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SemiSimpleEfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SemiSimpleEfaSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SemiSimpleEfaSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SemiSimpleEfaSeries)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FCCentre","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "FCCentre: system getter","filters" : [["IsAttributeStoringRep","Tester(FCCentre)"]]},{"rank" : 48,"comment" : "FCCentre: FCCentre for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 44,"comment" : "FCCentre: FCCentre for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "FCCentre: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FCCentre)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FCCentre): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FCCentre): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FCCentre)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotentByFinite","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsNilpotentByFinite: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNilpotentByFinite)"]]},{"rank" : 48,"comment" : "IsNilpotentByFinite: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "IsNilpotentByFinite: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNilpotentByFinite)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNilpotentByFinite): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNilpotentByFinite): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNilpotentByFinite)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalSubgroupClassesByIndexOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "MaximalSubgroupClassesByIndexOp: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedMaximalSubgroupClassesByIndexs","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedMaximalSubgroupClassesByIndexs: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedMaximalSubgroupClassesByIndexs)"]]},{"rank" : 33,"comment" : "ComputedMaximalSubgroupClassesByIndexs: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedMaximalSubgroupClassesByIndexs: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedMaximalSubgroupClassesByIndexs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedMaximalSubgroupClassesByIndexs): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedMaximalSubgroupClassesByIndexs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedMaximalSubgroupClassesByIndexs)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MaximalSubgroupClassesByIndex","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "MaximalSubgroupClassesByIndex: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasMaximalSubgroupClassesByIndex","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "HasMaximalSubgroupClassesByIndex: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetMaximalSubgroupClassesByIndex","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 52,"comment" : "SetMaximalSubgroupClassesByIndex: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LowIndexSubgroupClassesOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "LowIndexSubgroupClassesOp: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedLowIndexSubgroupClassess","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedLowIndexSubgroupClassess: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedLowIndexSubgroupClassess)"]]},{"rank" : 33,"comment" : "ComputedLowIndexSubgroupClassess: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedLowIndexSubgroupClassess: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedLowIndexSubgroupClassess)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedLowIndexSubgroupClassess): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedLowIndexSubgroupClassess): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedLowIndexSubgroupClassess)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LowIndexSubgroupClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "LowIndexSubgroupClasses: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasLowIndexSubgroupClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "HasLowIndexSubgroupClasses: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetLowIndexSubgroupClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 52,"comment" : "SetLowIndexSubgroupClasses: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LowIndexNormalSubgroupsOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 67,"comment" : "LowIndexNormalSubgroupsOp: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedLowIndexNormalSubgroupss","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedLowIndexNormalSubgroupss: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedLowIndexNormalSubgroupss)"]]},{"rank" : 33,"comment" : "ComputedLowIndexNormalSubgroupss: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedLowIndexNormalSubgroupss: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedLowIndexNormalSubgroupss)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedLowIndexNormalSubgroupss): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedLowIndexNormalSubgroupss): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedLowIndexNormalSubgroupss)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LowIndexNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "LowIndexNormalSubgroups: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasLowIndexNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "HasLowIndexNormalSubgroups: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetLowIndexNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 52,"comment" : "SetLowIndexNormalSubgroups: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SchurExtension","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "SchurExtension: system getter","filters" : [["IsAttributeStoringRep","Tester(SchurExtension)"]]},{"rank" : 33,"comment" : "SchurExtension: for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SchurExtension: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SchurExtension)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SchurExtension): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SchurExtension): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SchurExtension)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SchurExtensionEpimorphism","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "SchurExtensionEpimorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(SchurExtensionEpimorphism)"]]},{"rank" : 48,"comment" : "SchurExtensionEpimorphism: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "SchurExtensionEpimorphism: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SchurExtensionEpimorphism)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SchurExtensionEpimorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SchurExtensionEpimorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SchurExtensionEpimorphism)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NonAbelianTensorSquare","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "NonAbelianTensorSquare: system getter","filters" : [["IsAttributeStoringRep","Tester(NonAbelianTensorSquare)"]]},{"rank" : 48,"comment" : "NonAbelianTensorSquare","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "NonAbelianTensorSquare: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NonAbelianTensorSquare)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NonAbelianTensorSquare): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NonAbelianTensorSquare): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NonAbelianTensorSquare)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NonAbelianExteriorSquare","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "NonAbelianExteriorSquare: system getter","filters" : [["IsAttributeStoringRep","Tester(NonAbelianExteriorSquare)"]]},{"rank" : 48,"comment" : "NonAbelianExteriorSquare: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "NonAbelianExteriorSquare: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NonAbelianExteriorSquare)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NonAbelianExteriorSquare): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NonAbelianExteriorSquare): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NonAbelianExteriorSquare)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TorsionSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "TorsionSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(TorsionSubgroup)"]]},{"rank" : 48,"comment" : "TorsionSubgroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 44,"comment" : "TorsionSubgroup: for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 35,"comment" : "TorsionSubgroup: for torsion free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsTorsionFree","Tester(IsTorsionFree)"]]},{"rank" : 0,"comment" : "TorsionSubgroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TorsionSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TorsionSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TorsionSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TorsionSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalTorsionSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "NormalTorsionSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalTorsionSubgroup)"]]},{"rank" : 48,"comment" : "NormalTorsionSubgroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 44,"comment" : "NormalTorsionSubgroup: for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 35,"comment" : "NormalTorsionSubgroup: for torsion free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsTorsionFree","Tester(IsTorsionFree)"]]},{"rank" : 0,"comment" : "NormalTorsionSubgroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalTorsionSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalTorsionSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalTorsionSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalTorsionSubgroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FiniteSubgroupClasses","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "FiniteSubgroupClasses: system getter","filters" : [["IsAttributeStoringRep","Tester(FiniteSubgroupClasses)"]]},{"rank" : 48,"comment" : "FiniteSubgroupClasses: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "FiniteSubgroupClasses: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FiniteSubgroupClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FiniteSubgroupClasses): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FiniteSubgroupClasses): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FiniteSubgroupClasses)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTorsionFree","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsTorsionFree: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTorsionFree)"]]},{"rank" : 48,"comment" : "IsTorsionFree: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 45,"comment" : "IsTorsionFree","filters" : [["Tester(IsTrivial)","IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsTorsionFree: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTorsionFree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTorsionFree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTorsionFree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTorsionFree)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFreeAbelian","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsFreeAbelian: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFreeAbelian)"]]},{"rank" : 45,"comment" : "IsFreeAbelian","filters" : [["Tester(IsTrivial)","IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 35,"comment" : "IsFreeAbelian","filters" : [["IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)"]]},{"rank" : 0,"comment" : "IsFreeAbelian: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFreeAbelian)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFreeAbelian): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFreeAbelian): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFreeAbelian)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MemberFunction","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "MemberFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(MemberFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MemberFunction)","type" : "GAP_Operation","filters" : [[["IsClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MemberFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MemberFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MemberFunction)","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMemberOp","type" : "GAP_Operation","filters" : [[[],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10003,"comment" : "IsMemberOp: for class with member function","filters" : [[],["IsClass","Tester(MemberFunction)"]]},{"rank" : 372,"comment" : "IsMemberOp: handled by nice monomorphism","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 70,"comment" : "IsMemberOp: compute from LocalDefinitionFunction","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsSaturated","Tester(IsSaturated)","Tester(LocalDefinitionFunction)"]]},{"rank" : 63,"comment" : "IsMemberOp: compute from boundary","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsSchunckClass","Tester(IsSchunckClass)","Tester(BoundaryFunction)"]]},{"rank" : 56,"comment" : "IsMemberOp: if residual function is known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","Tester(ResidualFunction)"]]},{"rank" : 53,"comment" : "IsMemberOp: for Fitting\/formation product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFittingProductRep","IsFormationProductRep"]]},{"rank" : 49,"comment" : "IsMemberOp: if radical is known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["Tester(RadicalFunction)","IsFittingSetRep"]]},{"rank" : 48,"comment" : "IsMemberOp: for formation product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFormationProductRep"]]},{"rank" : 48,"comment" : "IsMemberOp: if ProjectorFunction is known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsSchunckClass","Tester(IsSchunckClass)","Tester(ProjectorFunction)"]]},{"rank" : 48,"comment" : "IsMemberOp: for FittingSetRep with inj function","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["Tester(InjectorFunction)","IsFittingSetRep"]]},{"rank" : 48,"comment" : "IsMemberOp: for Fitting product","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFittingProductRep"]]},{"rank" : 47,"comment" : "IsMemberOp: if radical is known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","Tester(RadicalFunction)"]]},{"rank" : 46,"comment" : "IsMemberOp: if injector is known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","Tester(InjectorFunction)"]]},{"rank" : 38,"comment" : "IsMemberOp:  for group class by list","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClassByListRep"]]},{"rank" : 35,"comment" : "IsMemberOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsSchunckClass","Tester(IsSchunckClass)"]]},{"rank" : 5,"comment" : "IsMemberOp: for IsClassByUnionRep","filters" : [[],["IsClassByUnionRep"]]},{"rank" : 5,"comment" : "IsMemberOp: for IsClassByIntersectionRep","filters" : [[],["IsClassByIntersectionRep"]]},{"rank" : 5,"comment" : "IsMemberOp: for IsClassByComplementRep","filters" : [[],["IsClassByComplementRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedIsMembers","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "ComputedIsMembers: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedIsMembers)"]]},{"rank" : 0,"comment" : "ComputedIsMembers: default method","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedIsMembers)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedIsMembers): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedIsMembers): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedIsMembers)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMember","type" : "GAP_Operation","filters" : [[[],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "IsMember: default method","filters" : [[],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasIsMember","type" : "GAP_Operation","filters" : [[[],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "HasIsMember: default method","filters" : [[],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetIsMember","type" : "GAP_Operation","filters" : [[[],["IsClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 2,"comment" : "SetIsMember: default method","filters" : [[],["IsClass"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Class","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 1,"comment" : "Class: defined by property function","filters" : [["IsFunction"]]},{"rank" : 1,"comment" : "Class: defined by property function","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Complement","type" : "GAP_Operation","filters" : [[["IsListOrCollection"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 5,"comment" : "Complement: for a class complement","filters" : [["IsClassByComplementRep"]]},{"rank" : 2,"comment" : "Complement: for a class","filters" : [["IsClass"]]},{"rank" : 1,"comment" : "Complement: for a list\/collection","filters" : [["IsListOrCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupClass","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "IsGroupClass: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupClass)"]]},{"rank" : 5,"comment" : "IsGroupClass","filters" : [["IsClassByUnionRep"]]},{"rank" : 5,"comment" : "IsGroupClass","filters" : [["IsClassByIntersectionRep"]]},{"rank" : 5,"comment" : "IsGroupClass","filters" : [["IsClassByComplementRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupClass)","type" : "GAP_Operation","filters" : [[["IsClass"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupClass)","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupClass","type" : "GAP_Operation","filters" : [[[]],[["IsList","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "GroupClass: system getter","filters" : [["IsAttributeStoringRep","Tester(GroupClass)"]]},{"rank" : 2,"comment" : "GroupClass: for group defined by list","filters" : [["IsList"]]},{"rank" : 1,"comment" : "GroupClass: for property function","filters" : [["IsFunction"]]},{"rank" : 1,"comment" : "GroupClass: for record","filters" : [["IsRecord"]]}],"2args" : [{"rank" : 3,"comment" : "GroupClass:  for list and function","filters" : [["IsList"],["IsFunction"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GroupClass)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GroupClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GroupClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GroupClass)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ContainsTrivialGroup","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "ContainsTrivialGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(ContainsTrivialGroup)"]]},{"rank" : 7,"comment" : "ContainsTrivialGroup","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByUnionRep"]]},{"rank" : 7,"comment" : "ContainsTrivialGroup","filters" : [["Tester(IsEmpty)","IsGroupClass","Tester(IsGroupClass)","IsQuotientClosed","Tester(IsQuotientClosed)"]]},{"rank" : 7,"comment" : "ContainsTrivialGroup","filters" : [["Tester(IsEmpty)","IsGroupClass","Tester(IsGroupClass)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)"]]},{"rank" : 7,"comment" : "ContainsTrivialGroup","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByUnionRep"]]},{"rank" : 7,"comment" : "ContainsTrivialGroup","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "ContainsTrivialGroup: for generic group class - test membership","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "ContainsTrivialGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ContainsTrivialGroup)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ContainsTrivialGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ContainsTrivialGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ContainsTrivialGroup)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSubgroupClosed","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsSubgroupClosed: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSubgroupClosed)"]]},{"rank" : 15,"comment" : "IsSubgroupClosed","filters" : [["IsFittingProductRep"]]},{"rank" : 9,"comment" : "IsSubgroupClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsClassByUnionRep"]]},{"rank" : 9,"comment" : "IsSubgroupClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsSubgroupClosed: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsSubgroupClosed: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSubgroupClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSubgroupClosed): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSubgroupClosed): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSubgroupClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormalSubgroupClosed","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsNormalSubgroupClosed: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNormalSubgroupClosed)"]]},{"rank" : 7,"comment" : "IsNormalSubgroupClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByUnionRep"]]},{"rank" : 7,"comment" : "IsNormalSubgroupClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsNormalSubgroupClosed: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsNormalSubgroupClosed: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNormalSubgroupClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNormalSubgroupClosed): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNormalSubgroupClosed): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNormalSubgroupClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsQuotientClosed","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsQuotientClosed: system getter","filters" : [["IsAttributeStoringRep","Tester(IsQuotientClosed)"]]},{"rank" : 7,"comment" : "IsQuotientClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByUnionRep"]]},{"rank" : 7,"comment" : "IsQuotientClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsQuotientClosed: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsQuotientClosed: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsQuotientClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsQuotientClosed): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsQuotientClosed): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsQuotientClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsResiduallyClosed","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsResiduallyClosed: system getter","filters" : [["IsAttributeStoringRep","Tester(IsResiduallyClosed)"]]},{"rank" : 9,"comment" : "IsResiduallyClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsResiduallyClosed: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsResiduallyClosed: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsResiduallyClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsResiduallyClosed): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsResiduallyClosed): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsResiduallyClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormalProductClosed","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsNormalProductClosed: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNormalProductClosed)"]]},{"rank" : 9,"comment" : "IsNormalProductClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsNormalProductClosed: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsNormalProductClosed: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNormalProductClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNormalProductClosed): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNormalProductClosed): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNormalProductClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsDirectProductClosed","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsDirectProductClosed: system getter","filters" : [["IsAttributeStoringRep","Tester(IsDirectProductClosed)"]]},{"rank" : 7,"comment" : "IsDirectProductClosed","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsDirectProductClosed: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsDirectProductClosed: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsDirectProductClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsDirectProductClosed): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsDirectProductClosed): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsDirectProductClosed)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSchunckClass","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsSchunckClass: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSchunckClass)"]]},{"rank" : 13,"comment" : "IsSchunckClass","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsQuotientClosed","Tester(IsQuotientClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsSaturated","Tester(IsSaturated)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsSchunckClass: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsSchunckClass: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSchunckClass)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSchunckClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSchunckClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSchunckClass)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSaturated","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "IsSaturated: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSaturated)"]]},{"rank" : 15,"comment" : "IsSaturated: test if char of top class is subset of char of bot class","filters" : [["IsFormationProductRep"]]},{"rank" : 15,"comment" : "IsSaturated","filters" : [["IsFormationProductRep"]]},{"rank" : 15,"comment" : "IsSaturated","filters" : [["IsFormationProductRep"]]},{"rank" : 7,"comment" : "IsSaturated","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByUnionRep"]]},{"rank" : 7,"comment" : "IsSaturated","filters" : [["IsGroupClass","Tester(IsGroupClass)","IsClassByIntersectionRep"]]},{"rank" : 4,"comment" : "IsSaturated: for generic group class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "IsSaturated: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSaturated)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSaturated): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSaturated): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSaturated)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FittingClass","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "FittingClass: system getter","filters" : [["IsAttributeStoringRep","Tester(FittingClass)"]]},{"rank" : 1,"comment" : "FittingClass","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FittingClass)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FittingClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FittingClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FittingClass)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FittingProduct","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "FittingProduct: for Fitting formation - use FormationProduct","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 24,"comment" : "FittingProduct: of two Fittng classes","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FittingSet","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 34,"comment" : "FittingSet","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFittingSet","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 50,"comment" : "IsFittingSet:  for IsFittingSetRep","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFittingSetRep"]]},{"rank" : 45,"comment" : "IsFittingSet:  for Fitting class","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImageFittingSet","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "ImageFittingSet: for Fitting set - injective case","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsFittingSetRep"]]},{"rank" : 31,"comment" : "ImageFittingSet: for Fitting class - injective case","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 31,"comment" : "ImageFittingSet: for Fitting set","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsFittingSetRep"]]},{"rank" : 29,"comment" : "ImageFittingSet: for Fitting class","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PreImageFittingSet","type" : "GAP_Operation","filters" : [[["IsGeneralMapping"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 33,"comment" : "PreImageFittingSet: for Fitting set - injective case","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsFittingSetRep"]]},{"rank" : 31,"comment" : "PreImageFittingSet: for Fitting class - injective case","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 31,"comment" : "PreImageFittingSet: for Fitting set","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsFittingSetRep"]]},{"rank" : 29,"comment" : "PreImageFittingSet: for Fitting class","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InjectorFunction","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "InjectorFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(InjectorFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InjectorFunction)","type" : "GAP_Operation","filters" : [[["IsClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InjectorFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InjectorFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InjectorFunction)","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RadicalFunction","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "RadicalFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(RadicalFunction)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RadicalFunction)","type" : "GAP_Operation","filters" : [[["IsClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RadicalFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RadicalFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RadicalFunction)","type" : "GAP_Operation","filters" : [[["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitiveSolvableGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsPrimitiveSolvableGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPrimitiveSolvableGroup)"]]},{"rank" : 33,"comment" : "IsPrimitiveSolvableGroup: for generic group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsPrimitiveSolvableGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPrimitiveSolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPrimitiveSolvableGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPrimitiveSolvableGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPrimitiveSolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SchunckClass","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "SchunckClass: system getter","filters" : [["IsAttributeStoringRep","Tester(SchunckClass)"]]},{"rank" : 1,"comment" : "SchunckClass: for record","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SchunckClass)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SchunckClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SchunckClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SchunckClass)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Boundary","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "Boundary: system getter","filters" : [["IsAttributeStoringRep","Tester(Boundary)"]]},{"rank" : 18,"comment" : "Boundary: if BoundaryFunction is known","filters" : [["IsSchunckClass","Tester(IsSchunckClass)","Tester(BoundaryFunction)"]]},{"rank" : 15,"comment" : "Boundary: for Schunck class with local definition","filters" : [["IsSchunckClass","Tester(IsSchunckClass)","Tester(LocalDefinitionFunction)"]]},{"rank" : 4,"comment" : "Boundary: for generic grp class","filters" : [["IsGroupClass","Tester(IsGroupClass)"]]},{"rank" : 0,"comment" : "Boundary: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Boundary)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Boundary): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Boundary): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Boundary)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectorFunction","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "ProjectorFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(ProjectorFunction)"]]},{"rank" : 0,"comment" : "ProjectorFunction: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ProjectorFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ProjectorFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ProjectorFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ProjectorFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BoundaryFunction","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "BoundaryFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(BoundaryFunction)"]]},{"rank" : 0,"comment" : "BoundaryFunction: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BoundaryFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BoundaryFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BoundaryFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BoundaryFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrdinaryFormation","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "OrdinaryFormation: system getter","filters" : [["IsAttributeStoringRep","Tester(OrdinaryFormation)"]]},{"rank" : 1,"comment" : "OrdinaryFormation","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrdinaryFormation)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrdinaryFormation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrdinaryFormation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrdinaryFormation)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FormationProduct","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "FormationProduct: of two Fitting formations","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 24,"comment" : "FormationProduct: of two formations","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SaturatedFormation","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "SaturatedFormation: system getter","filters" : [["IsAttributeStoringRep","Tester(SaturatedFormation)"]]},{"rank" : 1,"comment" : "SaturatedFormation","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SaturatedFormation)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SaturatedFormation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SaturatedFormation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SaturatedFormation)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FittingFormation","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "FittingFormation: system getter","filters" : [["IsAttributeStoringRep","Tester(FittingFormation)"]]},{"rank" : 1,"comment" : "FittingFormation","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FittingFormation)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FittingFormation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FittingFormation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FittingFormation)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FittingFormationProduct","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "FittingFormationProduct: of two Fitting formations","filters" : [["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SaturatedFittingFormation","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "SaturatedFittingFormation: system getter","filters" : [["IsAttributeStoringRep","Tester(SaturatedFittingFormation)"]]},{"rank" : 1,"comment" : "SaturatedFittingFormation","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SaturatedFittingFormation)","type" : "GAP_Operation","filters" : [[[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SaturatedFittingFormation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SaturatedFittingFormation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SaturatedFittingFormation)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ResidualFunction","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "ResidualFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(ResidualFunction)"]]},{"rank" : 0,"comment" : "ResidualFunction: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ResidualFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ResidualFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ResidualFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ResidualFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LocalDefinitionFunction","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20007,"comment" : "LocalDefinitionFunction: system getter","filters" : [["IsAttributeStoringRep","Tester(LocalDefinitionFunction)"]]},{"rank" : 19,"comment" : "LocalDefinitionFunction","filters" : [["IsSaturated","Tester(IsSaturated)","IsFormationProductRep"]]},{"rank" : 19,"comment" : "LocalDefinitionFunction","filters" : [["IsSaturated","Tester(IsSaturated)","IsFormationProductRep"]]},{"rank" : 15,"comment" : "LocalDefinitionFunction: test if char of top class is subset of char of bot class","filters" : [["IsFormationProductRep"]]},{"rank" : 0,"comment" : "LocalDefinitionFunction: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LocalDefinitionFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LocalDefinitionFunction): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LocalDefinitionFunction): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LocalDefinitionFunction)","type" : "GAP_Operation","filters" : [[["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectorOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10048,"comment" : "ProjectorOp: if ProjectorFunction is known","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsSchunckClass","Tester(IsSchunckClass)","Tester(ProjectorFunction)"]]},{"rank" : 397,"comment" : "ProjectorOp: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsSchunckClass","Tester(IsSchunckClass)"]]},{"rank" : 74,"comment" : "ProjectorOp: compute from LocalDefinitionFunction","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsSaturated","Tester(IsSaturated)","Tester(LocalDefinitionFunction)"]]},{"rank" : 71,"comment" : "ProjectorOp: for intersection of group classes which is a local formation","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsSaturated","Tester(IsSaturated)","IsClassByIntersectionRep"]]},{"rank" : 70,"comment" : "ProjectorOp: compute from boundary","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsSchunckClass","Tester(IsSchunckClass)","Tester(BoundaryFunction)"]]},{"rank" : 69,"comment" : "ProjectorOp: for intersection of group classes","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsSchunckClass","Tester(IsSchunckClass)","IsClassByIntersectionRep"]]},{"rank" : 67,"comment" : "ProjectorOp: use MemberFunction","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["Tester(MemberFunction)","IsSchunckClass","Tester(IsSchunckClass)"]]},{"rank" : 66,"comment" : "ProjectorOp: use only membership test","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsSchunckClass","Tester(IsSchunckClass)"]]},{"rank" : 62,"comment" : "ProjectorOp: handled by IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsSchunckClass","Tester(IsSchunckClass)"]]},{"rank" : 37,"comment" : "ProjectorOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedProjectors","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedProjectors: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedProjectors)"]]},{"rank" : 33,"comment" : "ComputedProjectors: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedProjectors: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedProjectors)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedProjectors): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedProjectors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedProjectors)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Projector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "Projector: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasProjector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "HasProjector: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetProjector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "SetProjector: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoveringSubgroupOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 47,"comment" : "CoveringSubgroupOp: for Schunck classes: return projector","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsSchunckClass","Tester(IsSchunckClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedCoveringSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedCoveringSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedCoveringSubgroups)"]]},{"rank" : 33,"comment" : "ComputedCoveringSubgroups: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedCoveringSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedCoveringSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedCoveringSubgroups): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedCoveringSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedCoveringSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoveringSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "CoveringSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasCoveringSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "HasCoveringSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetCoveringSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "SetCoveringSubgroup: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectorFromExtendedBoundaryFunction","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 66,"comment" : "ProjectorFromExtendedBoundaryFunction: for pc group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"],["IsRecord"],["IsBool"]]},{"rank" : 50,"comment" : "ProjectorFromExtendedBoundaryFunction: for solvable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsRecord"],["IsBool"]]},{"rank" : 35,"comment" : "ProjectorFromExtendedBoundaryFunction:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsRecord"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InjectorOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10063,"comment" : "InjectorOp: for FittingSetRep if injector function is known","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["Tester(InjectorFunction)","IsFittingSetRep"]]},{"rank" : 10061,"comment" : "InjectorOp: injector function is known","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","Tester(InjectorFunction)"]]},{"rank" : 395,"comment" : "InjectorOp: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 64,"comment" : "InjectorOp: for pcgs computable groups: use radical","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 62,"comment" : "InjectorOp: for FittingSetRep w\/o injector function","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFittingSetRep"]]},{"rank" : 60,"comment" : "InjectorOp: handled by IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 35,"comment" : "InjectorOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedInjectors","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedInjectors: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedInjectors)"]]},{"rank" : 33,"comment" : "ComputedInjectors: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedInjectors: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedInjectors)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedInjectors): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedInjectors): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedInjectors)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Injector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "Injector: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasInjector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "HasInjector: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetInjector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 35,"comment" : "SetInjector: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerOfPronormalSubgroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 401,"comment" : "NormalizerOfPronormalSubgroup: via nice hom.","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 85,"comment" : "NormalizerOfPronormalSubgroup: use pcgs method","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 81,"comment" : "NormalizerOfPronormalSubgroup: via IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 66,"comment" : "NormalizerOfPronormalSubgroup: for generic groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcgsNormalizerOfPronormalSubgroup","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 44,"comment" : "PcgsNormalizerOfPronormalSubgroup: for pcgs refining an el. ab. series","filters" : [["IsPcgs"],["IsPcgs","Tester(ParentPcgs)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InvariantComplementsOfElAbSection","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 146,"comment" : "InvariantComplementsOfElAbSection: for section of finite solvable group","filters" : [["IsListOrCollection"],["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsBool"]]}],"6args" : []}},{"name" : "ComplementsOfCentralSectionUnderActionNC","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 146,"comment" : "ComplementsOfCentralSectionUnderActionNC: for section of solvable group","filters" : [["IsListOrCollection"],["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsBool"]]}],"6args" : []}},{"name" : "RadicalOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10063,"comment" : "RadicalOp: for FittingSetRep with radical function","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["Tester(RadicalFunction)","IsFittingSetRep"]]},{"rank" : 10061,"comment" : "RadicalOp: if radical function is known","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","Tester(RadicalFunction)"]]},{"rank" : 395,"comment" : "RadicalOp: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 64,"comment" : "RadicalOp: if only in is known","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 63,"comment" : "RadicalOp: for FittingSetRep with injector function","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["Tester(InjectorFunction)","IsFittingSetRep"]]},{"rank" : 63,"comment" : "RadicalOp: for intersection of classes","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsClassByIntersectionRep"]]},{"rank" : 63,"comment" : "RadicalOp: for Fitting product","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFittingProductRep"]]},{"rank" : 63,"comment" : "RadicalOp: if injector is known","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","Tester(InjectorFunction)"]]},{"rank" : 62,"comment" : "RadicalOp: generic method for FittingSetRep","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFittingSetRep"]]},{"rank" : 60,"comment" : "RadicalOp: handled by IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)"]]},{"rank" : 35,"comment" : "RadicalOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedRadicals","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedRadicals: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedRadicals)"]]},{"rank" : 33,"comment" : "ComputedRadicals: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedRadicals: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedRadicals)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedRadicals): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedRadicals): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedRadicals)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Radical","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "Radical: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasRadical","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 35,"comment" : "HasRadical: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetRadical","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 35,"comment" : "SetRadical: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsClass"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OneInvariantSubgroupMaxWrtNProperty","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 51,"comment" : "OneInvariantSubgroupMaxWrtNProperty: for solvable group","filters" : [["IsListOrCollection"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFunction"],["IsFunction"],[]]},{"rank" : 0,"comment" : "OneInvariantSubgroupMaxWrtNProperty:  fallback method to test conditions","filters" : [["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"6args" : []}},{"name" : "AllInvariantSubgroupsWithNProperty","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 51,"comment" : "AllInvariantSubgroupsWithNProperty: for solvable group","filters" : [["IsListOrCollection"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFunction"],["IsFunction"],[]]},{"rank" : 0,"comment" : "AllInvariantSubgroupsWithNProperty:  fallback method to test conditions","filters" : [["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"6args" : []}},{"name" : "OneNormalSubgroupMaxWrtNProperty","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 35,"comment" : "OneNormalSubgroupMaxWrtNProperty: via OneInvariantSubgroupMaxWrtNProperty","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"5args" : [],"6args" : []}},{"name" : "AllNormalSubgroupsWithNProperty","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 35,"comment" : "AllNormalSubgroupsWithNProperty: via AllInvariantSubgroupsWithNProperty","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"5args" : [],"6args" : []}},{"name" : "ResidualOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 10061,"comment" : "ResidualOp: for group and formation with ResidualFunction","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","Tester(ResidualFunction)"]]},{"rank" : 395,"comment" : "ResidualOp: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)"]]},{"rank" : 69,"comment" : "ResidualOp: for locally defined formation","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsSaturated","Tester(IsSaturated)","Tester(LocalDefinitionFunction)"]]},{"rank" : 67,"comment" : "ResidualOp: for group and intersection of formations","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsClassByIntersectionRep"]]},{"rank" : 64,"comment" : "ResidualOp: generic method for pcgs computable group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)"]]},{"rank" : 63,"comment" : "ResidualOp: for group and formation product","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFormationProductRep"]]},{"rank" : 60,"comment" : "ResidualOp: handled by IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)"]]},{"rank" : 37,"comment" : "ResidualOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedResiduals","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedResiduals: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedResiduals)"]]},{"rank" : 33,"comment" : "ComputedResiduals: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedResiduals: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedResiduals)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedResiduals): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedResiduals): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedResiduals)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Residual","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "Residual: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasResidual","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 37,"comment" : "HasResidual: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetResidual","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 37,"comment" : "SetResidual: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsGroupClass","Tester(IsGroupClass)"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacteristicSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "CharacteristicSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(CharacteristicSubgroups)"]]},{"rank" : 379,"comment" : "CharacteristicSubgroups: via NiceMonomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 48,"comment" : "CharacteristicSubgroups: via IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 38,"comment" : "CharacteristicSubgroups: normal complement method for pcgs computable groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 0,"comment" : "CharacteristicSubgroups:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "CharacteristicSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CharacteristicSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CharacteristicSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CharacteristicSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CharacteristicSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OneInvariantSubgroupMinWrtQProperty","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 51,"comment" : "OneInvariantSubgroupMinWrtQProperty: for solvable group","filters" : [["IsListOrCollection"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFunction"],["IsFunction"],[]]},{"rank" : 0,"comment" : "OneInvariantSubgroupMinWrtQProperty:  fallback method to test conditions","filters" : [["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"6args" : []}},{"name" : "AllInvariantSubgroupsWithQProperty","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [{"rank" : 97,"comment" : "AllInvariantSubgroupsWithQProperty: for solvable group","filters" : [["IsListOrCollection"],["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsFunction"],["IsFunction"],[]]},{"rank" : 0,"comment" : "AllInvariantSubgroupsWithQProperty:  fallback method to test conditions","filters" : [["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"6args" : []}},{"name" : "OneNormalSubgroupMinWrtQProperty","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 35,"comment" : "OneNormalSubgroupMinWrtQProperty: try OneInvariantSubgroupMinWrtQProperty","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"5args" : [],"6args" : []}},{"name" : "AllNormalSubgroupsWithQProperty","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 35,"comment" : "AllNormalSubgroupsWithQProperty: try AllInvariantSubgroupsWithQProperty","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsFunction"],["IsFunction"],[]]}],"5args" : [],"6args" : []}},{"name" : "NormalGeneratorsOfNilpotentResidual","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "NormalGeneratorsOfNilpotentResidual: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalGeneratorsOfNilpotentResidual)"]]},{"rank" : 52,"comment" : "NormalGeneratorsOfNilpotentResidual: for pcgs computable group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 33,"comment" : "NormalGeneratorsOfNilpotentResidual: generic method - use lower central series","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NormalGeneratorsOfNilpotentResidual: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalGeneratorsOfNilpotentResidual)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalGeneratorsOfNilpotentResidual): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalGeneratorsOfNilpotentResidual): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalGeneratorsOfNilpotentResidual)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralizesLayer","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsModuloPcgs"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 23,"comment" : "CentralizesLayer: for empty list","filters" : [["IsListOrCollection","IsEmpty","Tester(IsEmpty)"],["IsModuloPcgs"]]},{"rank" : 21,"comment" : "CentralizesLayer: generic method","filters" : [["IsListOrCollection"],["IsModuloPcgs"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CompositionSeriesUnderAction","type" : "GAP_Operation","filters" : [[["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 36,"comment" : "CompositionSeriesUnderAction: for solvable group","filters" : [["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 0,"comment" : "CompositionSeriesUnderAction:  fallback method to test conditions","filters" : [["IsListOrCollection"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SiftedPcElementWrtPcSequence","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsListOrCollection"],["IsList"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 31,"comment" : "SiftedPcElementWrtPcSequence: method for an empty collection","filters" : [["IsPcgs"],["IsListOrCollection","IsEmpty","Tester(IsEmpty)"],["IsList"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 29,"comment" : "SiftedPcElementWrtPcSequence: generic method","filters" : [["IsPcgs"],["IsListOrCollection"],["IsList"],["IsMultiplicativeElementWithInverse"]]}],"5args" : [],"6args" : []}},{"name" : "AddPcElementToPcSequence","type" : "GAP_Operation","filters" : [[["IsPcgs"],["IsListOrCollection"],["IsList"],["IsMultiplicativeElementWithInverse"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 46,"comment" : "AddPcElementToPcSequence: method for an empty collection","filters" : [["IsPcgs"],["IsListOrCollection","IsEmpty","Tester(IsEmpty)"],["IsList","IsEmpty","Tester(IsEmpty)"],["IsMultiplicativeElementWithInverse"]]},{"rank" : 29,"comment" : "AddPcElementToPcSequence: generic method","filters" : [["IsPcgs"],["IsListOrCollection"],["IsList"],["IsMultiplicativeElementWithInverse"]]}],"5args" : [],"6args" : []}},{"name" : "PrimePowerGensPcSequence","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "PrimePowerGensPcSequence: system getter","filters" : [["IsAttributeStoringRep","Tester(PrimePowerGensPcSequence)"]]},{"rank" : 53,"comment" : "PrimePowerGensPcSequence: for group with special pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SpecialPcgs)"]]},{"rank" : 38,"comment" : "PrimePowerGensPcSequence: for group which can easily compute a pcgs","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 0,"comment" : "PrimePowerGensPcSequence: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PrimePowerGensPcSequence)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PrimePowerGensPcSequence): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PrimePowerGensPcSequence): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PrimePowerGensPcSequence)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NilpotentProjector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "NilpotentProjector: system getter","filters" : [["IsAttributeStoringRep","Tester(NilpotentProjector)"]]},{"rank" : 48,"comment" : "NilpotentProjector: for finite solvable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 0,"comment" : "NilpotentProjector:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "NilpotentProjector: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NilpotentProjector)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NilpotentProjector): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NilpotentProjector): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NilpotentProjector)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SupersolvableProjector","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "SupersolvableProjector: system getter","filters" : [["IsAttributeStoringRep","Tester(SupersolvableProjector)"]]},{"rank" : 48,"comment" : "SupersolvableProjector: for finite solvable groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 0,"comment" : "SupersolvableProjector:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SupersolvableProjector: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SupersolvableProjector)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SupersolvableProjector): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SupersolvableProjector): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SupersolvableProjector)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SolvableSocle","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "SolvableSocle: system getter","filters" : [["IsAttributeStoringRep","Tester(SolvableSocle)"]]},{"rank" : 379,"comment" : "SolvableSocle: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 52,"comment" : "SolvableSocle: for solvable group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "SolvableSocle: via IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 44,"comment" : "SolvableSocle: for finite group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SolvableSocle:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SolvableSocle: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SolvableSocle)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SolvableSocle): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SolvableSocle): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SolvableSocle)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SocleComponents","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "SocleComponents: system getter","filters" : [["IsAttributeStoringRep","Tester(SocleComponents)"]]},{"rank" : 379,"comment" : "SocleComponents: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 48,"comment" : "SocleComponents: for solvable group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 0,"comment" : "SocleComponents:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SocleComponents: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SocleComponents)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SocleComponents): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SocleComponents): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SocleComponents)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SolvableSocleComponents","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "SolvableSocleComponents: system getter","filters" : [["IsAttributeStoringRep","Tester(SolvableSocleComponents)"]]},{"rank" : 379,"comment" : "SolvableSocleComponents: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 53,"comment" : "SolvableSocleComponents: for solvable group with known Fitting subgroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingSubgroup)","CanEasilyComputePcgs"]]},{"rank" : 52,"comment" : "SolvableSocleComponents: for solvable group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "SolvableSocleComponents: via IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 48,"comment" : "SolvableSocleComponents: via IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 44,"comment" : "SolvableSocleComponents: for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SolvableSocleComponents:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SolvableSocleComponents: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SolvableSocleComponents)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SolvableSocleComponents): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SolvableSocleComponents): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SolvableSocleComponents)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PSocleComponentsOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 398,"comment" : "PSocleComponentsOp: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsInt","IsPosRat"]]},{"rank" : 67,"comment" : "PSocleComponentsOp: via IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsInt","IsPosRat"]]},{"rank" : 64,"comment" : "PSocleComponentsOp: for finite group with SolvableSocleComponents","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(SolvableSocleComponents)"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "PSocleComponentsOp: for finite group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "PSocleComponentsOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedPSocleComponentss","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedPSocleComponentss: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedPSocleComponentss)"]]},{"rank" : 33,"comment" : "ComputedPSocleComponentss: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedPSocleComponentss: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedPSocleComponentss)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedPSocleComponentss): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedPSocleComponentss): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedPSocleComponentss)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PSocleComponents","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "PSocleComponents: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasPSocleComponents","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "HasPSocleComponents: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPSocleComponents","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 52,"comment" : "SetPSocleComponents: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PSocleOp","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 398,"comment" : "PSocleOp: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsInt","IsPosRat"]]},{"rank" : 71,"comment" : "PSocleOp: for pcgs computable group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"],["IsInt","IsPosRat"]]},{"rank" : 67,"comment" : "PSocleOp: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsInt","IsPosRat"]]},{"rank" : 63,"comment" : "PSocleOp: for finite group","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]},{"rank" : 0,"comment" : "PSocleOp:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedPSocles","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "ComputedPSocles: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedPSocles)"]]},{"rank" : 33,"comment" : "ComputedPSocles: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "ComputedPSocles: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedPSocles)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedPSocles): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedPSocles): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedPSocles)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PSocle","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "PSocle: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasPSocle","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 52,"comment" : "HasPSocle: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetPSocle","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 52,"comment" : "SetPSocle: default method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AbelianMinimalNormalSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "AbelianMinimalNormalSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(AbelianMinimalNormalSubgroups)"]]},{"rank" : 379,"comment" : "AbelianMinimalNormalSubgroups: handled by nice monomorphism","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 53,"comment" : "AbelianMinimalNormalSubgroups: complements of chief factors, for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(FittingSubgroup)","CanEasilyComputePcgs"]]},{"rank" : 52,"comment" : "AbelianMinimalNormalSubgroups: complements of chief factors, for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CanEasilyComputePcgs"]]},{"rank" : 48,"comment" : "AbelianMinimalNormalSubgroups: handled by IsomorphismPcGroup","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 44,"comment" : "AbelianMinimalNormalSubgroups: complements of chief factors, for finite groups","filters" : [["IsFinite","Tester(IsFinite)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "AbelianMinimalNormalSubgroups:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "AbelianMinimalNormalSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AbelianMinimalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AbelianMinimalNormalSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AbelianMinimalNormalSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AbelianMinimalNormalSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LinesOfStraightLineDecision","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "LinesOfStraightLineDecision: system getter","filters" : [["IsAttributeStoringRep","Tester(LinesOfStraightLineDecision)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LinesOfStraightLineDecision)","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LinesOfStraightLineDecision): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LinesOfStraightLineDecision): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LinesOfStraightLineDecision)","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NrInputsOfStraightLineDecision","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "NrInputsOfStraightLineDecision: system getter","filters" : [["IsAttributeStoringRep","Tester(NrInputsOfStraightLineDecision)"]]},{"rank" : 1,"comment" : "NrInputsOfStraightLineDecision: for a straight line decision","filters" : [["IsStraightLineDecision"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NrInputsOfStraightLineDecision)","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NrInputsOfStraightLineDecision): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NrInputsOfStraightLineDecision): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NrInputsOfStraightLineDecision)","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ResultOfStraightLineDecision","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"],["IsHomogeneousList"]],[["IsStraightLineDecision"],["IsHomogeneousList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 5,"comment" : "ResultOfStraightLineDecision: for a straight line decision, and a homogeneous list","filters" : [["IsStraightLineDecision"],["IsHomogeneousList"]]}],"3args" : [{"rank" : 6,"comment" : "ResultOfStraightLineDecision: for a straight line decision, a homogeneous list, and a function","filters" : [["IsStraightLineDecision"],["IsHomogeneousList"],["IsFunction"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StraightLineProgramFromStraightLineDecision","type" : "GAP_Operation","filters" : [[["IsStraightLineDecision"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 1,"comment" : "StraightLineProgramFromStraightLineDecision: for a straight line decision","filters" : [["IsStraightLineDecision"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsBBoxProgram","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]],[["IsStraightLineDecision"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AsBBoxProgram: system getter","filters" : [["IsAttributeStoringRep","Tester(AsBBoxProgram)"]]},{"rank" : 1,"comment" : "AsBBoxProgram: for a straight line decision","filters" : [["IsStraightLineDecision"]]},{"rank" : 1,"comment" : "AsBBoxProgram: for a straight line program","filters" : [["IsStraightLineProgram"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsBBoxProgram)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"],[]],[["IsStraightLineDecision"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsBBoxProgram): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsBBoxProgram): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsBBoxProgram)","type" : "GAP_Operation","filters" : [[["IsStraightLineProgram"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsStraightLineProgram","type" : "GAP_Operation","filters" : [[["IsBBoxProgram"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AsStraightLineProgram: system getter","filters" : [["IsAttributeStoringRep","Tester(AsStraightLineProgram)"]]},{"rank" : 1,"comment" : "AsStraightLineProgram: for a black box program","filters" : [["IsBBoxProgram"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsStraightLineProgram)","type" : "GAP_Operation","filters" : [[["IsBBoxProgram"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsStraightLineProgram): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsStraightLineProgram): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsStraightLineProgram)","type" : "GAP_Operation","filters" : [[["IsBBoxProgram"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsStraightLineDecision","type" : "GAP_Operation","filters" : [[["IsBBoxProgram"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "AsStraightLineDecision: system getter","filters" : [["IsAttributeStoringRep","Tester(AsStraightLineDecision)"]]},{"rank" : 1,"comment" : "AsStraightLineDecision: for a black box program","filters" : [["IsBBoxProgram"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AsStraightLineDecision)","type" : "GAP_Operation","filters" : [[["IsBBoxProgram"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AsStraightLineDecision): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AsStraightLineDecision): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AsStraightLineDecision)","type" : "GAP_Operation","filters" : [[["IsBBoxProgram"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MeatAxeString","type" : "GAP_Operation","filters" : [[["IsTable"],["IsInt","IsPosRat"]],[["IsList","CategoryCollections(IsPerm)"],["IsInt","IsPosRat"]],[["IsPerm"],["IsInt","IsPosRat"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 82,"comment" : "MeatAxeString: for list of permutations, and degree","filters" : [["IsList","CategoryCollections(IsPerm)"],["IsInt","IsPosRat"]]},{"rank" : 61,"comment" : "MeatAxeString: for matrix over a finite field, and field order","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsFFE))"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 29,"comment" : "MeatAxeString: for permutation, field order, and dimensions","filters" : [["IsPerm"],["IsInt","IsPosRat"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Maxes","type" : "GAP_Operation","filters" : [[["IsUnknown"]],[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20019,"comment" : "Maxes: system getter","filters" : [["IsAttributeStoringRep","Tester(Maxes)"]]},{"rank" : 16,"comment" : "Maxes","filters" : [["IsUnknown"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Maxes)","type" : "GAP_Operation","filters" : [[["IsUnknown"],[]],[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Maxes): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Maxes): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Maxes)","type" : "GAP_Operation","filters" : [[["IsUnknown"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AtlasRepInfoRecord","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "AtlasRepInfoRecord: system getter","filters" : [["IsAttributeStoringRep","Tester(AtlasRepInfoRecord)"]]},{"rank" : 0,"comment" : "AtlasRepInfoRecord: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AtlasRepInfoRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AtlasRepInfoRecord): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AtlasRepInfoRecord): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AtlasRepInfoRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Browse","type" : "GAP_Operation","filters" : [[[]],[[],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 52,"comment" : "Browse: [ IsFFECollColl and IsMatrix ]","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 42,"comment" : "Browse: [ IsFFECollColl and IsMatrix ]","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsFFE))"]]},{"rank" : 41,"comment" : "Browse: [ IsZmodnZObjNonprimeCollColl and IsMatrix ]","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]]},{"rank" : 20,"comment" : "Browse: [ IsNearlyCharacterTable ]","filters" : [["IsNearlyCharacterTable"]]},{"rank" : 3,"comment" : "Browse: [ IsDenseList ]","filters" : [["IsDenseList"]]},{"rank" : 1,"comment" : "Browse: [ IsTableOfMarks ]","filters" : [["IsTableOfMarks"]]}],"2args" : [{"rank" : 21,"comment" : "Browse: [ IsNearlyCharacterTable, IsRecord ]","filters" : [["IsNearlyCharacterTable"],["IsRecord"]]},{"rank" : 2,"comment" : "Browse: [ IsTableOfMarks, IsRecord ]","filters" : [["IsTableOfMarks"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CASInfo","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "CASInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(CASInfo)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CASInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CASInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CASInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CASInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConstructionInfoCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ConstructionInfoCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(ConstructionInfoCharacterTable)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConstructionInfoCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConstructionInfoCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConstructionInfoCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConstructionInfoCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FusionToTom","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "FusionToTom: system getter","filters" : [["IsAttributeStoringRep","Tester(FusionToTom)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FusionToTom)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FusionToTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FusionToTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FusionToTom)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ProjectivesInfo","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ProjectivesInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(ProjectivesInfo)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ProjectivesInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ProjectivesInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ProjectivesInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ProjectivesInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExtensionInfoCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "ExtensionInfoCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(ExtensionInfoCharacterTable)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ExtensionInfoCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ExtensionInfoCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ExtensionInfoCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ExtensionInfoCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupInfoForCharacterTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "GroupInfoForCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(GroupInfoForCharacterTable)"]]},{"rank" : 25,"comment" : "GroupInfoForCharacterTable: [ IsOrdinaryTable and IsLibraryCharacterTableRep ]","filters" : [["IsOrdinaryTable","IsLibraryCharacterTableRep"]]},{"rank" : 5,"comment" : "GroupInfoForCharacterTable: [ IsString ]","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GroupInfoForCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GroupInfoForCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GroupInfoForCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GroupInfoForCharacterTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KnowsSomeGroupInfo","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "KnowsSomeGroupInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(KnowsSomeGroupInfo)"]]},{"rank" : 22,"comment" : "KnowsSomeGroupInfo: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KnowsSomeGroupInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KnowsSomeGroupInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KnowsSomeGroupInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KnowsSomeGroupInfo)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNontrivialDirectProduct","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsNontrivialDirectProduct: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNontrivialDirectProduct)"]]},{"rank" : 22,"comment" : "IsNontrivialDirectProduct: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNontrivialDirectProduct)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNontrivialDirectProduct): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNontrivialDirectProduct): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNontrivialDirectProduct)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "KnowsDeligneLusztigNames","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "KnowsDeligneLusztigNames: system getter","filters" : [["IsAttributeStoringRep","Tester(KnowsDeligneLusztigNames)"]]},{"rank" : 22,"comment" : "KnowsDeligneLusztigNames: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(KnowsDeligneLusztigNames)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(KnowsDeligneLusztigNames): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(KnowsDeligneLusztigNames): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(KnowsDeligneLusztigNames)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsDuplicateTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IsDuplicateTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IsDuplicateTable)"]]},{"rank" : 22,"comment" : "IsDuplicateTable: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsDuplicateTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsDuplicateTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsDuplicateTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsDuplicateTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdentifierOfMainTable","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IdentifierOfMainTable: system getter","filters" : [["IsAttributeStoringRep","Tester(IdentifierOfMainTable)"]]},{"rank" : 22,"comment" : "IdentifierOfMainTable: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdentifierOfMainTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdentifierOfMainTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdentifierOfMainTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdentifierOfMainTable)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdentifiersOfDuplicateTables","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "IdentifiersOfDuplicateTables: system getter","filters" : [["IsAttributeStoringRep","Tester(IdentifiersOfDuplicateTables)"]]},{"rank" : 22,"comment" : "IdentifiersOfDuplicateTables: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]},{"rank" : 5,"comment" : "IdentifiersOfDuplicateTables: [ IsString ]","filters" : [["IsString"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdentifiersOfDuplicateTables)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdentifiersOfDuplicateTables): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdentifiersOfDuplicateTables): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdentifiersOfDuplicateTables)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeligneLusztigNames","type" : "GAP_Operation","filters" : [[["IsCharacterTable"]],[["IsString"]],[["IsRecord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20024,"comment" : "DeligneLusztigNames: system getter","filters" : [["IsAttributeStoringRep","Tester(DeligneLusztigNames)"]]},{"rank" : 21,"comment" : "DeligneLusztigNames: [ IsCharacterTable ]","filters" : [["IsCharacterTable"]]},{"rank" : 5,"comment" : "DeligneLusztigNames: [ IsString ]","filters" : [["IsString"]]},{"rank" : 1,"comment" : "DeligneLusztigNames: [ IsRecord ]","filters" : [["IsRecord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DeligneLusztigNames)","type" : "GAP_Operation","filters" : [[["IsCharacterTable"],[]],[["IsString"],[]],[["IsRecord"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DeligneLusztigNames): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DeligneLusztigNames): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DeligneLusztigNames)","type" : "GAP_Operation","filters" : [[["IsCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DeligneLusztigName","type" : "GAP_Operation","filters" : [[["IsCharacter","Tester(IsCharacter)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "DeligneLusztigName: system getter","filters" : [["IsAttributeStoringRep","Tester(DeligneLusztigName)"]]},{"rank" : 35,"comment" : "DeligneLusztigName: [ IsCharacter ]","filters" : [["IsCharacter","Tester(IsCharacter)"]]},{"rank" : 0,"comment" : "DeligneLusztigName: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DeligneLusztigName)","type" : "GAP_Operation","filters" : [[["IsCharacter","Tester(IsCharacter)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DeligneLusztigName): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DeligneLusztigName): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DeligneLusztigName)","type" : "GAP_Operation","filters" : [[["IsCharacter","Tester(IsCharacter)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnipotentCharacter","type" : "GAP_Operation","filters" : [[["IsCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 21,"comment" : "UnipotentCharacter: [ IsCharacterTable, IsObject ]","filters" : [["IsCharacterTable"],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FingerprintOfCharacterTable","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20025,"comment" : "FingerprintOfCharacterTable: system getter","filters" : [["IsAttributeStoringRep","Tester(FingerprintOfCharacterTable)"]]},{"rank" : 22,"comment" : "FingerprintOfCharacterTable: [ IsOrdinaryTable ]","filters" : [["IsOrdinaryTable"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FingerprintOfCharacterTable)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FingerprintOfCharacterTable): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FingerprintOfCharacterTable): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FingerprintOfCharacterTable)","type" : "GAP_Operation","filters" : [[["IsOrdinaryTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpinSymIngredients","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20023,"comment" : "SpinSymIngredients: system getter","filters" : [["IsAttributeStoringRep","Tester(SpinSymIngredients)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SpinSymIngredients)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SpinSymIngredients): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SpinSymIngredients): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SpinSymIngredients)","type" : "GAP_Operation","filters" : [[["IsNearlyCharacterTable"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NamesLibTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]],[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "NamesLibTom: system getter","filters" : [["IsAttributeStoringRep","Tester(NamesLibTom)"]]},{"rank" : 5,"comment" : "NamesLibTom","filters" : [["IsString"]]},{"rank" : 4,"comment" : "NamesLibTom","filters" : [["IsTableOfMarks","IsLibTomRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NamesLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"],[]],[["IsString"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NamesLibTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NamesLibTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NamesLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NotifiedFusionsOfLibTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]],[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "NotifiedFusionsOfLibTom: system getter","filters" : [["IsAttributeStoringRep","Tester(NotifiedFusionsOfLibTom)"]]},{"rank" : 5,"comment" : "NotifiedFusionsOfLibTom","filters" : [["IsString"]]},{"rank" : 4,"comment" : "NotifiedFusionsOfLibTom","filters" : [["IsTableOfMarks","IsLibTomRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NotifiedFusionsOfLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"],[]],[["IsString"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NotifiedFusionsOfLibTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NotifiedFusionsOfLibTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NotifiedFusionsOfLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FusionsOfLibTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]],[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FusionsOfLibTom: system getter","filters" : [["IsAttributeStoringRep","Tester(FusionsOfLibTom)"]]},{"rank" : 5,"comment" : "FusionsOfLibTom","filters" : [["IsString"]]},{"rank" : 4,"comment" : "FusionsOfLibTom","filters" : [["IsTableOfMarks","IsLibTomRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FusionsOfLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"],[]],[["IsString"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FusionsOfLibTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FusionsOfLibTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FusionsOfLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NotifiedFusionsToLibTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]],[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "NotifiedFusionsToLibTom: system getter","filters" : [["IsAttributeStoringRep","Tester(NotifiedFusionsToLibTom)"]]},{"rank" : 5,"comment" : "NotifiedFusionsToLibTom","filters" : [["IsString"]]},{"rank" : 4,"comment" : "NotifiedFusionsToLibTom","filters" : [["IsTableOfMarks","IsLibTomRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NotifiedFusionsToLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"],[]],[["IsString"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NotifiedFusionsToLibTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NotifiedFusionsToLibTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NotifiedFusionsToLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FusionsToLibTom","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]],[["IsString"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20005,"comment" : "FusionsToLibTom: system getter","filters" : [["IsAttributeStoringRep","Tester(FusionsToLibTom)"]]},{"rank" : 5,"comment" : "FusionsToLibTom","filters" : [["IsString"]]},{"rank" : 4,"comment" : "FusionsToLibTom","filters" : [["IsTableOfMarks","IsLibTomRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FusionsToLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"],[]],[["IsString"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FusionsToLibTom): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FusionsToLibTom): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FusionsToLibTom)","type" : "GAP_Operation","filters" : [[["IsTableOfMarks","IsLibTomRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "StandardGeneratorsInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["IsTableOfMarks"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "StandardGeneratorsInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(StandardGeneratorsInfo)"]]},{"rank" : 0,"comment" : "StandardGeneratorsInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(StandardGeneratorsInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["IsTableOfMarks"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(StandardGeneratorsInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(StandardGeneratorsInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(StandardGeneratorsInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IteratedF","type" : "GAP_Operation","filters" : [[["IsList"],["IsFunction"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 3,"comment" : "IteratedF","filters" : [["IsList"],["IsFunction"]]}],"3args" : [{"rank" : 3,"comment" : "IteratedF","filters" : [["IsList"],["IsFunction"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TrivialInvAutomaton","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 48,"comment" : "TrivialInvAutomaton","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InvAutomatonInsertGenerator","type" : "GAP_Operation","filters" : [[["IsMutable","IsInvAutomatonCategory"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 15,"comment" : "InvAutomatonInsertGenerator","filters" : [["IsMutable","IsSimpleInvAutomatonRep"],["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FGA_States","type" : "GAP_Operation","filters" : [[["IsInvAutomatonCategory"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "FGA_States: system getter","filters" : [["IsAttributeStoringRep","Tester(FGA_States)"]]},{"rank" : 6,"comment" : "FGA_States: for simple inverse Automata","filters" : [["IsSimpleInvAutomatonRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FGA_States)","type" : "GAP_Operation","filters" : [[["IsInvAutomatonCategory"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FGA_States): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FGA_States): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FGA_States)","type" : "GAP_Operation","filters" : [[["IsInvAutomatonCategory"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FGA_GeneratorsLetterRep","type" : "GAP_Operation","filters" : [[["IsInvAutomatonCategory"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "FGA_GeneratorsLetterRep: system getter","filters" : [["IsAttributeStoringRep","Tester(FGA_GeneratorsLetterRep)"]]},{"rank" : 6,"comment" : "FGA_GeneratorsLetterRep: for simple inverse Automata","filters" : [["IsSimpleInvAutomatonRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FGA_GeneratorsLetterRep)","type" : "GAP_Operation","filters" : [[["IsInvAutomatonCategory"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FGA_GeneratorsLetterRep): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FGA_GeneratorsLetterRep): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FGA_GeneratorsLetterRep)","type" : "GAP_Operation","filters" : [[["IsInvAutomatonCategory"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGeneratorsOfGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "FreeGeneratorsOfGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGeneratorsOfGroup)"]]},{"rank" : 50,"comment" : "FreeGeneratorsOfGroup: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 11,"comment" : "FreeGeneratorsOfGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGeneratorsOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGeneratorsOfGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGeneratorsOfGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGeneratorsOfGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RankOfFreeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "RankOfFreeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(RankOfFreeGroup)"]]},{"rank" : 51,"comment" : "RankOfFreeGroup: for a whole free group","filters" : [["IsWholeFamily","Tester(IsWholeFamily)","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 50,"comment" : "RankOfFreeGroup: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 11,"comment" : "RankOfFreeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RankOfFreeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RankOfFreeGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RankOfFreeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RankOfFreeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGroupAutomaton","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "FreeGroupAutomaton: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGroupAutomaton)"]]},{"rank" : 50,"comment" : "FreeGroupAutomaton: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 11,"comment" : "FreeGroupAutomaton: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGroupAutomaton)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGroupAutomaton): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGroupAutomaton): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGroupAutomaton)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FreeGroupExtendedAutomaton","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "FreeGroupExtendedAutomaton: system getter","filters" : [["IsAttributeStoringRep","Tester(FreeGroupExtendedAutomaton)"]]},{"rank" : 50,"comment" : "FreeGroupExtendedAutomaton: for a subgroup of a free group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 11,"comment" : "FreeGroupExtendedAutomaton: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FreeGroupExtendedAutomaton)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FreeGroupExtendedAutomaton): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FreeGroupExtendedAutomaton): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FreeGroupExtendedAutomaton)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsWordLetterRepInFreeGenerators","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 57,"comment" : "AsWordLetterRepInFreeGenerators: for an element in a free group","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsWordLetterRepInGenerators","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 58,"comment" : "AsWordLetterRepInGenerators: for an element in a free group","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"],["IsMagmaWithInverses","Tester(GeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CyclicallyReducedWord","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 7,"comment" : "CyclicallyReducedWord: for an element in a free group","filters" : [["IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWord"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FindPowLetterRep","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsList"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [{"rank" : 56,"comment" : "FindPowLetterRep","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],["IsList"],["IsList"],["IsList"]]}],"5args" : [],"6args" : []}},{"name" : "NormalizerInWholeGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "NormalizerInWholeGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizerInWholeGroup)"]]},{"rank" : 50,"comment" : "NormalizerInWholeGroup","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 13,"comment" : "NormalizerInWholeGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizerInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizerInWholeGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizerInWholeGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizerInWholeGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FGA_Source","type" : "GAP_Operation","filters" : [[["IsFromFpGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20030,"comment" : "FGA_Source: system getter","filters" : [["IsAttributeStoringRep","Tester(FGA_Source)"]]},{"rank" : 30,"comment" : "FGA_Source","filters" : [["Tester(MappingGeneratorsImages)","IsFromFpGroupGeneralMappingByImages"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FGA_Source)","type" : "GAP_Operation","filters" : [[["IsFromFpGroupGeneralMappingByImages"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FGA_Source): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FGA_Source): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FGA_Source)","type" : "GAP_Operation","filters" : [[["IsFromFpGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FGA_Image","type" : "GAP_Operation","filters" : [[["IsToFpGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20019,"comment" : "FGA_Image: system getter","filters" : [["IsAttributeStoringRep","Tester(FGA_Image)"]]},{"rank" : 19,"comment" : "FGA_Image","filters" : [["Tester(MappingGeneratorsImages)","IsToFpGroupGeneralMappingByImages"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FGA_Image)","type" : "GAP_Operation","filters" : [[["IsToFpGroupGeneralMappingByImages"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FGA_Image): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FGA_Image): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FGA_Image)","type" : "GAP_Operation","filters" : [[["IsToFpGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FGA_WhiteheadParams","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20020,"comment" : "FGA_WhiteheadParams: system getter","filters" : [["IsAttributeStoringRep","Tester(FGA_WhiteheadParams)"]]},{"rank" : 0,"comment" : "FGA_WhiteheadParams: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FGA_WhiteheadParams)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FGA_WhiteheadParams): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FGA_WhiteheadParams): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FGA_WhiteheadParams)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsInverses","Tester(RespectsInverses)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FGA_WhiteheadAutomorphisms","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "FGA_WhiteheadAutomorphisms: system getter","filters" : [["IsAttributeStoringRep","Tester(FGA_WhiteheadAutomorphisms)"]]},{"rank" : 50,"comment" : "FGA_WhiteheadAutomorphisms: for finitely generated free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 13,"comment" : "FGA_WhiteheadAutomorphisms: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FGA_WhiteheadAutomorphisms)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FGA_WhiteheadAutomorphisms): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FGA_WhiteheadAutomorphisms): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FGA_WhiteheadAutomorphisms)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FGA_NielsenAutomorphisms","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "FGA_NielsenAutomorphisms: system getter","filters" : [["IsAttributeStoringRep","Tester(FGA_NielsenAutomorphisms)"]]},{"rank" : 50,"comment" : "FGA_NielsenAutomorphisms: for finitely generated free groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]},{"rank" : 13,"comment" : "FGA_NielsenAutomorphisms: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FGA_NielsenAutomorphisms)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FGA_NielsenAutomorphisms): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FGA_NielsenAutomorphisms): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FGA_NielsenAutomorphisms)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIrreducibleMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsIrreducibleMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIrreducibleMatrixGroup)"]]},{"rank" : 43,"comment" : "IsIrreducibleMatrixGroup: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IsIrreducibleMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [{"rank" : 95,"comment" : "IsIrreducibleMatrixGroup: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIrreducibleMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIrreducibleMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIrreducibleMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [{"rank" : 95,"comment" : "Setter(IsIrreducibleMatrixGroup): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIrreducibleMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 95,"comment" : "Tester(IsIrreducibleMatrixGroup): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIrreducibleMatrixGroupOp","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 148,"comment" : "IsIrreducibleMatrixGroupOp: for matrix group and finite field - for absolutely irreducible matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsAbsolutelyIrreducibleMatrixGroup","Tester(IsAbsolutelyIrreducibleMatrixGroup)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 103,"comment" : "IsIrreducibleMatrixGroupOp: for matrix group and finite field - test attr IsIrreducibleMatrixGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(IsIrreducibleMatrixGroup)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 102,"comment" : "IsIrreducibleMatrixGroupOp: for matrix group and finite field - use MeatAxe","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedIsIrreducibleMatrixGroups","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "ComputedIsIrreducibleMatrixGroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedIsIrreducibleMatrixGroups)"]]},{"rank" : 43,"comment" : "ComputedIsIrreducibleMatrixGroups: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "ComputedIsIrreducibleMatrixGroups: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedIsIrreducibleMatrixGroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedIsIrreducibleMatrixGroups): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedIsIrreducibleMatrixGroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedIsIrreducibleMatrixGroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAbsolutelyIrreducible","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 43,"comment" : "IsAbsolutelyIrreducible: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAbsolutelyIrreducibleMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsAbsolutelyIrreducibleMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAbsolutelyIrreducibleMatrixGroup)"]]},{"rank" : 46,"comment" : "IsAbsolutelyIrreducibleMatrixGroup: for mat group over finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IsAbsolutelyIrreducibleMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAbsolutelyIrreducibleMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAbsolutelyIrreducibleMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAbsolutelyIrreducibleMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAbsolutelyIrreducibleMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPrimitiveMatrixGroupOp","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 442,"comment" : "IsPrimitiveMatrixGroupOp: for matrix group over finite field, try if IsPrimitive is set","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(IsPrimitive)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 439,"comment" : "IsPrimitiveMatrixGroupOp: for matrix group over finite field, use RepresentationIsomorphism","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(RepresentationIsomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 437,"comment" : "IsPrimitiveMatrixGroupOp: for matrix group over finite field, use nice monomorphism","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 104,"comment" : "IsPrimitiveMatrixGroupOp: for matrix group over finite field, construct IsomorphismPcGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedIsPrimitiveMatrixGroups","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "ComputedIsPrimitiveMatrixGroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedIsPrimitiveMatrixGroups)"]]},{"rank" : 43,"comment" : "ComputedIsPrimitiveMatrixGroups: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "ComputedIsPrimitiveMatrixGroups: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedIsPrimitiveMatrixGroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedIsPrimitiveMatrixGroups): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedIsPrimitiveMatrixGroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedIsPrimitiveMatrixGroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalBlockDimensionOfMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "MinimalBlockDimensionOfMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimalBlockDimensionOfMatrixGroup)"]]},{"rank" : 43,"comment" : "MinimalBlockDimensionOfMatrixGroup: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "MinimalBlockDimensionOfMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [{"rank" : 95,"comment" : "MinimalBlockDimensionOfMatrixGroup: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimalBlockDimensionOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimalBlockDimensionOfMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimalBlockDimensionOfMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [{"rank" : 95,"comment" : "Setter(MinimalBlockDimensionOfMatrixGroup): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimalBlockDimensionOfMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 95,"comment" : "Tester(MinimalBlockDimensionOfMatrixGroup): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalBlockDimensionOfMatrixGroupOp","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 439,"comment" : "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field which has MinimalBlockDimension","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MinimalBlockDimension)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 439,"comment" : "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field with representation homomorphism","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(RepresentationIsomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 437,"comment" : "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field, use NiceMonomorphism","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 104,"comment" : "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 99,"comment" : "MinimalBlockDimensionOfMatrixGroupOp: for matrix group having imprimitivity systems","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(ComputedImprimitivitySystemss)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedMinimalBlockDimensionOfMatrixGroups","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "ComputedMinimalBlockDimensionOfMatrixGroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedMinimalBlockDimensionOfMatrixGroups)"]]},{"rank" : 43,"comment" : "ComputedMinimalBlockDimensionOfMatrixGroups: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "ComputedMinimalBlockDimensionOfMatrixGroups: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedMinimalBlockDimensionOfMatrixGroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedMinimalBlockDimensionOfMatrixGroups): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedMinimalBlockDimensionOfMatrixGroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedMinimalBlockDimensionOfMatrixGroups)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CharacteristicOfField","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "CharacteristicOfField: system getter","filters" : [["IsAttributeStoringRep","Tester(CharacteristicOfField)"]]},{"rank" : 43,"comment" : "CharacteristicOfField: for matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "CharacteristicOfField: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CharacteristicOfField)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CharacteristicOfField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CharacteristicOfField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CharacteristicOfField)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentationIsomorphism","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "RepresentationIsomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(RepresentationIsomorphism)"]]},{"rank" : 378,"comment" : "RepresentationIsomorphism: for mat group handled by nice mono.","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]]},{"rank" : 43,"comment" : "RepresentationIsomorphism: solvable group: inverse of IsomorphismPcGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "RepresentationIsomorphism: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RepresentationIsomorphism)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RepresentationIsomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RepresentationIsomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RepresentationIsomorphism)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"]]},{"rank" : -14,"comment" : "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImprimitivitySystems","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "ImprimitivitySystems: system getter","filters" : [["IsAttributeStoringRep","Tester(ImprimitivitySystems)"]]},{"rank" : 46,"comment" : "ImprimitivitySystems: for matrix group: use FieldOfMatrixGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "ImprimitivitySystems: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [{"rank" : 95,"comment" : "ImprimitivitySystems: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ImprimitivitySystems)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ImprimitivitySystems): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ImprimitivitySystems): default method, does nothing","filters" : [[],[]]}],"3args" : [{"rank" : 95,"comment" : "Setter(ImprimitivitySystems): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ImprimitivitySystems)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]],[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 95,"comment" : "Tester(ImprimitivitySystems): default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ImprimitivitySystemsOp","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsNonTrivial","Tester(IsNonTrivial)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 437,"comment" : "ImprimitivitySystemsOp: for matrix group handled by nice mono. and finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]},{"rank" : 437,"comment" : "ImprimitivitySystemsOp: for matrix group handled by nice mono. and finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"],["IsNonTrivial","Tester(IsNonTrivial)","IsFinite","Tester(IsFinite)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsEuclideanRing"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedImprimitivitySystemss","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "ComputedImprimitivitySystemss: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedImprimitivitySystemss)"]]},{"rank" : 43,"comment" : "ComputedImprimitivitySystemss: default method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "ComputedImprimitivitySystemss: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedImprimitivitySystemss)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedImprimitivitySystemss): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedImprimitivitySystemss): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedImprimitivitySystemss)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TraceField","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "TraceField: system getter","filters" : [["IsAttributeStoringRep","Tester(TraceField)"]]},{"rank" : 394,"comment" : "TraceField: for irreducible matrix group over finite field","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 390,"comment" : "TraceField: generic method for finite matrix groups via conjugacy classes","filters" : [["IsFinite","Tester(IsFinite)","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "TraceField:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "TraceField: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TraceField)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TraceField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TraceField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TraceField)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugatingMatTraceField","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "ConjugatingMatTraceField: system getter","filters" : [["IsAttributeStoringRep","Tester(ConjugatingMatTraceField)"]]},{"rank" : 46,"comment" : "ConjugatingMatTraceField: for irreducible FFE matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "ConjugatingMatTraceField: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ConjugatingMatTraceField)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ConjugatingMatTraceField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ConjugatingMatTraceField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ConjugatingMatTraceField)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "FingerprintMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "FingerprintMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(FingerprintMatrixGroup)"]]},{"rank" : 46,"comment" : "FingerprintMatrixGroup: for irreducible FFE matrix group","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "FingerprintMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(FingerprintMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(FingerprintMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(FingerprintMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(FingerprintMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdIrreducibleSolvableMatrixGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IdIrreducibleSolvableMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IdIrreducibleSolvableMatrixGroup)"]]},{"rank" : 50,"comment" : "IdIrreducibleSolvableMatrixGroup: for irreducible solvable matrix group over finite field","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","IsSolvableGroup","Tester(IsSolvableGroup)","IsIrreducibleMatrixGroup","Tester(IsIrreducibleMatrixGroup)"]]},{"rank" : 0,"comment" : "IdIrreducibleSolvableMatrixGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IdIrreducibleSolvableMatrixGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdIrreducibleSolvableMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdIrreducibleSolvableMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdIrreducibleSolvableMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdIrreducibleSolvableMatrixGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IdPrimitiveSolvableGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IdPrimitiveSolvableGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IdPrimitiveSolvableGroup)"]]},{"rank" : 48,"comment" : "IdPrimitiveSolvableGroup: for solvable group","filters" : [["IsFinite","Tester(IsFinite)","IsSolvableGroup","Tester(IsSolvableGroup)"]]},{"rank" : 0,"comment" : "IdPrimitiveSolvableGroup:  fallback method to test conditions","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IdPrimitiveSolvableGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IdPrimitiveSolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IdPrimitiveSolvableGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IdPrimitiveSolvableGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IdPrimitiveSolvableGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieNilpotentOverFp","type" : "GAP_Operation","filters" : [[["IsLieNilpotent","Tester(IsLieNilpotent)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsLieNilpotentOverFp: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieNilpotentOverFp)"]]},{"rank" : 46,"comment" : "IsLieNilpotentOverFp","filters" : [["IsLieNilpotent","Tester(IsLieNilpotent)"]]},{"rank" : 0,"comment" : "IsLieNilpotentOverFp: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieNilpotentOverFp)","type" : "GAP_Operation","filters" : [[["IsLieNilpotent","Tester(IsLieNilpotent)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieNilpotentOverFp): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieNilpotentOverFp): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieNilpotentOverFp)","type" : "GAP_Operation","filters" : [[["IsLieNilpotent","Tester(IsLieNilpotent)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AutomorphismGroupOfNilpotentLieAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "AutomorphismGroupOfNilpotentLieAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(AutomorphismGroupOfNilpotentLieAlgebra)"]]},{"rank" : 42,"comment" : "AutomorphismGroupOfNilpotentLieAlgebra: for nilpotent Lie algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "AutomorphismGroupOfNilpotentLieAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AutomorphismGroupOfNilpotentLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AutomorphismGroupOfNilpotentLieAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AutomorphismGroupOfNilpotentLieAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AutomorphismGroupOfNilpotentLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DescendantsOfStep1OfAbelianLieAlgebra","type" : "GAP_Operation","filters" : [[["IsInt","IsPosRat"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 38,"comment" : "DescendantsOfStep1OfAbelianLieAlgebra: for abelian Lie algebras","filters" : [["IsInt","IsPosRat"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Descendants","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 61,"comment" : "Descendants: for nilpotent Lie algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "MinimalGeneratorNumber","type" : "GAP_Operation","filters" : [[["IsLieNilpotent","Tester(IsLieNilpotent)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "MinimalGeneratorNumber: system getter","filters" : [["IsAttributeStoringRep","Tester(MinimalGeneratorNumber)"]]},{"rank" : 48,"comment" : "MinimalGeneratorNumber: for nilpotent Lie algebras","filters" : [["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]},{"rank" : 0,"comment" : "MinimalGeneratorNumber: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(MinimalGeneratorNumber)","type" : "GAP_Operation","filters" : [[["IsLieNilpotent","Tester(IsLieNilpotent)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(MinimalGeneratorNumber): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(MinimalGeneratorNumber): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(MinimalGeneratorNumber)","type" : "GAP_Operation","filters" : [[["IsLieNilpotent","Tester(IsLieNilpotent)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LiftAutorphismToLieCover","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "LiftAutorphismToLieCover: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LinearActionOnMultiplicator","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 22,"comment" : "LinearActionOnMultiplicator: for nilpotent Lie algebra automorphisms","filters" : [["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsNilpotentLieAutomorphismRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NilpotentLieAutomorphism","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 52,"comment" : "NilpotentLieAutomorphism: for nilpotent Lie algebras","filters" : [["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"],["IsList"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieCover","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "IsLieCover: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieCover)"]]},{"rank" : 48,"comment" : "IsLieCover: for nilpotent Lie algebras with nilpotent presentation","filters" : [["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]},{"rank" : 0,"comment" : "IsLieCover: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieCover)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieCover): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieCover): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieCover)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoverOf","type" : "GAP_Operation","filters" : [[["IsLieCover","Tester(IsLieCover)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20053,"comment" : "CoverOf: system getter","filters" : [["IsAttributeStoringRep","Tester(CoverOf)"]]},{"rank" : 50,"comment" : "CoverOf: for nilpotent Lie algebras with nilpotent presentation","filters" : [["IsLieCover","Tester(IsLieCover)"]]},{"rank" : 0,"comment" : "CoverOf: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoverOf)","type" : "GAP_Operation","filters" : [[["IsLieCover","Tester(IsLieCover)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoverOf): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoverOf): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoverOf)","type" : "GAP_Operation","filters" : [[["IsLieCover","Tester(IsLieCover)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoverHomomorphism","type" : "GAP_Operation","filters" : [[["IsLieCover","Tester(IsLieCover)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20053,"comment" : "CoverHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(CoverHomomorphism)"]]},{"rank" : 50,"comment" : "CoverHomomorphism: for nilpotent Lie algebras with nilpotent presentation","filters" : [["IsLieCover","Tester(IsLieCover)"]]},{"rank" : 0,"comment" : "CoverHomomorphism: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoverHomomorphism)","type" : "GAP_Operation","filters" : [[["IsLieCover","Tester(IsLieCover)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoverHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoverHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoverHomomorphism)","type" : "GAP_Operation","filters" : [[["IsLieCover","Tester(IsLieCover)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieCover","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieCover: system getter","filters" : [["IsAttributeStoringRep","Tester(LieCover)"]]},{"rank" : 42,"comment" : "LieCover: for nilpotent Lie algebras with nilpotent presentation","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieCover: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieCover)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieCover): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieCover): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieCover)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieNucleus","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "LieNucleus: system getter","filters" : [["IsAttributeStoringRep","Tester(LieNucleus)"]]},{"rank" : 48,"comment" : "LieNucleus: for nilpotent Lie algebras","filters" : [["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]},{"rank" : 0,"comment" : "LieNucleus: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieNucleus)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieNucleus): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieNucleus): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieNucleus)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieMultiplicator","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "LieMultiplicator: system getter","filters" : [["IsAttributeStoringRep","Tester(LieMultiplicator)"]]},{"rank" : 48,"comment" : "LieMultiplicator: for nilpotent Lie algebras","filters" : [["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]},{"rank" : 0,"comment" : "LieMultiplicator: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieMultiplicator)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieMultiplicator): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieMultiplicator): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieMultiplicator)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LiftIsomorphismToLieCover","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 114,"comment" : "LiftIsomorphismToLieCover: for nilpotent Lie algebras with nilpotent presentation","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AreIsomorphicNilpotentLieAlgebras","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 84,"comment" : "AreIsomorphicNilpotentLieAlgebras: for nilpotent Lie algebras with nilpotent presentation","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieAlgebraWithNB","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "IsLieAlgebraWithNB: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieAlgebraWithNB)"]]},{"rank" : 48,"comment" : "IsLieAlgebraWithNB: for nilpotent Lie algebras","filters" : [["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]},{"rank" : 0,"comment" : "IsLieAlgebraWithNB: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieAlgebraWithNB)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieAlgebraWithNB): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieAlgebraWithNB): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieAlgebraWithNB)","type" : "GAP_Operation","filters" : [[["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NilpotentBasis","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "NilpotentBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(NilpotentBasis)"]]},{"rank" : 42,"comment" : "NilpotentBasis: for nilpotent Lie algebras","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "NilpotentBasis: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NilpotentBasis)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NilpotentBasis): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NilpotentBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NilpotentBasis)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNilpotentBasis","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsNilpotentBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNilpotentBasis)"]]},{"rank" : 7,"comment" : "IsNilpotentBasis: for bases of Lie algebras","filters" : [["IsBasis"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNilpotentBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNilpotentBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNilpotentBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNilpotentBasis)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieNBDefinitions","type" : "GAP_Operation","filters" : [[["IsNilpotentBasis","Tester(IsNilpotentBasis)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "LieNBDefinitions: system getter","filters" : [["IsAttributeStoringRep","Tester(LieNBDefinitions)"]]},{"rank" : 9,"comment" : "LieNBDefinitions: for NB bases of Lie algebras","filters" : [["IsNilpotentBasis","Tester(IsNilpotentBasis)"]]},{"rank" : 0,"comment" : "LieNBDefinitions: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieNBDefinitions)","type" : "GAP_Operation","filters" : [[["IsNilpotentBasis","Tester(IsNilpotentBasis)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieNBDefinitions): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieNBDefinitions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieNBDefinitions)","type" : "GAP_Operation","filters" : [[["IsNilpotentBasis","Tester(IsNilpotentBasis)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieNBWeights","type" : "GAP_Operation","filters" : [[["IsNilpotentBasis","Tester(IsNilpotentBasis)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20012,"comment" : "LieNBWeights: system getter","filters" : [["IsAttributeStoringRep","Tester(LieNBWeights)"]]},{"rank" : 9,"comment" : "LieNBWeights: for NB bases of Lie algebras","filters" : [["IsNilpotentBasis","Tester(IsNilpotentBasis)"]]},{"rank" : 0,"comment" : "LieNBWeights: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieNBWeights)","type" : "GAP_Operation","filters" : [[["IsNilpotentBasis","Tester(IsNilpotentBasis)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieNBWeights): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieNBWeights): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieNBWeights)","type" : "GAP_Operation","filters" : [[["IsNilpotentBasis","Tester(IsNilpotentBasis)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupAlgebra","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20041,"comment" : "IsGroupAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupAlgebra)"]]},{"rank" : 38,"comment" : "IsGroupAlgebra","filters" : [["IsGroupRing","Tester(IsGroupRing)"]]},{"rank" : 0,"comment" : "IsGroupAlgebra: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupAlgebra)","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupAlgebra)","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFModularGroupAlgebra","type" : "GAP_Operation","filters" : [[["IsGroupAlgebra","Tester(IsGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20043,"comment" : "IsFModularGroupAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFModularGroupAlgebra)"]]},{"rank" : 40,"comment" : "IsFModularGroupAlgebra","filters" : [["IsGroupAlgebra","Tester(IsGroupAlgebra)"]]},{"rank" : 0,"comment" : "IsFModularGroupAlgebra: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFModularGroupAlgebra)","type" : "GAP_Operation","filters" : [[["IsGroupAlgebra","Tester(IsGroupAlgebra)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFModularGroupAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFModularGroupAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFModularGroupAlgebra)","type" : "GAP_Operation","filters" : [[["IsGroupAlgebra","Tester(IsGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPModularGroupAlgebra","type" : "GAP_Operation","filters" : [[["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsPModularGroupAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 42,"comment" : "IsPModularGroupAlgebra","filters" : [["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "IsPModularGroupAlgebra: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPModularGroupAlgebra)","type" : "GAP_Operation","filters" : [[["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPModularGroupAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPModularGroupAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPModularGroupAlgebra)","type" : "GAP_Operation","filters" : [[["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingRing","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"]],[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20041,"comment" : "UnderlyingRing: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingRing)"]]},{"rank" : 38,"comment" : "UnderlyingRing","filters" : [["IsGroupRing","Tester(IsGroupRing)"]]},{"rank" : 0,"comment" : "UnderlyingRing: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingRing)","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],[]],[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingRing)","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingField","type" : "GAP_Operation","filters" : [[["IsGroupAlgebra","Tester(IsGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20043,"comment" : "UnderlyingField: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingField)"]]},{"rank" : 40,"comment" : "UnderlyingField","filters" : [["IsGroupAlgebra","Tester(IsGroupAlgebra)"]]},{"rank" : 0,"comment" : "UnderlyingField: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingField)","type" : "GAP_Operation","filters" : [[["IsGroupAlgebra","Tester(IsGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingField)","type" : "GAP_Operation","filters" : [[["IsGroupAlgebra","Tester(IsGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Support","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Support: system getter","filters" : [["IsAttributeStoringRep","Tester(Support)"]]},{"rank" : 13,"comment" : "Support: LAGUNA: for an element of a magma ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Support)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Support): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Support): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Support)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CoefficientsBySupport","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "CoefficientsBySupport: system getter","filters" : [["IsAttributeStoringRep","Tester(CoefficientsBySupport)"]]},{"rank" : 13,"comment" : "CoefficientsBySupport: LAGUNA: for an element of a magma ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CoefficientsBySupport)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CoefficientsBySupport): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CoefficientsBySupport): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CoefficientsBySupport)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TraceOfMagmaRingElement","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "TraceOfMagmaRingElement: system getter","filters" : [["IsAttributeStoringRep","Tester(TraceOfMagmaRingElement)"]]},{"rank" : 13,"comment" : "TraceOfMagmaRingElement: LAGUNA: for an element of a magma ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TraceOfMagmaRingElement)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TraceOfMagmaRingElement): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TraceOfMagmaRingElement): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TraceOfMagmaRingElement)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Augmentation","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "Augmentation: system getter","filters" : [["IsAttributeStoringRep","Tester(Augmentation)"]]},{"rank" : 13,"comment" : "Augmentation: LAGUNA: for an element of a magma ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Augmentation)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Augmentation): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Augmentation): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Augmentation)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PartialAugmentations","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 51,"comment" : "PartialAugmentations: LAGUNA: for a group ring and its element","filters" : [["IsGroupRing","Tester(IsGroupRing)"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Involution","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 13,"comment" : "Involution: LAGUNA: classical involution for an element of a group ring ","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [{"rank" : 24,"comment" : "Involution: LAGUNA: for a group ring element and a group endomapping of order 2","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]}],"3args" : [{"rank" : 35,"comment" : "Involution: LAGUNA: for a group ring element, and a group endomapping of order 2 and a mapping from the group to a ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSymmetric","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsSymmetric: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSymmetric)"]]},{"rank" : 13,"comment" : "IsSymmetric: LAGUNA: for group ring elements","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSymmetric)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSymmetric): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSymmetric): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSymmetric)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUnitary","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20016,"comment" : "IsUnitary: system getter","filters" : [["IsAttributeStoringRep","Tester(IsUnitary)"]]},{"rank" : 13,"comment" : "IsUnitary: LAGUNA: for group ring elements","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsUnitary)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsUnitary): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsUnitary): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsUnitary)","type" : "GAP_Operation","filters" : [[["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LeftIdealBySubgroup","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "LeftIdealBySubgroup: LAGUNA: for a group ring and a subgroup of underlying group","filters" : [["IsGroupRing","Tester(IsGroupRing)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RightIdealBySubgroup","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "RightIdealBySubgroup: LAGUNA: for a group ring and a subgroup of underlying group","filters" : [["IsGroupRing","Tester(IsGroupRing)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TwoSidedIdealBySubgroup","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 71,"comment" : "TwoSidedIdealBySubgroup: LAGUNA: for a group ring and a subgroup of underlying group","filters" : [["IsGroupRing","Tester(IsGroupRing)"],["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WeightedBasis","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "WeightedBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(WeightedBasis)"]]},{"rank" : 44,"comment" : "WeightedBasis: LAGUNA: for modular group algebra of a finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "WeightedBasis: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WeightedBasis)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WeightedBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WeightedBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WeightedBasis)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentationIdealPowerSeries","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "AugmentationIdealPowerSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentationIdealPowerSeries)"]]},{"rank" : 44,"comment" : "AugmentationIdealPowerSeries: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "AugmentationIdealPowerSeries: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentationIdealPowerSeries)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentationIdealPowerSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentationIdealPowerSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentationIdealPowerSeries)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentationIdealNilpotencyIndex","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "AugmentationIdealNilpotencyIndex: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentationIdealNilpotencyIndex)"]]},{"rank" : 44,"comment" : "AugmentationIdealNilpotencyIndex: LAGUNA: for a modular group algebra of a finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "AugmentationIdealNilpotencyIndex: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentationIdealNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentationIdealNilpotencyIndex): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentationIdealNilpotencyIndex): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentationIdealNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentationIdealOfDerivedSubgroupNilpotencyIndex","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "AugmentationIdealOfDerivedSubgroupNilpotencyIndex: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)"]]},{"rank" : 44,"comment" : "AugmentationIdealOfDerivedSubgroupNilpotencyIndex: LAGUNA: for a modular group algebra of a finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "AugmentationIdealOfDerivedSubgroupNilpotencyIndex: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentationIdealOfDerivedSubgroupNilpotencyIndex): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentationIdealOfDerivedSubgroupNilpotencyIndex): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsGroupOfUnitsOfMagmaRing","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsGroupOfUnitsOfMagmaRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsGroupOfUnitsOfMagmaRing)"]]},{"rank" : 0,"comment" : "IsGroupOfUnitsOfMagmaRing: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsGroupOfUnitsOfMagmaRing)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsGroupOfUnitsOfMagmaRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsGroupOfUnitsOfMagmaRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsGroupOfUnitsOfMagmaRing)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsUnitGroupOfGroupRing","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "IsUnitGroupOfGroupRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsUnitGroupOfGroupRing)"]]},{"rank" : 0,"comment" : "IsUnitGroupOfGroupRing: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsUnitGroupOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsUnitGroupOfGroupRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsUnitGroupOfGroupRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsUnitGroupOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsNormalizedUnitGroupOfGroupRing","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "IsNormalizedUnitGroupOfGroupRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsNormalizedUnitGroupOfGroupRing)"]]},{"rank" : 0,"comment" : "IsNormalizedUnitGroupOfGroupRing: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsNormalizedUnitGroupOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsNormalizedUnitGroupOfGroupRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsNormalizedUnitGroupOfGroupRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsNormalizedUnitGroupOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingGroupRing","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "UnderlyingGroupRing: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingGroupRing)"]]},{"rank" : 0,"comment" : "UnderlyingGroupRing: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingGroupRing)","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingGroupRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingGroupRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingGroupRing)","type" : "GAP_Operation","filters" : [[["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizedUnitCF","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 57,"comment" : "NormalizedUnitCF: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizedUnitCFmod","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 76,"comment" : "NormalizedUnitCFmod: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizedUnitGroup","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "NormalizedUnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizedUnitGroup)"]]},{"rank" : 44,"comment" : "NormalizedUnitGroup: LAGUNA: for modular group algebra of a finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "NormalizedUnitGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizedUnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizedUnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcNormalizedUnitGroup","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "PcNormalizedUnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(PcNormalizedUnitGroup)"]]},{"rank" : 44,"comment" : "PcNormalizedUnitGroup: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "PcNormalizedUnitGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcNormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcNormalizedUnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcNormalizedUnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcNormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentationIdealPowerFactorGroupOp","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "AugmentationIdealPowerFactorGroupOp: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ComputedAugmentationIdealPowerFactorGroups","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "ComputedAugmentationIdealPowerFactorGroups: system getter","filters" : [["IsAttributeStoringRep","Tester(ComputedAugmentationIdealPowerFactorGroups)"]]},{"rank" : 44,"comment" : "ComputedAugmentationIdealPowerFactorGroups: default method","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "ComputedAugmentationIdealPowerFactorGroups: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ComputedAugmentationIdealPowerFactorGroups)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ComputedAugmentationIdealPowerFactorGroups): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ComputedAugmentationIdealPowerFactorGroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ComputedAugmentationIdealPowerFactorGroups)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentationIdealPowerFactorGroup","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "AugmentationIdealPowerFactorGroup: default method","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HasAugmentationIdealPowerFactorGroup","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 63,"comment" : "HasAugmentationIdealPowerFactorGroup: default method","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SetAugmentationIdealPowerFactorGroup","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 63,"comment" : "SetAugmentationIdealPowerFactorGroup: default method","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],["IsInt","IsPosRat"],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcUnits","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "PcUnits: system getter","filters" : [["IsAttributeStoringRep","Tester(PcUnits)"]]},{"rank" : 44,"comment" : "PcUnits: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "PcUnits: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PcUnits)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PcUnits): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PcUnits): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PcUnits)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalBijectionToPcNormalizedUnitGroup","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "NaturalBijectionToPcNormalizedUnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalBijectionToPcNormalizedUnitGroup)"]]},{"rank" : 44,"comment" : "NaturalBijectionToPcNormalizedUnitGroup: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "NaturalBijectionToPcNormalizedUnitGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalBijectionToPcNormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalBijectionToPcNormalizedUnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalBijectionToPcNormalizedUnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalBijectionToPcNormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalBijectionToNormalizedUnitGroup","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "NaturalBijectionToNormalizedUnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalBijectionToNormalizedUnitGroup)"]]},{"rank" : 44,"comment" : "NaturalBijectionToNormalizedUnitGroup: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "NaturalBijectionToNormalizedUnitGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalBijectionToNormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalBijectionToNormalizedUnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalBijectionToNormalizedUnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalBijectionToNormalizedUnitGroup)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GroupBases","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "GroupBases: system getter","filters" : [["IsAttributeStoringRep","Tester(GroupBases)"]]},{"rank" : 44,"comment" : "GroupBases: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "GroupBases: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GroupBases)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GroupBases): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GroupBases): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GroupBases)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BassCyclicUnit","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],[],["IsInt","IsPosRat"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 32,"comment" : "BassCyclicUnit: for uderlying group element, embedded into group ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 57,"comment" : "BassCyclicUnit: for uderlying group element, not embedded into group ring","filters" : [["IsGroupRing","Tester(IsGroupRing)"],[],["IsInt","IsPosRat"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BicyclicUnitOfType1","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "BicyclicUnitOfType1: for uderlying group elements, embedded into group ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"3args" : [{"rank" : 38,"comment" : "BicyclicUnitOfType1: for uderlying group elements, not embedded into group ring","filters" : [["IsGroupRing","Tester(IsGroupRing)"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BicyclicUnitOfType2","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],[],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 26,"comment" : "BicyclicUnitOfType2: for uderlying group elements, embedded into group ring","filters" : [["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"],["IsElementOfMagmaRingModuloRelations","IsMagmaRingObjDefaultRep"]]}],"3args" : [{"rank" : 38,"comment" : "BicyclicUnitOfType2: for uderlying group elements, not embedded into group ring","filters" : [["IsGroupRing","Tester(IsGroupRing)"],[],[]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BicyclicUnitGroup","type" : "GAP_Operation","filters" : [[["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20040,"comment" : "BicyclicUnitGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(BicyclicUnitGroup)"]]},{"rank" : 42,"comment" : "BicyclicUnitGroup: for the normalized unit group in pc-presentation","filters" : [["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]},{"rank" : 42,"comment" : "BicyclicUnitGroup: for the normalized unit group in natural representation","filters" : [["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]},{"rank" : 0,"comment" : "BicyclicUnitGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BicyclicUnitGroup)","type" : "GAP_Operation","filters" : [[["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BicyclicUnitGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BicyclicUnitGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BicyclicUnitGroup)","type" : "GAP_Operation","filters" : [[["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnitarySubgroup","type" : "GAP_Operation","filters" : [[["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20040,"comment" : "UnitarySubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(UnitarySubgroup)"]]},{"rank" : 42,"comment" : "UnitarySubgroup: for the normalized unit group in pc-presentation","filters" : [["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]},{"rank" : 42,"comment" : "UnitarySubgroup: for the normalized unit group in natural representation","filters" : [["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]},{"rank" : 0,"comment" : "UnitarySubgroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnitarySubgroup)","type" : "GAP_Operation","filters" : [[["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnitarySubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnitarySubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnitarySubgroup)","type" : "GAP_Operation","filters" : [[["IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingAssociativeAlgebra","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "UnderlyingAssociativeAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingAssociativeAlgebra)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingAssociativeAlgebra)","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingAssociativeAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingAssociativeAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingAssociativeAlgebra)","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieAlgebraOfGroupRing","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsLieAlgebraOfGroupRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 43,"comment" : "IsLieAlgebraOfGroupRing: LAGUNA: for a Lie algebra","filters" : [["IsLieAlgebraByAssociativeAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieAlgebraOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieAlgebraOfGroupRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieAlgebraOfGroupRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieAlgebraOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsBasisOfLieAlgebraOfGroupRing","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20010,"comment" : "IsBasisOfLieAlgebraOfGroupRing: system getter","filters" : [["IsAttributeStoringRep","Tester(IsBasisOfLieAlgebraOfGroupRing)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsBasisOfLieAlgebraOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsBasis"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsBasisOfLieAlgebraOfGroupRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsBasisOfLieAlgebraOfGroupRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsBasisOfLieAlgebraOfGroupRing)","type" : "GAP_Operation","filters" : [[["IsBasis"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalBijectionToLieAlgebra","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20041,"comment" : "NaturalBijectionToLieAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalBijectionToLieAlgebra)"]]},{"rank" : 38,"comment" : "NaturalBijectionToLieAlgebra: LAGUNA: for an associative algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -55,"comment" : "NaturalBijectionToLieAlgebra: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalBijectionToLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalBijectionToLieAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalBijectionToLieAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalBijectionToLieAlgebra)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsAssociative","Tester(IsAssociative)","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalBijectionToAssociativeAlgebra","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "NaturalBijectionToAssociativeAlgebra: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalBijectionToAssociativeAlgebra)"]]},{"rank" : 43,"comment" : "NaturalBijectionToAssociativeAlgebra: LAGUNA: for a Lie algebra","filters" : [["IsLieAlgebraByAssociativeAlgebra"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalBijectionToAssociativeAlgebra)","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalBijectionToAssociativeAlgebra): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalBijectionToAssociativeAlgebra): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalBijectionToAssociativeAlgebra)","type" : "GAP_Operation","filters" : [[["IsLieAlgebraByAssociativeAlgebra"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AugmentationHomomorphism","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsGroupRing","Tester(IsGroupRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "AugmentationHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(AugmentationHomomorphism)"]]},{"rank" : 43,"comment" : "AugmentationHomomorphism: LAGUNA: for a group ring","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsGroupRing","Tester(IsGroupRing)"]]},{"rank" : -66,"comment" : "AugmentationHomomorphism: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AugmentationHomomorphism)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsGroupRing","Tester(IsGroupRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AugmentationHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AugmentationHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AugmentationHomomorphism)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsGroupRing","Tester(IsGroupRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieMetabelian","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsLieMetabelian: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieMetabelian)"]]},{"rank" : 45,"comment" : "IsLieMetabelian: LAGUNA: for a Lie algebra of a group ring","filters" : [["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 42,"comment" : "IsLieMetabelian: LAGUNA: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "IsLieMetabelian: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieMetabelian)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieMetabelian): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieMetabelian): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieMetabelian)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsLieCentreByMetabelian","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "IsLieCentreByMetabelian: system getter","filters" : [["IsAttributeStoringRep","Tester(IsLieCentreByMetabelian)"]]},{"rank" : 45,"comment" : "IsLieCentreByMetabelian: LAGUNA: for a Lie algebra of a group ring","filters" : [["IsLieAlgebraByAssociativeAlgebra","IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]]},{"rank" : 43,"comment" : "IsLieCentreByMetabelian: LAGUNA: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","Tester(LieDerivedSeries)"]]},{"rank" : 42,"comment" : "IsLieCentreByMetabelian: LAGUNA: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "IsLieCentreByMetabelian: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsLieCentreByMetabelian)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsLieCentreByMetabelian): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsLieCentreByMetabelian): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsLieCentreByMetabelian)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieUpperNilpotencyIndex","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "LieUpperNilpotencyIndex: system getter","filters" : [["IsAttributeStoringRep","Tester(LieUpperNilpotencyIndex)"]]},{"rank" : 44,"comment" : "LieUpperNilpotencyIndex: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "LieUpperNilpotencyIndex: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieUpperNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieUpperNilpotencyIndex): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieUpperNilpotencyIndex): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieUpperNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieLowerNilpotencyIndex","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20047,"comment" : "LieLowerNilpotencyIndex: system getter","filters" : [["IsAttributeStoringRep","Tester(LieLowerNilpotencyIndex)"]]},{"rank" : 44,"comment" : "LieLowerNilpotencyIndex: LAGUNA: for modular group algebra of finite p-group","filters" : [["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]},{"rank" : 0,"comment" : "LieLowerNilpotencyIndex: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieLowerNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieLowerNilpotencyIndex): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieLowerNilpotencyIndex): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieLowerNilpotencyIndex)","type" : "GAP_Operation","filters" : [[["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieDerivedLength","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20045,"comment" : "LieDerivedLength: system getter","filters" : [["IsAttributeStoringRep","Tester(LieDerivedLength)"]]},{"rank" : 42,"comment" : "LieDerivedLength: LAGUNA: for a Lie algebra","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]},{"rank" : -55,"comment" : "LieDerivedLength: default method requiring categories and checking properties","filters" : [["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieDerivedLength)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieDerivedLength): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieDerivedLength): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieDerivedLength)","type" : "GAP_Operation","filters" : [[["IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubgroupsOfIndexTwo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "SubgroupsOfIndexTwo: system getter","filters" : [["IsAttributeStoringRep","Tester(SubgroupsOfIndexTwo)"]]},{"rank" : 34,"comment" : "SubgroupsOfIndexTwo: LAGUNA: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MaximalNormalSubgroups)"]]},{"rank" : 34,"comment" : "SubgroupsOfIndexTwo: LAGUNA: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MaximalSubgroupClassReps)"]]},{"rank" : 33,"comment" : "SubgroupsOfIndexTwo: LAGUNA: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "SubgroupsOfIndexTwo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SubgroupsOfIndexTwo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SubgroupsOfIndexTwo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SubgroupsOfIndexTwo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SubgroupsOfIndexTwo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DihedralDepth","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "DihedralDepth: system getter","filters" : [["IsAttributeStoringRep","Tester(DihedralDepth)"]]},{"rank" : 33,"comment" : "DihedralDepth: LAGUNA: for a group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DihedralDepth: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DihedralDepth)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DihedralDepth): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DihedralDepth): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DihedralDepth)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "DimensionBasis","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "DimensionBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(DimensionBasis)"]]},{"rank" : 33,"comment" : "DimensionBasis: LAGUNA: for a finite p-group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "DimensionBasis: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(DimensionBasis)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(DimensionBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(DimensionBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(DimensionBasis)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieDimensionSubgroups","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "LieDimensionSubgroups: system getter","filters" : [["IsAttributeStoringRep","Tester(LieDimensionSubgroups)"]]},{"rank" : 33,"comment" : "LieDimensionSubgroups: LAGUNA: for a finite p-group","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "LieDimensionSubgroups: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieDimensionSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieDimensionSubgroups): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieDimensionSubgroups): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieDimensionSubgroups)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "LieUpperCodimensionSeries","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20041,"comment" : "LieUpperCodimensionSeries: system getter","filters" : [["IsAttributeStoringRep","Tester(LieUpperCodimensionSeries)"]]},{"rank" : 38,"comment" : "LieUpperCodimensionSeries: LAGUNA: for a modular group algebra of a finite p-group using V(KG)","filters" : [["IsGroupRing","Tester(IsGroupRing)"]]},{"rank" : 33,"comment" : "LieUpperCodimensionSeries: LAGUNA: for a p-group - underlying group of its modular group algebra","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "LieUpperCodimensionSeries: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(LieUpperCodimensionSeries)","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"],[]],[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(LieUpperCodimensionSeries): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(LieUpperCodimensionSeries): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(LieUpperCodimensionSeries)","type" : "GAP_Operation","filters" : [[["IsGroupRing","Tester(IsGroupRing)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RootsAsMatrices","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "RootsAsMatrices: system getter","filters" : [["IsAttributeStoringRep","Tester(RootsAsMatrices)"]]},{"rank" : 19,"comment" : "RootsAsMatrices: rational polynomials","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "RootsAsMatrices: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(RootsAsMatrices)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(RootsAsMatrices): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(RootsAsMatrices): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(RootsAsMatrices)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSolvablePolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "IsSolvablePolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSolvablePolynomial)"]]},{"rank" : 19,"comment" : "IsSolvablePolynomial: for a rational polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "IsSolvablePolynomial: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSolvablePolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSolvablePolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSolvablePolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSolvablePolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSeparablePolynomial","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "IsSeparablePolynomial: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSeparablePolynomial)"]]},{"rank" : 19,"comment" : "IsSeparablePolynomial: for rational polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "IsSeparablePolynomial: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSeparablePolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSeparablePolynomial): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSeparablePolynomial): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSeparablePolynomial)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsomorphismMatrixField","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20057,"comment" : "IsomorphismMatrixField: system getter","filters" : [["IsAttributeStoringRep","Tester(IsomorphismMatrixField)"]]},{"rank" : 0,"comment" : "IsomorphismMatrixField: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsomorphismMatrixField)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsomorphismMatrixField): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsomorphismMatrixField): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsomorphismMatrixField)","type" : "GAP_Operation","filters" : [[["IsNumberField","Tester(IsNumberField)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "GaloisGroupOnRoots","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20022,"comment" : "GaloisGroupOnRoots: system getter","filters" : [["IsAttributeStoringRep","Tester(GaloisGroupOnRoots)"]]},{"rank" : 19,"comment" : "GaloisGroupOnRoots: for rational polynomial","filters" : [["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]},{"rank" : 0,"comment" : "GaloisGroupOnRoots: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(GaloisGroupOnRoots)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(GaloisGroupOnRoots): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(GaloisGroupOnRoots): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(GaloisGroupOnRoots)","type" : "GAP_Operation","filters" : [[["IsPolynomial","Tester(IsPolynomial)","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAffineCrystGroupOnRight","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsAffineCrystGroupOnRight: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 46,"comment" : "IsAffineCrystGroupOnRight: fallback method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsAffineCrystGroupOnRight: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAffineCrystGroupOnRight)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAffineCrystGroupOnRight): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAffineCrystGroupOnRight): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAffineCrystGroupOnRight)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAffineCrystGroupOnLeft","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsAffineCrystGroupOnLeft: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 46,"comment" : "IsAffineCrystGroupOnLeft: fallback method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsAffineCrystGroupOnLeft: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAffineCrystGroupOnLeft)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAffineCrystGroupOnLeft): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAffineCrystGroupOnLeft): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAffineCrystGroupOnLeft)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAffineCrystGroupOnLeftOrRight","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsAffineCrystGroupOnLeftOrRight: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : -30,"comment" : "IsAffineCrystGroupOnLeftOrRight: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAffineCrystGroupOnLeftOrRight)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAffineCrystGroupOnLeftOrRight): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAffineCrystGroupOnLeftOrRight): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAffineCrystGroupOnLeftOrRight)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSpaceGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsSpaceGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSpaceGroup)"]]},{"rank" : 46,"comment" : "IsSpaceGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsSpaceGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSpaceGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSpaceGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSpaceGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSpaceGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsStandardAffineCrystGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsStandardAffineCrystGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsStandardAffineCrystGroup)"]]},{"rank" : 46,"comment" : "IsStandardAffineCrystGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsStandardAffineCrystGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsStandardAffineCrystGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsStandardAffineCrystGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsStandardAffineCrystGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsStandardAffineCrystGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSymmorphicSpaceGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsSymmorphicSpaceGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsSymmorphicSpaceGroup)"]]},{"rank" : 48,"comment" : "IsSymmorphicSpaceGroup: generic method","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : -30,"comment" : "IsSymmorphicSpaceGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsSymmorphicSpaceGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsSymmorphicSpaceGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsSymmorphicSpaceGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsSymmorphicSpaceGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPointGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20049,"comment" : "IsPointGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPointGroup)"]]},{"rank" : 46,"comment" : "IsPointGroup: fallback method","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -30,"comment" : "IsPointGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPointGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPointGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPointGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPointGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NormalizerPointGroupInGLnZ","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "NormalizerPointGroupInGLnZ: system getter","filters" : [["IsAttributeStoringRep","Tester(NormalizerPointGroupInGLnZ)"]]},{"rank" : 48,"comment" : "NormalizerPointGroupInGLnZ","filters" : [["IsPointGroup","Tester(IsPointGroup)"]]},{"rank" : 0,"comment" : "NormalizerPointGroupInGLnZ: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NormalizerPointGroupInGLnZ)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NormalizerPointGroupInGLnZ): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NormalizerPointGroupInGLnZ): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NormalizerPointGroupInGLnZ)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CentralizerPointGroupInGLnZ","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "CentralizerPointGroupInGLnZ: system getter","filters" : [["IsAttributeStoringRep","Tester(CentralizerPointGroupInGLnZ)"]]},{"rank" : 48,"comment" : "CentralizerPointGroupInGLnZ: via NormalizerPointGroupInGLnZ","filters" : [["IsPointGroup","Tester(IsPointGroup)"]]},{"rank" : 0,"comment" : "CentralizerPointGroupInGLnZ: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CentralizerPointGroupInGLnZ)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CentralizerPointGroupInGLnZ): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CentralizerPointGroupInGLnZ): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CentralizerPointGroupInGLnZ)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AffineCrystGroupOfPointGroup","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "AffineCrystGroupOfPointGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(AffineCrystGroupOfPointGroup)"]]},{"rank" : 0,"comment" : "AffineCrystGroupOfPointGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AffineCrystGroupOfPointGroup)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AffineCrystGroupOfPointGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AffineCrystGroupOfPointGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AffineCrystGroupOfPointGroup)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PointGroup","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "PointGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(PointGroup)"]]},{"rank" : 53,"comment" : "PointGroup: for colored AffineCrystGroups","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)","IsColorGroup","Tester(IsColorGroup)"]]},{"rank" : 48,"comment" : "PointGroup","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 0,"comment" : "PointGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PointGroup)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PointGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PointGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PointGroup)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PointHomomorphism","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "PointHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(PointHomomorphism)"]]},{"rank" : 48,"comment" : "PointHomomorphism","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 0,"comment" : "PointHomomorphism: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(PointHomomorphism)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(PointHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(PointHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(PointHomomorphism)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TranslationBasis","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "TranslationBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(TranslationBasis)"]]},{"rank" : 48,"comment" : "TranslationBasis","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 0,"comment" : "TranslationBasis: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TranslationBasis)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TranslationBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TranslationBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TranslationBasis)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "InternalBasis","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "InternalBasis: system getter","filters" : [["IsAttributeStoringRep","Tester(InternalBasis)"]]},{"rank" : 48,"comment" : "InternalBasis","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 0,"comment" : "InternalBasis: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(InternalBasis)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(InternalBasis): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(InternalBasis): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(InternalBasis)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TransParts","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "TransParts: system getter","filters" : [["IsAttributeStoringRep","Tester(TransParts)"]]},{"rank" : 48,"comment" : "TransParts","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 0,"comment" : "TransParts: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TransParts)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TransParts): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TransParts): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TransParts)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "TranslationNormalizer","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "TranslationNormalizer: system getter","filters" : [["IsAttributeStoringRep","Tester(TranslationNormalizer)"]]},{"rank" : 55,"comment" : "TranslationNormalizer: for SpaceGroup acting OnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)","IsSpaceGroup","Tester(IsSpaceGroup)"]]},{"rank" : 55,"comment" : "TranslationNormalizer: for SpaceGroup acting OnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)","IsSpaceGroup","Tester(IsSpaceGroup)"]]},{"rank" : 0,"comment" : "TranslationNormalizer:  fallback method to test conditions","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 0,"comment" : "TranslationNormalizer:  fallback method to test conditions","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 0,"comment" : "TranslationNormalizer: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(TranslationNormalizer)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(TranslationNormalizer): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(TranslationNormalizer): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(TranslationNormalizer)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AffineNormalizer","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "AffineNormalizer: system getter","filters" : [["IsAttributeStoringRep","Tester(AffineNormalizer)"]]},{"rank" : 55,"comment" : "AffineNormalizer: for SpaceGroup acting OnLeft","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)","IsSpaceGroup","Tester(IsSpaceGroup)"]]},{"rank" : 55,"comment" : "AffineNormalizer: for SpaceGroup acting OnRight","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)","IsSpaceGroup","Tester(IsSpaceGroup)"]]},{"rank" : 0,"comment" : "AffineNormalizer:  fallback method to test conditions","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 0,"comment" : "AffineNormalizer:  fallback method to test conditions","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 0,"comment" : "AffineNormalizer: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AffineNormalizer)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AffineNormalizer): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AffineNormalizer): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AffineNormalizer)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPointHomomorphism","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IsPointHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(IsPointHomomorphism)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsPointHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsPointHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsPointHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsPointHomomorphism)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NiceToCryst","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "NiceToCryst: system getter","filters" : [["IsAttributeStoringRep","Tester(NiceToCryst)"]]},{"rank" : 0,"comment" : "NiceToCryst: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NiceToCryst)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NiceToCryst): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NiceToCryst): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NiceToCryst)","type" : "GAP_Operation","filters" : [[["IsPointGroup","Tester(IsPointGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFromAffineCrystGroupToFpGroup","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IsFromAffineCrystGroupToFpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFromAffineCrystGroupToFpGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFromAffineCrystGroupToFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFromAffineCrystGroupToFpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFromAffineCrystGroupToFpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFromAffineCrystGroupToFpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsFromAffineCrystGroupToPcpGroup","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20018,"comment" : "IsFromAffineCrystGroupToPcpGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsFromAffineCrystGroupToPcpGroup)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsFromAffineCrystGroupToPcpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsFromAffineCrystGroupToPcpGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsFromAffineCrystGroupToPcpGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsFromAffineCrystGroupToPcpGroup)","type" : "GAP_Operation","filters" : [[["IsGroupGeneralMappingByImages"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WyckoffSpaceGroup","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "WyckoffSpaceGroup","filters" : [["IsWyckoffPosition"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WyckoffTranslation","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "WyckoffTranslation","filters" : [["IsWyckoffPosition"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WyckoffBasis","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 3,"comment" : "WyckoffBasis","filters" : [["IsWyckoffPosition"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WyckoffStabilizer","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "WyckoffStabilizer: system getter","filters" : [["IsAttributeStoringRep","Tester(WyckoffStabilizer)"]]},{"rank" : 3,"comment" : "WyckoffStabilizer","filters" : [["IsWyckoffPosition"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WyckoffStabilizer)","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WyckoffStabilizer): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WyckoffStabilizer): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WyckoffStabilizer)","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WyckoffOrbit","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "WyckoffOrbit: system getter","filters" : [["IsAttributeStoringRep","Tester(WyckoffOrbit)"]]},{"rank" : 3,"comment" : "WyckoffOrbit","filters" : [["IsWyckoffPosition"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WyckoffOrbit)","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WyckoffOrbit): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WyckoffOrbit): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WyckoffOrbit)","type" : "GAP_Operation","filters" : [[["IsWyckoffPosition"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WyckoffPositions","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "WyckoffPositions: system getter","filters" : [["IsAttributeStoringRep","Tester(WyckoffPositions)"]]},{"rank" : 51,"comment" : "WyckoffPositions: for AffineCrystGroupOnLeftOrRight","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 0,"comment" : "WyckoffPositions: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(WyckoffPositions)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(WyckoffPositions): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(WyckoffPositions): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(WyckoffPositions)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "WyckoffGraph","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],["IsRecord"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 51,"comment" : "WyckoffGraph","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]},{"rank" : 2,"comment" : "WyckoffGraph","filters" : [["IsList"]]}],"2args" : [{"rank" : 52,"comment" : "WyckoffGraph","filters" : [["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],["IsRecord"]]},{"rank" : 3,"comment" : "WyckoffGraph","filters" : [["IsList"],["IsRecord"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpaceGroupsByPointGroupOnRight","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "SpaceGroupsByPointGroupOnRight","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 48,"comment" : "SpaceGroupsByPointGroupOnRight","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [{"rank" : 49,"comment" : "SpaceGroupsByPointGroupOnRight","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpaceGroupsByPointGroupOnLeft","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "SpaceGroupsByPointGroupOnLeft","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 48,"comment" : "SpaceGroupsByPointGroupOnLeft","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [{"rank" : 49,"comment" : "SpaceGroupsByPointGroupOnLeft","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpaceGroupsByPointGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "SpaceGroupsByPointGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 48,"comment" : "SpaceGroupsByPointGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"]]}],"3args" : [{"rank" : 49,"comment" : "SpaceGroupsByPointGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsList"],["IsBool"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpaceGroupTypesByPointGroupOnRight","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "SpaceGroupTypesByPointGroupOnRight","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 47,"comment" : "SpaceGroupTypesByPointGroupOnRight","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpaceGroupTypesByPointGroupOnLeft","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "SpaceGroupTypesByPointGroupOnLeft","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 47,"comment" : "SpaceGroupTypesByPointGroupOnLeft","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SpaceGroupTypesByPointGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "SpaceGroupTypesByPointGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 47,"comment" : "SpaceGroupTypesByPointGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CocVecs","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20051,"comment" : "CocVecs: system getter","filters" : [["IsAttributeStoringRep","Tester(CocVecs)"]]},{"rank" : 53,"comment" : "CocVecs","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 53,"comment" : "CocVecs","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]},{"rank" : 0,"comment" : "CocVecs: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CocVecs)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CocVecs): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CocVecs): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CocVecs)","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsColorGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsColorGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsColorGroup)"]]},{"rank" : 33,"comment" : "IsColorGroup: fallback method","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsColorGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsColorGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsColorGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsColorGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsColorGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ColorSubgroup","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "ColorSubgroup: system getter","filters" : [["IsAttributeStoringRep","Tester(ColorSubgroup)"]]},{"rank" : 36,"comment" : "ColorSubgroup: for subgroups","filters" : [["Tester(ParentAttr)","IsColorGroup","Tester(IsColorGroup)"]]},{"rank" : 0,"comment" : "ColorSubgroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ColorSubgroup)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ColorSubgroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ColorSubgroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ColorSubgroup)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ColorCosetList","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "ColorCosetList: system getter","filters" : [["IsAttributeStoringRep","Tester(ColorCosetList)"]]},{"rank" : 35,"comment" : "ColorCosetList: generic","filters" : [["IsColorGroup","Tester(IsColorGroup)"]]},{"rank" : 0,"comment" : "ColorCosetList: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ColorCosetList)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ColorCosetList): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ColorCosetList): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ColorCosetList)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ColorPermGroup","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "ColorPermGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(ColorPermGroup)"]]},{"rank" : 35,"comment" : "ColorPermGroup: generic","filters" : [["IsColorGroup","Tester(IsColorGroup)"]]},{"rank" : 0,"comment" : "ColorPermGroup: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ColorPermGroup)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ColorPermGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ColorPermGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ColorPermGroup)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ColorHomomorphism","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20038,"comment" : "ColorHomomorphism: system getter","filters" : [["IsAttributeStoringRep","Tester(ColorHomomorphism)"]]},{"rank" : 35,"comment" : "ColorHomomorphism: generic","filters" : [["IsColorGroup","Tester(IsColorGroup)"]]},{"rank" : 0,"comment" : "ColorHomomorphism: default method requiring categories and checking properties","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(ColorHomomorphism)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(ColorHomomorphism): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(ColorHomomorphism): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(ColorHomomorphism)","type" : "GAP_Operation","filters" : [[["IsColorGroup","Tester(IsColorGroup)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ConjugatorSpaceGroups","type" : "GAP_Operation","filters" : [[["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"],["IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 110,"comment" : "ConjugatorSpaceGroups","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)","IsSpaceGroup","Tester(IsSpaceGroup)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)","IsSpaceGroup","Tester(IsSpaceGroup)"]]},{"rank" : 110,"comment" : "ConjugatorSpaceGroups","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)","IsSpaceGroup","Tester(IsSpaceGroup)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)","IsSpaceGroup","Tester(IsSpaceGroup)"]]},{"rank" : 0,"comment" : "ConjugatorSpaceGroups:  fallback method to test conditions","filters" : [["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"],["IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)"]]},{"rank" : 0,"comment" : "ConjugatorSpaceGroups:  fallback method to test conditions","filters" : [["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"],["IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "CrystCatRecord","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "CrystCatRecord: system getter","filters" : [["IsAttributeStoringRep","Tester(CrystCatRecord)"]]},{"rank" : 0,"comment" : "CrystCatRecord: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(CrystCatRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(CrystCatRecord): system mutable setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(CrystCatRecord): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(CrystCatRecord)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAlmostCrystallographic","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsAlmostCrystallographic: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAlmostCrystallographic)"]]},{"rank" : 48,"comment" : "IsAlmostCrystallographic: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 33,"comment" : "IsAlmostCrystallographic: for groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 0,"comment" : "IsAlmostCrystallographic: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAlmostCrystallographic)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAlmostCrystallographic): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAlmostCrystallographic): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAlmostCrystallographic)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsAlmostBieberbachGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "IsAlmostBieberbachGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsAlmostBieberbachGroup)"]]},{"rank" : 48,"comment" : "IsAlmostBieberbachGroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "IsAlmostBieberbachGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsAlmostBieberbachGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsAlmostBieberbachGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsAlmostBieberbachGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsAlmostBieberbachGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AlmostCrystallographicInfo","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "AlmostCrystallographicInfo: system getter","filters" : [["IsAttributeStoringRep","Tester(AlmostCrystallographicInfo)"]]},{"rank" : 0,"comment" : "AlmostCrystallographicInfo: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(AlmostCrystallographicInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(AlmostCrystallographicInfo): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(AlmostCrystallographicInfo): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(AlmostCrystallographicInfo)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NaturalHomomorphismOnHolonomyGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "NaturalHomomorphismOnHolonomyGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(NaturalHomomorphismOnHolonomyGroup)"]]},{"rank" : 50,"comment" : "NaturalHomomorphismOnHolonomyGroup: for ac pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)","IsAlmostCrystallographic","Tester(IsAlmostCrystallographic)"]]},{"rank" : 0,"comment" : "NaturalHomomorphismOnHolonomyGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NaturalHomomorphismOnHolonomyGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NaturalHomomorphismOnHolonomyGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NaturalHomomorphismOnHolonomyGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NaturalHomomorphismOnHolonomyGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "HolonomyGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "HolonomyGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(HolonomyGroup)"]]},{"rank" : 50,"comment" : "HolonomyGroup: for ac pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)","IsAlmostCrystallographic","Tester(IsAlmostCrystallographic)"]]},{"rank" : 0,"comment" : "HolonomyGroup: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(HolonomyGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(HolonomyGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(HolonomyGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(HolonomyGroup)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "OrientationModule","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "OrientationModule: system getter","filters" : [["IsAttributeStoringRep","Tester(OrientationModule)"]]},{"rank" : 48,"comment" : "OrientationModule: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "OrientationModule: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(OrientationModule)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(OrientationModule): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(OrientationModule): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(OrientationModule)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BettiNumber","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 66,"comment" : "BettiNumber: for torsion-free pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "BettiNumbers","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20036,"comment" : "BettiNumbers: system getter","filters" : [["IsAttributeStoringRep","Tester(BettiNumbers)"]]},{"rank" : 48,"comment" : "BettiNumbers: for torsion-free pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]},{"rank" : 0,"comment" : "BettiNumbers: default method requiring categories and checking properties","filters" : [["IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(BettiNumbers)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(BettiNumbers): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(BettiNumbers): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(BettiNumbers)","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PcpGroupByMatGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 48,"comment" : "PcpGroupByMatGroup: for rational matrix groups (Polenta)","filters" : [["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)"]]},{"rank" : 46,"comment" : "PcpGroupByMatGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : 46,"comment" : "PcpGroupByMatGroup: for matrix groups over a finite field (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 64,"comment" : "PcpGroupByMatGroup: for polycyclic matrix groups (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIsomorphismByFinitePolycyclicMatrixGroup","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "IsIsomorphismByFinitePolycyclicMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"]]},{"rank" : 0,"comment" : "IsIsomorphismByFinitePolycyclicMatrixGroup: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIsomorphismByFinitePolycyclicMatrixGroup)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIsomorphismByFinitePolycyclicMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIsomorphismByFinitePolycyclicMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsIsomorphismByPolycyclicMatrixGroup","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20014,"comment" : "IsIsomorphismByPolycyclicMatrixGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsIsomorphismByPolycyclicMatrixGroup)"]]},{"rank" : 0,"comment" : "IsIsomorphismByPolycyclicMatrixGroup: default method requiring categories and checking properties","filters" : [["IsGeneralMapping"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsIsomorphismByPolycyclicMatrixGroup)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsIsomorphismByPolycyclicMatrixGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsIsomorphismByPolycyclicMatrixGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsIsomorphismByPolycyclicMatrixGroup)","type" : "GAP_Operation","filters" : [[["IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPolycyclicMatGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 43,"comment" : "IsPolycyclicMatGroup","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsTriangularizableMatGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20046,"comment" : "IsTriangularizableMatGroup: system getter","filters" : [["IsAttributeStoringRep","Tester(IsTriangularizableMatGroup)"]]},{"rank" : 48,"comment" : "IsTriangularizableMatGroup: for matrix groups over Q (Polenta)","filters" : [["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)"]]},{"rank" : 46,"comment" : "IsTriangularizableMatGroup:  fallback method to test conditions","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]},{"rank" : -14,"comment" : "IsTriangularizableMatGroup: default method requiring categories and checking properties","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsTriangularizableMatGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsTriangularizableMatGroup): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsTriangularizableMatGroup): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsTriangularizableMatGroup)","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RadicalSeriesSolvableMatGroup","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 46,"comment" : "RadicalSeriesSolvableMatGroup: for solvable matrix groups (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SubgroupsUnipotentByAbelianByFinite","type" : "GAP_Operation","filters" : [[["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 43,"comment" : "SubgroupsUnipotentByAbelianByFinite: for polycyclic matrix groups (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"]]}],"2args" : [{"rank" : 61,"comment" : "SubgroupsUnipotentByAbelianByFinite: for polycyclic matrix groups (Polenta)","filters" : [["CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)"],["IsInt"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsPolyInfiniteCyclicGroup","type" : "GAP_Operation","filters" : [[["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 48,"comment" : "IsPolyInfiniteCyclicGroup: for pcp groups","filters" : [["IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","CategoryCollections(IsPcpElement)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsCommuting","type" : "GAP_Operation","filters" : [[["IsMultiplicativeElement"],["IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 6,"comment" : "IsCommuting: fallback method (ResClasses)","filters" : [["IsMultiplicativeElement"],["IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Z_piCons","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : -26,"comment" : "Z_piCons: natural Z_pi (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZ_pi","type" : "GAP_Operation","filters" : [[["IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20034,"comment" : "IsZ_pi: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZ_pi)"]]},{"rank" : 0,"comment" : "IsZ_pi: for non-Z_(pi) (ResClasses)","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZ_pi)","type" : "GAP_Operation","filters" : [[["IsEuclideanRing"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZ_pi): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZ_pi): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZ_pi)","type" : "GAP_Operation","filters" : [[["IsEuclideanRing"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NoninvertiblePrimes","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "NoninvertiblePrimes: system getter","filters" : [["IsAttributeStoringRep","Tester(NoninvertiblePrimes)"]]},{"rank" : -14,"comment" : "NoninvertiblePrimes: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(NoninvertiblePrimes)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(NoninvertiblePrimes): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(NoninvertiblePrimes): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(NoninvertiblePrimes)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ResidueClassUnionCons","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsList"],["IsList"],["IsList"]],[["IsResidueClassUnion"],["IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsList"],["IsList"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : [{"rank" : -6,"comment" : "ResidueClassUnionCons: residue list rep, mod. as vector, for Z^2 (ResClasses)","filters" : [["IsResidueClassUnion"],["IsRowModule","Tester(IsRowModule)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"],["IsList"],["IsList"],["IsList"]]},{"rank" : -6,"comment" : "ResidueClassUnionCons: residue list representation, for Z^2 (ResClasses)","filters" : [["IsResidueClassUnion"],["IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsList"],["IsList"],["IsList"]]},{"rank" : -6,"comment" : "ResidueClassUnionCons: residue list rep., for Z, Z_pi and GF(q)[x] (ResClasses)","filters" : [["IsResidueClassUnion"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsList"],["IsList"],["IsList"]]}]}},{"name" : "IsResidueClass","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsResidueClass: system getter","filters" : [["IsAttributeStoringRep","Tester(IsResidueClass)"]]},{"rank" : 0,"comment" : "IsResidueClass: general method (ResClasses)","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsResidueClass)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsResidueClass): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsResidueClass): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsResidueClass)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Modulus","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"]],[["IsUnionOfResidueClassesWithFixedRepresentatives"]],[["IsResidueClassWithFixedRepresentative","Tester(IsResidueClassWithFixedRepresentative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 10002,"comment" : "Modulus: for residue classes with fixed representative (ResClasses)","filters" : [["IsResidueClassWithFixedRepresentative","Tester(IsResidueClassWithFixedRepresentative)"]]},{"rank" : 27,"comment" : "Modulus: for the base module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "Modulus: for the base ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 17,"comment" : "Modulus: for the empty set (ResClasses)","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 9,"comment" : "Modulus: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 6,"comment" : "Modulus: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 2,"comment" : "Modulus: for finite sets (ResClasses)","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Residues","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 27,"comment" : "Residues: for the base module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "Residues: for the base ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 9,"comment" : "Residues: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 2,"comment" : "Residues: for finite sets (ResClasses)","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Residue","type" : "GAP_Operation","filters" : [[["IsResidueClass","Tester(IsResidueClass)"]],[["IsResidueClassWithFixedRepresentative","Tester(IsResidueClassWithFixedRepresentative)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 27,"comment" : "Residue: for the base module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "Residue: for the base ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 2,"comment" : "Residue: for residue classes with fixed representative (ResClasses)","filters" : [["IsResidueClassWithFixedRepresentative","Tester(IsResidueClassWithFixedRepresentative)"]]},{"rank" : 2,"comment" : "Residue: for residue classes (ResClasses)","filters" : [["IsResidueClass","Tester(IsResidueClass)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IncludedElements","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 27,"comment" : "IncludedElements: for the base module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "IncludedElements: for the base ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 9,"comment" : "IncludedElements: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 2,"comment" : "IncludedElements: for finite sets (ResClasses)","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExcludedElements","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 27,"comment" : "ExcludedElements: for the base module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "ExcludedElements: for the base ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 9,"comment" : "ExcludedElements: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion","IsResidueClassUnionResidueListRep"]]},{"rank" : 2,"comment" : "ExcludedElements: for finite sets (ResClasses)","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IncludedLines","type" : "GAP_Operation","filters" : [[["IsResidueClassUnionOfZxZ"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "ExcludedLines","type" : "GAP_Operation","filters" : [[["IsResidueClassUnionOfZxZ"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnderlyingIndeterminate","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20004,"comment" : "UnderlyingIndeterminate: system getter","filters" : [["IsAttributeStoringRep","Tester(UnderlyingIndeterminate)"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(UnderlyingIndeterminate)","type" : "GAP_Operation","filters" : [[["IsFamily"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(UnderlyingIndeterminate): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(UnderlyingIndeterminate): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(UnderlyingIndeterminate)","type" : "GAP_Operation","filters" : [[["IsFamily"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsZxZ","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsZxZ: system getter","filters" : [["IsAttributeStoringRep","Tester(IsZxZ)"]]},{"rank" : 0,"comment" : "IsZxZ: general method (ResClasses)","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsZxZ)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsZxZ): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsZxZ): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsZxZ)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AllResidues","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]],[["IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 57,"comment" : "AllResidues: for lattice in Z^2 (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 34,"comment" : "AllResidues: for Z, Z_pi and GF(q)[x] (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "NumberOfResidues","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]],[["IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 57,"comment" : "NumberOfResidues: for lattice in Z^2 (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]},{"rank" : 34,"comment" : "NumberOfResidues: for Z, Z_pi and GF(q)[x] (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsSublattice","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 60,"comment" : "IsSublattice: for lattices in Z^n (ResClasses)","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"],["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Superlattices","type" : "GAP_Operation","filters" : [[["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 30,"comment" : "Superlattices: for a lattice in Z^2 (ResClasses)","filters" : [["IsTable","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SizeOfSmallestResidueClassRing","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20029,"comment" : "SizeOfSmallestResidueClassRing: system getter","filters" : [["IsAttributeStoringRep","Tester(SizeOfSmallestResidueClassRing)"]]},{"rank" : 27,"comment" : "SizeOfSmallestResidueClassRing: for Z^2 (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "SizeOfSmallestResidueClassRing: for Z, Z_pi and GF(q)[x] (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : -14,"comment" : "SizeOfSmallestResidueClassRing: default method requiring categories and checking properties","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(SizeOfSmallestResidueClassRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(SizeOfSmallestResidueClassRing): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(SizeOfSmallestResidueClassRing): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(SizeOfSmallestResidueClassRing)","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsUnionOfFewClasses","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 28,"comment" : "AsUnionOfFewClasses: for pure residue class unions of Z, 2 (ResClasses)","filters" : [["IsResidueClassUnionOfZ"]]},{"rank" : 27,"comment" : "AsUnionOfFewClasses: for a row module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "AsUnionOfFewClasses: for a ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 7,"comment" : "AsUnionOfFewClasses: for pure residue class unions of Z^2 (ResClasses)","filters" : [["IsResidueClassUnionOfZxZ"]]},{"rank" : 6,"comment" : "AsUnionOfFewClasses: for pure residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 2,"comment" : "AsUnionOfFewClasses: for finite sets of elements (ResClasses)","filters" : [["IsList"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "SplittedClass","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]],[["IsResidueClassUnion"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 45,"comment" : "SplittedClass: for Z, Z_pi or GF(q)[x] (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]]},{"rank" : 42,"comment" : "SplittedClass: for GF(q)[x] and a polynomial (ResClasses)","filters" : [["IsFiniteFieldPolynomialRing"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 39,"comment" : "SplittedClass: for Z^2 (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]},{"rank" : 28,"comment" : "SplittedClass: for residue classes of GF(q)[x] (ResClasses)","filters" : [["IsResidueClassUnionOfGFqx","IsResidueClass","Tester(IsResidueClass)"],["IsInt","IsPosRat"]]},{"rank" : 28,"comment" : "SplittedClass: for residue classes of Z or Z_pi (ResClasses)","filters" : [["IsResidueClassUnionOfZorZ_pi","IsResidueClass","Tester(IsResidueClass)"],["IsInt","IsPosRat"]]},{"rank" : 23,"comment" : "SplittedClass: for a res.-class of GF(q)[x] and a polynomial (ResClasses)","filters" : [["IsResidueClassUnionOfGFqx","IsResidueClass","Tester(IsResidueClass)"],["IsPolynomial","Tester(IsPolynomial)"]]},{"rank" : 21,"comment" : "SplittedClass: for residue classes of Z^2 (ResClasses)","filters" : [["IsResidueClassUnionOfZxZ","IsResidueClass","Tester(IsResidueClass)"],["IsHomogeneousList","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsOddAdditiveNestingDepthObject"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "PartitionsIntoResidueClasses","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]],[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 45,"comment" : "PartitionsIntoResidueClasses: general method (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"]]}],"3args" : [{"rank" : 61,"comment" : "PartitionsIntoResidueClasses: method for Z (ResClasses)","filters" : [["IsIntegers"],["IsInt","IsPosRat"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RandomPartitionIntoResidueClasses","type" : "GAP_Operation","filters" : [[["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : 49,"comment" : "RandomPartitionIntoResidueClasses: for GF(q)[x] (ResClasses)","filters" : [["IsFiniteFieldPolynomialRing"],["IsInt","IsPosRat"],["IsList"]]},{"rank" : 47,"comment" : "RandomPartitionIntoResidueClasses: for Z or Z_pi (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsInt","IsPosRat"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Density","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "Density: system getter","filters" : [["IsAttributeStoringRep","Tester(Density)"]]},{"rank" : 27,"comment" : "Density: for the whole base module (ResClasses)","filters" : [["IsRowModule","Tester(IsRowModule)"]]},{"rank" : 26,"comment" : "Density: for the whole base ring (ResClasses)","filters" : [["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"]]},{"rank" : 17,"comment" : "Density: for the empty set (ResClasses)","filters" : [["IsList","IsEmpty","Tester(IsEmpty)"]]},{"rank" : 6,"comment" : "Density: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 6,"comment" : "Density: for residue class unions (ResClasses)","filters" : [["IsResidueClassUnion"]]},{"rank" : 5,"comment" : "Density: for finite sets (ResClasses)","filters" : [["IsList","IsCollection"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Density)","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Density): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Density): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Density)","type" : "GAP_Operation","filters" : [[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "UnionOfResidueClassesWithFixedRepresentativesCons","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [{"rank" : -6,"comment" : "UnionOfResidueClassesWithFixedRepresentativesCons: for Z, Z_pi and GF(q)[x] (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsMagma","IsNearAdditiveMagma","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)"],["IsList"]]}],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsResidueClassWithFixedRepresentative","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20003,"comment" : "IsResidueClassWithFixedRepresentative: system getter","filters" : [["IsAttributeStoringRep","Tester(IsResidueClassWithFixedRepresentative)"]]},{"rank" : 0,"comment" : "IsResidueClassWithFixedRepresentative: general method (ResClasses)","filters" : [[]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsResidueClassWithFixedRepresentative)","type" : "GAP_Operation","filters" : [[[],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsResidueClassWithFixedRepresentative): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsResidueClassWithFixedRepresentative): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsResidueClassWithFixedRepresentative)","type" : "GAP_Operation","filters" : [[[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Classes","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "Classes: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsListOfClasses","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "AsListOfClasses: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Multiplicity","type" : "GAP_Operation","filters" : [[[],["IsUnionOfResidueClassesWithFixedRepresentatives"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 14,"comment" : "Multiplicity: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)","filters" : [["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]},{"rank" : 12,"comment" : "Multiplicity: for a res.-cl. and union of res.-cl. with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsUnionOfResidueClassesWithFixedRepresentatives"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "IsOverlappingFree","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "IsOverlappingFree: system getter","filters" : [["IsAttributeStoringRep","Tester(IsOverlappingFree)"]]},{"rank" : 6,"comment" : "IsOverlappingFree: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(IsOverlappingFree)","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsBool"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(IsOverlappingFree): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(IsOverlappingFree): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(IsOverlappingFree)","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "AsOrdinaryUnionOfResidueClasses","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 6,"comment" : "AsOrdinaryUnionOfResidueClasses: for unions of residue classes with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesWithFixedRepresentatives"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "RepresentativeStabilizingRefinement","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"],["IsNearAdditiveElementWithInverse","IsAdditiveElement","IsMultiplicativeElement"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 28,"comment" : "RepresentativeStabilizingRefinement: for a union of residue classes of Z with fixed rep's and 0 (simplify) (ResClasses)","filters" : [["IsUnionOfResidueClassesOfZWithFixedRepresentatives"],["IsInt","IsZero","Tester(IsZero)"]]},{"rank" : 27,"comment" : "RepresentativeStabilizingRefinement: for a union of residue classes of Z with fixed rep's and a positive integer (ResClasses)","filters" : [["IsUnionOfResidueClassesOfZWithFixedRepresentatives"],["IsInt","IsPosRat"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Rho","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"]],[["IsResidueClassUnion"]]],"methods" : {"0args" : [],"1args" : [{"rank" : 20009,"comment" : "Rho: system getter","filters" : [["IsAttributeStoringRep","Tester(Rho)"]]},{"rank" : 8,"comment" : "Rho: for unions of residue classes of Z with fixed rep's (ResClasses)","filters" : [["IsUnionOfResidueClassesOfZWithFixedRepresentatives"]]},{"rank" : 8,"comment" : "Rho: for residue class unions of Z (ResClasses)","filters" : [["IsResidueClassUnionOfZ"]]}],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Setter(Rho)","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"],[]],[["IsResidueClassUnion"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 2,"comment" : "Setter(Rho): system setter","filters" : [["IsAttributeStoringRep"],[]]},{"rank" : 0,"comment" : "Setter(Rho): default method, does nothing","filters" : [[],[]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "Tester(Rho)","type" : "GAP_Operation","filters" : [[["IsUnionOfResidueClassesWithFixedRepresentatives"]]],"methods" : {"0args" : [],"1args" : [],"2args" : [],"3args" : [],"4args" : [],"5args" : [],"6args" : []}},{"name" : "_GapToJsonStreamInternal","type" : "GAP_Operation","filters" : [[["IsOutputStream"],[]]],"methods" : {"0args" : [],"1args" : [],"2args" : [{"rank" : 20,"comment" : "_GapToJsonStreamInternal","filters" : [["IsOutputStream"],["IsInt"]]},{"rank" : 15,"comment" : "_GapToJsonStreamInternal","filters" : [["IsOutputStream"],["IsFloat"]]},{"rank" : 7,"comment" : "_GapToJsonStreamInternal","filters" : [["IsOutputStream"],["IsString"]]},{"rank" : 4,"comment" : "_GapToJsonStreamInternal","filters" : [["IsOutputStream"],["IsList"]]},{"rank" : 3,"comment" : "_GapToJsonStreamInternal","filters" : [["IsOutputStream"],["IsRecord"]]},{"rank" : 3,"comment" : "_GapToJsonStreamInternal","filters" : [["IsOutputStream"],["IsBool"]]}],"3args" : [],"4args" : [],"5args" : [],"6args" : []}}]
\ No newline at end of file
+[
+    {
+        "implied": [],
+        "name": "IsObject",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsMutable",
+            "IsCopyable"
+        ],
+        "name": "IsMutable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable"
+        ],
+        "name": "IsCopyable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFunction"
+        ],
+        "name": "IsFunction",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFunction",
+            "IsOperation"
+        ],
+        "name": "IsOperation",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsInt",
+            "IsRat",
+            "IsCyc",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic"
+        ],
+        "name": "IsInt",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsRat",
+            "IsCyc",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic"
+        ],
+        "name": "IsRat",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCyc",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic"
+        ],
+        "name": "IsCyc",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(CONDUCTOR)"
+        ],
+        "name": "Tester(CONDUCTOR)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsFFE",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement"
+        ],
+        "name": "IsFFE",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsPerm",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsFiniteOrderElement"
+        ],
+        "name": "IsPerm",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsTransformation",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement"
+        ],
+        "name": "IsTransformation",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsPartialPerm",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement"
+        ],
+        "name": "IsPartialPerm",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsBool"
+        ],
+        "name": "IsBool",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsRecord"
+        ],
+        "name": "IsRecord",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsListOrCollection"
+        ],
+        "name": "IsList",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsListOrCollection"
+        ],
+        "name": "IsDenseList",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsListOrCollection"
+        ],
+        "name": "IsHomogeneousList",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsTable",
+            "IsListOrCollection",
+            "IsCollection"
+        ],
+        "name": "IsTable",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LENGTH)"
+        ],
+        "name": "Tester(LENGTH)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSSortedList",
+            "Tester(IS_SSORT_LIST)",
+            "IsSortedList",
+            "Tester(IsSortedList)"
+        ],
+        "name": "IsSSortedList",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IS_SSORT_LIST)"
+        ],
+        "name": "Tester(IS_SSORT_LIST)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNSortedList",
+            "Tester(IS_NSORT_LIST)"
+        ],
+        "name": "IsNSortedList",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IS_NSORT_LIST)"
+        ],
+        "name": "Tester(IS_NSORT_LIST)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPositionsList",
+            "Tester(IS_POSS_LIST)"
+        ],
+        "name": "IsPositionsList",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IS_POSS_LIST)"
+        ],
+        "name": "Tester(IS_POSS_LIST)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "Tester(LENGTH)",
+            "IsPlistRep",
+            "IsInternalRep"
+        ],
+        "name": "IsPlistRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsBlist",
+            "IsListOrCollection"
+        ],
+        "name": "IsBlist",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsBlistRep",
+            "IsInternalRep"
+        ],
+        "name": "IsBlistRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsRange",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "IsNearAdditiveElement",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "IsNearAdditiveElementWithZero",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "IsNearAdditiveElementWithInverse",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "IsAdditiveElement",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsAdditivelyCommutativeElement)",
+            "CategoryCollections(IsCommutativeElement)",
+            "CategoryCollections(IsCyclotomic)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "IsRange",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsRangeRep",
+            "IsInternalRep"
+        ],
+        "name": "IsRangeRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsString",
+            "IsListOrCollection"
+        ],
+        "name": "IsString",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStringRep",
+            "IsInternalRep"
+        ],
+        "name": "IsStringRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsWeakPointerObject",
+            "IsListOrCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsSmallList",
+            "Tester(IsSmallList)"
+        ],
+        "name": "IsWeakPointerObject",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsNoImmediateMethodsObject"
+        ],
+        "name": "IsNoImmediateMethodsObject",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsInternalRep"
+        ],
+        "name": "IsInternalRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep"
+        ],
+        "name": "IsPositionalObjectRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep"
+        ],
+        "name": "IsComponentObjectRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep"
+        ],
+        "name": "IsDataObjectRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsNonAtomicComponentObjectRep"
+        ],
+        "name": "IsNonAtomicComponentObjectRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsReadOnlyPositionalObjectRep"
+        ],
+        "name": "IsReadOnlyPositionalObjectRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsAtomicPositionalObjectRep"
+        ],
+        "name": "IsAtomicPositionalObjectRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep"
+        ],
+        "name": "IsAttributeStoringRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsFamily"
+        ],
+        "name": "IsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsType"
+        ],
+        "name": "IsType",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsFamilyOfFamilies"
+        ],
+        "name": "IsFamilyOfFamilies",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsFamilyOfTypes"
+        ],
+        "name": "IsFamilyOfTypes",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsFamilyDefaultRep"
+        ],
+        "name": "IsFamilyDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsTypeDefaultRep"
+        ],
+        "name": "IsTypeDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(Name)"
+        ],
+        "name": "Tester(Name)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InfoText)"
+        ],
+        "name": "Tester(InfoText)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(String)"
+        ],
+        "name": "Tester(String)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsImpossible)"
+        ],
+        "name": "Tester(IsImpossible)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsPackedElementDefaultRep"
+        ],
+        "name": "IsPackedElementDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsToBeDefinedObj"
+        ],
+        "name": "IsToBeDefinedObj",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsLVarsBag"
+        ],
+        "name": "IsLVarsBag",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection"
+        ],
+        "name": "IsListOrCollection",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection"
+        ],
+        "name": "IsCollection",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(CollectionsFamily)"
+        ],
+        "name": "Tester(CollectionsFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsCollection)"
+        ],
+        "name": "CategoryFamily(IsCollection)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(ElementsFamily)"
+        ],
+        "name": "Tester(ElementsFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsStandardIterator"
+        ],
+        "name": "IsStandardIterator",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsIterator"
+        ],
+        "name": "IsIterator",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsEmpty",
+            "Tester(IsEmpty)"
+        ],
+        "name": "IsEmpty",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsEmpty)"
+        ],
+        "name": "Tester(IsEmpty)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsTrivial",
+            "Tester(IsTrivial)",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "CanComputeSize"
+        ],
+        "name": "IsTrivial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTrivial)"
+        ],
+        "name": "Tester(IsTrivial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNonTrivial",
+            "Tester(IsNonTrivial)"
+        ],
+        "name": "IsNonTrivial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNonTrivial)"
+        ],
+        "name": "Tester(IsNonTrivial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFinite",
+            "Tester(IsFinite)"
+        ],
+        "name": "IsFinite",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFinite)"
+        ],
+        "name": "Tester(IsFinite)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsWholeFamily",
+            "Tester(IsWholeFamily)"
+        ],
+        "name": "IsWholeFamily",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsWholeFamily)"
+        ],
+        "name": "Tester(IsWholeFamily)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(Size)",
+            "CanComputeSize"
+        ],
+        "name": "Tester(Size)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Representative)"
+        ],
+        "name": "Tester(Representative)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RepresentativeSmallest)"
+        ],
+        "name": "Tester(RepresentativeSmallest)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PseudoRandomSeed)"
+        ],
+        "name": "Tester(PseudoRandomSeed)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Enumerator)"
+        ],
+        "name": "Tester(Enumerator)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EnumeratorSorted)"
+        ],
+        "name": "Tester(EnumeratorSorted)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingCollection)"
+        ],
+        "name": "Tester(UnderlyingCollection)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsList)"
+        ],
+        "name": "Tester(AsList)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsSortedList)"
+        ],
+        "name": "Tester(AsSortedList)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsSSortedList)"
+        ],
+        "name": "Tester(AsSSortedList)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CanEasilyCompareElements",
+            "Tester(CanEasilyCompareElements)"
+        ],
+        "name": "CanEasilyCompareElements",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(CanEasilyCompareElements)"
+        ],
+        "name": "Tester(CanEasilyCompareElements)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "CanEasilyCompareElements",
+            "Tester(CanEasilyCompareElements)",
+            "CanEasilySortElements",
+            "Tester(CanEasilySortElements)"
+        ],
+        "name": "CanEasilySortElements",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(CanEasilySortElements)"
+        ],
+        "name": "Tester(CanEasilySortElements)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "CanComputeSize"
+        ],
+        "name": "CanComputeSize",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(RandomizerAttr)"
+        ],
+        "name": "Tester(RandomizerAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CheapRandomizerAttr)"
+        ],
+        "name": "Tester(CheapRandomizerAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsListOrCollection",
+            "IsConstantTimeAccessList"
+        ],
+        "name": "IsConstantTimeAccessList",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsSmallList",
+            "Tester(IsSmallList)"
+        ],
+        "name": "IsSmallList",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSmallList)"
+        ],
+        "name": "Tester(IsSmallList)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ConstantTimeAccessList)"
+        ],
+        "name": "Tester(ConstantTimeAccessList)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSortedList",
+            "Tester(IsSortedList)"
+        ],
+        "name": "IsSortedList",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSortedList)"
+        ],
+        "name": "Tester(IsSortedList)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)"
+        ],
+        "name": "IsDuplicateFree",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsDuplicateFree)"
+        ],
+        "name": "Tester(IsDuplicateFree)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsQuickPositionList"
+        ],
+        "name": "IsQuickPositionList",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(AsDuplicateFreeList)"
+        ],
+        "name": "Tester(AsDuplicateFreeList)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SortingPerm)"
+        ],
+        "name": "Tester(SortingPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement"
+        ],
+        "name": "IsExtAElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)"
+        ],
+        "name": "CategoryCollections(IsExtAElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(CategoryCollections(IsExtAElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsExtAElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement"
+        ],
+        "name": "IsNearAdditiveElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)"
+        ],
+        "name": "CategoryCollections(IsNearAdditiveElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero"
+        ],
+        "name": "IsNearAdditiveElementWithZero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)"
+        ],
+        "name": "CategoryCollections(IsNearAdditiveElementWithZero)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse"
+        ],
+        "name": "IsNearAdditiveElementWithInverse",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)"
+        ],
+        "name": "CategoryCollections(IsNearAdditiveElementWithInverse)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsAdditiveElement"
+        ],
+        "name": "IsAdditiveElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsAdditiveElement)"
+        ],
+        "name": "CategoryCollections(IsAdditiveElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement"
+        ],
+        "name": "IsExtLElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)"
+        ],
+        "name": "CategoryCollections(IsExtLElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(CategoryCollections(IsExtLElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsExtLElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtRElement"
+        ],
+        "name": "IsExtRElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)"
+        ],
+        "name": "CategoryCollections(IsExtRElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(CategoryCollections(IsExtRElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsExtRElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement"
+        ],
+        "name": "IsMultiplicativeElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "CategoryCollections(IsMultiplicativeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne"
+        ],
+        "name": "IsMultiplicativeElementWithOne",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)"
+        ],
+        "name": "CategoryCollections(IsMultiplicativeElementWithOne)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "IsMultiplicativeElementWithInverse",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)"
+        ],
+        "name": "CategoryCollections(IsMultiplicativeElementWithInverse)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsOddAdditiveNestingDepthFamily"
+        ],
+        "name": "IsOddAdditiveNestingDepthFamily",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsOddAdditiveNestingDepthObject"
+        ],
+        "name": "IsOddAdditiveNestingDepthObject",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsListOrCollection",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsGeneralizedRowVector"
+        ],
+        "name": "IsGeneralizedRowVector",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsListOrCollection",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsGeneralizedRowVector",
+            "IsMultiplicativeGeneralizedRowVector"
+        ],
+        "name": "IsMultiplicativeGeneralizedRowVector",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(NestingDepthA)"
+        ],
+        "name": "Tester(NestingDepthA)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NestingDepthM)"
+        ],
+        "name": "Tester(NestingDepthM)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))"
+        ],
+        "name": "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))"
+        ],
+        "name": "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE"
+        ],
+        "name": "IsZDFRE",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)"
+        ],
+        "name": "CategoryCollections(IsZDFRE)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsZDFRE))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsZDFRE))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))"
+        ],
+        "name": "CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsTable",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "IsNearAdditiveElement",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "IsNearAdditiveElementWithZero",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "IsNearAdditiveElementWithInverse",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "IsAdditiveElement",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "IsMultiplicativeElement",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsGeneralizedRowVector",
+            "IsMultiplicativeGeneralizedRowVector",
+            "IsOrdinaryMatrix"
+        ],
+        "name": "IsOrdinaryMatrix",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))",
+            "CategoryCollections(IsOrdinaryMatrix)"
+        ],
+        "name": "CategoryCollections(IsOrdinaryMatrix)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsTable",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "IsNearAdditiveElement",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "IsNearAdditiveElementWithZero",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "IsNearAdditiveElementWithInverse",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "IsAdditiveElement",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "IsMultiplicativeElement",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsGeneralizedRowVector",
+            "IsLieMatrix"
+        ],
+        "name": "IsLieMatrix",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement"
+        ],
+        "name": "IsAssociativeElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(IsAssociativeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsAdditiveElement",
+            "IsAdditivelyCommutativeElement"
+        ],
+        "name": "IsAdditivelyCommutativeElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsAdditivelyCommutativeElement)"
+        ],
+        "name": "CategoryCollections(IsAdditivelyCommutativeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsAdditivelyCommutativeElement)"
+        ],
+        "name": "CategoryFamily(IsAdditivelyCommutativeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsCommutativeElement"
+        ],
+        "name": "IsCommutativeElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsCommutativeElement)"
+        ],
+        "name": "CategoryCollections(IsCommutativeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsCommutativeElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsFiniteOrderElement"
+        ],
+        "name": "IsFiniteOrderElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsFiniteOrderElement)"
+        ],
+        "name": "CategoryCollections(IsFiniteOrderElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsFiniteOrderElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsFiniteOrderElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsJacobianElement"
+        ],
+        "name": "IsJacobianElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsJacobianElement)"
+        ],
+        "name": "CategoryCollections(IsJacobianElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsJacobianElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsJacobianElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsJacobianElement",
+            "IsRestrictedJacobianElement"
+        ],
+        "name": "IsRestrictedJacobianElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsJacobianElement)",
+            "CategoryCollections(IsRestrictedJacobianElement)"
+        ],
+        "name": "CategoryCollections(IsRestrictedJacobianElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsJacobianElement))",
+            "CategoryCollections(CategoryCollections(IsRestrictedJacobianElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsRestrictedJacobianElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsZeroSquaredElement"
+        ],
+        "name": "IsZeroSquaredElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsZeroSquaredElement)"
+        ],
+        "name": "CategoryCollections(IsZeroSquaredElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsZeroSquaredElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsZeroSquaredElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsZero",
+            "Tester(IsZero)"
+        ],
+        "name": "IsZero",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZero)"
+        ],
+        "name": "Tester(IsZero)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsOne",
+            "Tester(IsOne)"
+        ],
+        "name": "IsOne",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsOne)"
+        ],
+        "name": "Tester(IsOne)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ZeroImmutable)"
+        ],
+        "name": "Tester(ZeroImmutable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AdditiveInverseImmutable)"
+        ],
+        "name": "Tester(AdditiveInverseImmutable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OneImmutable)"
+        ],
+        "name": "Tester(OneImmutable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InverseImmutable)"
+        ],
+        "name": "Tester(InverseImmutable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Int)"
+        ],
+        "name": "Tester(Int)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Rat)"
+        ],
+        "name": "Tester(Rat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Characteristic)"
+        ],
+        "name": "Tester(Characteristic)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Order)"
+        ],
+        "name": "Tester(Order)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormedRowVector)"
+        ],
+        "name": "Tester(NormedRowVector)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCommutativeFamily",
+            "Tester(IsCommutativeFamily)"
+        ],
+        "name": "IsCommutativeFamily",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCommutativeFamily)"
+        ],
+        "name": "Tester(IsCommutativeFamily)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSkewFieldFamily",
+            "Tester(IsSkewFieldFamily)"
+        ],
+        "name": "IsSkewFieldFamily",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSkewFieldFamily)"
+        ],
+        "name": "Tester(IsSkewFieldFamily)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsUFDFamily",
+            "Tester(IsUFDFamily)"
+        ],
+        "name": "IsUFDFamily",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsUFDFamily)"
+        ],
+        "name": "Tester(IsUFDFamily)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAdditiveElementAsMultiplicativeElementRep"
+        ],
+        "name": "IsAdditiveElementAsMultiplicativeElementRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(AdditiveElementsAsMultiplicativeElementsFamily)"
+        ],
+        "name": "Tester(AdditiveElementsAsMultiplicativeElementsFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AdditiveElementAsMultiplicativeElement)"
+        ],
+        "name": "Tester(AdditiveElementAsMultiplicativeElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsIdempotent",
+            "Tester(IsIdempotent)"
+        ],
+        "name": "IsIdempotent",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIdempotent)"
+        ],
+        "name": "Tester(IsIdempotent)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsAdditivelyCommutativeElement)",
+            "CategoryCollections(IsCommutativeElement)",
+            "CategoryCollections(IsFFE)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(IsFFE)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsZDFRE))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))",
+            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+            "CategoryCollections(CategoryCollections(IsFFE))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsFFE))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFFE",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsLexOrderedFFE"
+        ],
+        "name": "IsLexOrderedFFE",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFFE",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsLogOrderedFFE"
+        ],
+        "name": "IsLogOrderedFFE",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsAdditivelyCommutativeElement)",
+            "CategoryFamily(IsFFE)"
+        ],
+        "name": "CategoryFamily(IsFFE)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(DegreeFFE)"
+        ],
+        "name": "Tester(DegreeFFE)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IntFFE)"
+        ],
+        "name": "Tester(IntFFE)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IntFFESymm)"
+        ],
+        "name": "Tester(IntFFESymm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsInternalFFE)"
+        ],
+        "name": "Tester(AsInternalFFE)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsGeneralizedDomain"
+        ],
+        "name": "IsGeneralizedDomain",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfDomain)"
+        ],
+        "name": "Tester(GeneratorsOfDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ParentAttr)"
+        ],
+        "name": "Tester(ParentAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsChar"
+        ],
+        "name": "IsChar",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(IsChar)"
+        ],
+        "name": "CategoryCollections(IsChar)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic"
+        ],
+        "name": "IsCyclotomic",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsAdditivelyCommutativeElement)",
+            "CategoryCollections(IsCommutativeElement)",
+            "CategoryCollections(IsCyclotomic)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(IsCyclotomic)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsZDFRE))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))",
+            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+            "CategoryCollections(CategoryCollections(IsCyclotomic))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsCyclotomic))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsRat",
+            "IsCyc",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic",
+            "IsPosRat"
+        ],
+        "name": "IsPosRat",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsRat",
+            "IsCyc",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic",
+            "IsNegRat"
+        ],
+        "name": "IsNegRat",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsInt",
+            "IsRat",
+            "IsCyc",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsZero",
+            "Tester(IsZero)",
+            "IsCyclotomic",
+            "IsZeroCyc"
+        ],
+        "name": "IsZeroCyc",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsSmallIntRep"
+        ],
+        "name": "IsSmallIntRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic",
+            "IsInfinity"
+        ],
+        "name": "IsInfinity",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic",
+            "IsNegInfinity"
+        ],
+        "name": "IsNegInfinity",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsIntegralCyclotomic",
+            "Tester(IsIntegralCyclotomic)"
+        ],
+        "name": "IsIntegralCyclotomic",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIntegralCyclotomic)"
+        ],
+        "name": "Tester(IsIntegralCyclotomic)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(IsRecord)"
+        ],
+        "name": "CategoryCollections(IsRecord)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(CategoryCollections(IsRecord))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsRecord))",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(RecNames)"
+        ],
+        "name": "Tester(RecNames)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsEnumeratorByFunctionsRep"
+        ],
+        "name": "IsEnumeratorByFunctionsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsIteratorByFunctionsRep"
+        ],
+        "name": "IsIteratorByFunctionsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsListOrCollection",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsGeneralizedRowVector",
+            "IsMultiplicativeGeneralizedRowVector",
+            "IsListDefault"
+        ],
+        "name": "IsListDefault",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsTable",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRectangularTable",
+            "Tester(IsRectangularTable)"
+        ],
+        "name": "IsRectangularTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRectangularTable)"
+        ],
+        "name": "Tester(IsRectangularTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsFiniteOrderElement)",
+            "CategoryCollections(IsPerm)",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "IsSubsetLocallyFiniteGroup",
+            "Tester(IsSubsetLocallyFiniteGroup)"
+        ],
+        "name": "CategoryCollections(IsPerm)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsFiniteOrderElement))",
+            "CategoryCollections(CategoryCollections(IsPerm))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsPerm))",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(SmallestGeneratorPerm)"
+        ],
+        "name": "Tester(SmallestGeneratorPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SmallestMovedPoint)"
+        ],
+        "name": "Tester(SmallestMovedPoint)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LargestMovedPoint)"
+        ],
+        "name": "Tester(LargestMovedPoint)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrMovedPoints)"
+        ],
+        "name": "Tester(NrMovedPoints)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MovedPoints)"
+        ],
+        "name": "Tester(MovedPoints)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SignPerm)"
+        ],
+        "name": "Tester(SignPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CycleStructurePerm)"
+        ],
+        "name": "Tester(CycleStructurePerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsPerm2Rep"
+        ],
+        "name": "IsPerm2Rep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsPerm4Rep"
+        ],
+        "name": "IsPerm4Rep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsTransformation)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(IsTransformation)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsTransformation))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsTransformation))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsTrans2Rep"
+        ],
+        "name": "IsTrans2Rep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsTrans4Rep"
+        ],
+        "name": "IsTrans4Rep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsPartialPerm)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "IsGeneratorsOfInverseSemigroup",
+            "Tester(IsGeneratorsOfInverseSemigroup)"
+        ],
+        "name": "CategoryCollections(IsPartialPerm)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsPartialPerm))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsPartialPerm))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsPPerm2Rep"
+        ],
+        "name": "IsPPerm2Rep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsPPerm4Rep"
+        ],
+        "name": "IsPPerm4Rep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsInfoClass"
+        ],
+        "name": "IsInfoClass",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(IsInfoClass)"
+        ],
+        "name": "CategoryCollections(IsInfoClass)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsDirectory"
+        ],
+        "name": "IsDirectory",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsInputTextStringRep"
+        ],
+        "name": "IsInputTextStringRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsClosedStream"
+        ],
+        "name": "IsClosedStream",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream"
+        ],
+        "name": "IsStream",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream",
+            "IsInputStream"
+        ],
+        "name": "IsInputStream",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream",
+            "IsInputStream",
+            "IsInputTextStream"
+        ],
+        "name": "IsInputTextStream",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream",
+            "IsInputStream",
+            "IsInputTextStream",
+            "IsInputTextNone"
+        ],
+        "name": "IsInputTextNone",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream",
+            "IsOutputStream"
+        ],
+        "name": "IsOutputStream",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream",
+            "IsOutputStream",
+            "IsOutputTextStream"
+        ],
+        "name": "IsOutputTextStream",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream",
+            "IsOutputStream",
+            "IsOutputTextStream",
+            "IsOutputTextNone"
+        ],
+        "name": "IsOutputTextNone",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStream",
+            "IsInputStream",
+            "IsOutputStream",
+            "IsInputOutputStream"
+        ],
+        "name": "IsInputOutputStream",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsRowVectorObj"
+        ],
+        "name": "IsRowVectorObj",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMatrixObj"
+        ],
+        "name": "IsMatrixObj",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMatrixObj",
+            "IsRowListMatrix"
+        ],
+        "name": "IsRowListMatrix",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMatrixObj",
+            "IsFlatMatrix"
+        ],
+        "name": "IsFlatMatrix",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsDataObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsRowVectorObj",
+            "IsGF2VectorRep"
+        ],
+        "name": "IsGF2VectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsPositionalObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMatrixObj",
+            "IsRowListMatrix",
+            "IsGF2MatrixRep"
+        ],
+        "name": "IsGF2MatrixRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsDataObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsRowVectorObj",
+            "Is8BitVectorRep"
+        ],
+        "name": "Is8BitVectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsPositionalObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMatrixObj",
+            "IsRowListMatrix",
+            "Is8BitMatrixRep"
+        ],
+        "name": "Is8BitMatrixRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsInfoClassListRep"
+        ],
+        "name": "IsInfoClassListRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsRandomSource"
+        ],
+        "name": "IsRandomSource",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsRandomSource",
+            "IsGlobalRandomSource"
+        ],
+        "name": "IsGlobalRandomSource",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsRandomSource",
+            "IsGAPRandomSource"
+        ],
+        "name": "IsGAPRandomSource",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsRandomSource",
+            "IsMersenneTwister"
+        ],
+        "name": "IsMersenneTwister",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsObjSet"
+        ],
+        "name": "IsObjSet",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsObjMap"
+        ],
+        "name": "IsObjMap",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsCommutativeElement",
+            "IsFloat"
+        ],
+        "name": "IsFloat",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsCommutativeElement",
+            "IsFloat",
+            "IsFloatInterval"
+        ],
+        "name": "IsFloatInterval",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsCommutativeElement",
+            "IsFloat",
+            "IsComplexFloat"
+        ],
+        "name": "IsComplexFloat",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsCommutativeElement",
+            "IsFloat",
+            "IsFloatInterval",
+            "IsComplexFloat",
+            "IsComplexFloatInterval"
+        ],
+        "name": "IsComplexFloatInterval",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsFloat)"
+        ],
+        "name": "CategoryFamily(IsFloat)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsCommutativeElement)",
+            "CategoryCollections(IsFloat)"
+        ],
+        "name": "CategoryCollections(IsFloat)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsZDFRE))",
+            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+            "CategoryCollections(CategoryCollections(IsFloat))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsFloat))",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(Cos)"
+        ],
+        "name": "Tester(Cos)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Sin)"
+        ],
+        "name": "Tester(Sin)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Tan)"
+        ],
+        "name": "Tester(Tan)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Sec)"
+        ],
+        "name": "Tester(Sec)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Csc)"
+        ],
+        "name": "Tester(Csc)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Cot)"
+        ],
+        "name": "Tester(Cot)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Asin)"
+        ],
+        "name": "Tester(Asin)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Acos)"
+        ],
+        "name": "Tester(Acos)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Atan)"
+        ],
+        "name": "Tester(Atan)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Cosh)"
+        ],
+        "name": "Tester(Cosh)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Sinh)"
+        ],
+        "name": "Tester(Sinh)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Tanh)"
+        ],
+        "name": "Tester(Tanh)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Sech)"
+        ],
+        "name": "Tester(Sech)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Csch)"
+        ],
+        "name": "Tester(Csch)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Coth)"
+        ],
+        "name": "Tester(Coth)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Asinh)"
+        ],
+        "name": "Tester(Asinh)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Acosh)"
+        ],
+        "name": "Tester(Acosh)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Atanh)"
+        ],
+        "name": "Tester(Atanh)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Log2)"
+        ],
+        "name": "Tester(Log2)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Log10)"
+        ],
+        "name": "Tester(Log10)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Log1p)"
+        ],
+        "name": "Tester(Log1p)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Exp)"
+        ],
+        "name": "Tester(Exp)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Exp2)"
+        ],
+        "name": "Tester(Exp2)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Exp10)"
+        ],
+        "name": "Tester(Exp10)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Expm1)"
+        ],
+        "name": "Tester(Expm1)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CubeRoot)"
+        ],
+        "name": "Tester(CubeRoot)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Square)"
+        ],
+        "name": "Tester(Square)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Ceil)"
+        ],
+        "name": "Tester(Ceil)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Floor)"
+        ],
+        "name": "Tester(Floor)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Round)"
+        ],
+        "name": "Tester(Round)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Trunc)"
+        ],
+        "name": "Tester(Trunc)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FrExp)"
+        ],
+        "name": "Tester(FrExp)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Argument)"
+        ],
+        "name": "Tester(Argument)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AbsoluteValue)"
+        ],
+        "name": "Tester(AbsoluteValue)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Frac)"
+        ],
+        "name": "Tester(Frac)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SinCos)"
+        ],
+        "name": "Tester(SinCos)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Erf)"
+        ],
+        "name": "Tester(Erf)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Zeta)"
+        ],
+        "name": "Tester(Zeta)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Gamma)"
+        ],
+        "name": "Tester(Gamma)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComplexI)"
+        ],
+        "name": "Tester(ComplexI)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PrecisionFloat)"
+        ],
+        "name": "Tester(PrecisionFloat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SignFloat)"
+        ],
+        "name": "Tester(SignFloat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Sup)"
+        ],
+        "name": "Tester(Sup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Inf)"
+        ],
+        "name": "Tester(Inf)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Mid)"
+        ],
+        "name": "Tester(Mid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AbsoluteDiameter)"
+        ],
+        "name": "Tester(AbsoluteDiameter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RelativeDiameter)"
+        ],
+        "name": "Tester(RelativeDiameter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPInfinity",
+            "Tester(IsPInfinity)"
+        ],
+        "name": "IsPInfinity",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPInfinity)"
+        ],
+        "name": "Tester(IsPInfinity)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNInfinity",
+            "Tester(IsNInfinity)"
+        ],
+        "name": "IsNInfinity",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNInfinity)"
+        ],
+        "name": "Tester(IsNInfinity)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsXInfinity",
+            "Tester(IsXInfinity)"
+        ],
+        "name": "IsXInfinity",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsXInfinity)"
+        ],
+        "name": "Tester(IsXInfinity)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNaN",
+            "Tester(IsNaN)"
+        ],
+        "name": "IsNaN",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNaN)"
+        ],
+        "name": "Tester(IsNaN)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsInternalRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsCommutativeElement",
+            "IsFloat",
+            "IsIEEE754FloatRep"
+        ],
+        "name": "IsIEEE754FloatRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsDirectoryRep"
+        ],
+        "name": "IsDirectoryRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsInputTextFileRep"
+        ],
+        "name": "IsInputTextFileRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsInputTextNoneRep"
+        ],
+        "name": "IsInputTextNoneRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsOutputTextStringRep"
+        ],
+        "name": "IsOutputTextStringRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsOutputTextFileRep"
+        ],
+        "name": "IsOutputTextFileRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsOutputTextNoneRep"
+        ],
+        "name": "IsOutputTextNoneRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsInputOutputStreamByPtyRep"
+        ],
+        "name": "IsInputOutputStreamByPtyRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsList",
+            "IsDenseList",
+            "IsListOrCollection",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsDirectProductElement"
+        ],
+        "name": "IsDirectProductElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsDirectProductElement)"
+        ],
+        "name": "CategoryFamily(IsDirectProductElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsDirectProductElement)"
+        ],
+        "name": "CategoryCollections(IsDirectProductElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(ComponentsOfDirectProductElementsFamily)"
+        ],
+        "name": "Tester(ComponentsOfDirectProductElementsFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsList",
+            "IsDenseList",
+            "IsPositionalObjectRep",
+            "IsListOrCollection",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsDirectProductElement",
+            "IsDefaultDirectProductElementRep"
+        ],
+        "name": "IsDefaultDirectProductElementRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(EmptyRowVector)"
+        ],
+        "name": "Tester(EmptyRowVector)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsAdditiveElement",
+            "IsGeneralizedDomain",
+            "IsExtASet"
+        ],
+        "name": "IsExtASet",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsAdditiveElement",
+            "IsGeneralizedDomain",
+            "IsExtASet",
+            "IsAssociativeAOpDSum"
+        ],
+        "name": "IsAssociativeAOpDSum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsAdditiveElement",
+            "IsGeneralizedDomain",
+            "IsExtASet",
+            "IsAssociativeAOpESum"
+        ],
+        "name": "IsAssociativeAOpESum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsAdditiveElement",
+            "IsGeneralizedDomain",
+            "IsExtASet",
+            "IsTrivialAOpEZero"
+        ],
+        "name": "IsTrivialAOpEZero",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfExtASet)"
+        ],
+        "name": "Tester(GeneratorsOfExtASet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AdditivelyActingDomain)"
+        ],
+        "name": "Tester(AdditivelyActingDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet"
+        ],
+        "name": "IsExtLSet",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "IsAssociativeLOpDProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd"
+        ],
+        "name": "IsAssociativeLOpEProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsDistributiveLOpDProd"
+        ],
+        "name": "IsDistributiveLOpDProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum"
+        ],
+        "name": "IsDistributiveLOpDSum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsDistributiveLOpEProd"
+        ],
+        "name": "IsDistributiveLOpEProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsDistributiveLOpESum"
+        ],
+        "name": "IsDistributiveLOpESum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsTrivialLOpEOne"
+        ],
+        "name": "IsTrivialLOpEOne",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsTrivialLOpEZero"
+        ],
+        "name": "IsTrivialLOpEZero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsLeftActedOnByRing"
+        ],
+        "name": "IsLeftActedOnByRing",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)"
+        ],
+        "name": "IsLeftActedOnByDivisionRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLeftActedOnByDivisionRing)"
+        ],
+        "name": "Tester(IsLeftActedOnByDivisionRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsLeftActedOnBySuperset"
+        ],
+        "name": "IsLeftActedOnBySuperset",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfExtLSet)"
+        ],
+        "name": "Tester(GeneratorsOfExtLSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LeftActingDomain)"
+        ],
+        "name": "Tester(LeftActingDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet"
+        ],
+        "name": "IsExtRSet",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsAssociativeROpDProd"
+        ],
+        "name": "IsAssociativeROpDProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsAssociativeROpEProd"
+        ],
+        "name": "IsAssociativeROpEProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsDistributiveROpDProd"
+        ],
+        "name": "IsDistributiveROpDProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsDistributiveROpDSum"
+        ],
+        "name": "IsDistributiveROpDSum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsDistributiveROpEProd"
+        ],
+        "name": "IsDistributiveROpEProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsDistributiveROpESum"
+        ],
+        "name": "IsDistributiveROpESum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsTrivialROpEOne"
+        ],
+        "name": "IsTrivialROpEOne",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsTrivialROpEZero"
+        ],
+        "name": "IsTrivialROpEZero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsRightActedOnByRing"
+        ],
+        "name": "IsRightActedOnByRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsRightActedOnByRing",
+            "IsRightActedOnByDivisionRing"
+        ],
+        "name": "IsRightActedOnByDivisionRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtRSet",
+            "IsRightActedOnBySuperset"
+        ],
+        "name": "IsRightActedOnBySuperset",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfExtRSet)"
+        ],
+        "name": "Tester(GeneratorsOfExtRSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RightActingDomain)"
+        ],
+        "name": "Tester(RightActingDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet"
+        ],
+        "name": "IsExtUSet",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsAssociativeUOpDProd"
+        ],
+        "name": "IsAssociativeUOpDProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsAssociativeUOpEProd"
+        ],
+        "name": "IsAssociativeUOpEProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsDistributiveUOpDProd"
+        ],
+        "name": "IsDistributiveUOpDProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsDistributiveUOpDSum"
+        ],
+        "name": "IsDistributiveUOpDSum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsDistributiveUOpEProd"
+        ],
+        "name": "IsDistributiveUOpEProd",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsDistributiveUOpESum"
+        ],
+        "name": "IsDistributiveUOpESum",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsTrivialUOpEOne"
+        ],
+        "name": "IsTrivialUOpEOne",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsTrivialUOpEZero"
+        ],
+        "name": "IsTrivialUOpEZero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsUpperActedOnByGroup"
+        ],
+        "name": "IsUpperActedOnByGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtUSet",
+            "IsUpperActedOnBySuperset"
+        ],
+        "name": "IsUpperActedOnBySuperset",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfExtUSet)"
+        ],
+        "name": "Tester(GeneratorsOfExtUSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UpperActingDomain)"
+        ],
+        "name": "Tester(UpperActingDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary"
+        ],
+        "name": "IsDictionary",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsLookupDictionary"
+        ],
+        "name": "IsLookupDictionary",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsLookupDictionary",
+            "IsHash"
+        ],
+        "name": "IsHash",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsDictionaryDefaultRep"
+        ],
+        "name": "IsDictionaryDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsDictionaryDefaultRep",
+            "IsListDictionary"
+        ],
+        "name": "IsListDictionary",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsLookupDictionary",
+            "IsDictionaryDefaultRep",
+            "IsListDictionary",
+            "IsListLookupDictionary"
+        ],
+        "name": "IsListLookupDictionary",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsDictionaryDefaultRep",
+            "IsListDictionary",
+            "IsSortDictionary"
+        ],
+        "name": "IsSortDictionary",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsLookupDictionary",
+            "IsDictionaryDefaultRep",
+            "IsListDictionary",
+            "IsListLookupDictionary",
+            "IsSortDictionary",
+            "IsSortLookupDictionary"
+        ],
+        "name": "IsSortLookupDictionary",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsDictionaryDefaultRep",
+            "IsPositionDictionary"
+        ],
+        "name": "IsPositionDictionary",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsLookupDictionary",
+            "IsDictionaryDefaultRep",
+            "IsPositionDictionary",
+            "IsPositionDictionary"
+        ],
+        "name": "IsPositionDictionary",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "TableHasIntKeyFun"
+        ],
+        "name": "TableHasIntKeyFun",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsLookupDictionary",
+            "IsHash",
+            "IsDenseHashRep"
+        ],
+        "name": "IsDenseHashRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDictionary",
+            "IsLookupDictionary",
+            "IsHash",
+            "IsSparseHashRep"
+        ],
+        "name": "IsSparseHashRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping"
+        ],
+        "name": "IsGeneralMapping",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping"
+        ],
+        "name": "IsSPGeneralMapping",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsNonSPGeneralMapping"
+        ],
+        "name": "IsNonSPGeneralMapping",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsGeneralMapping)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "CategoryCollections(IsGeneralMapping)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsGeneralMapping)"
+        ],
+        "name": "CategoryFamily(IsGeneralMapping)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(FamilyRange)"
+        ],
+        "name": "Tester(FamilyRange)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FamilySource)"
+        ],
+        "name": "Tester(FamilySource)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FamiliesOfGeneralMappingsAndRanges)"
+        ],
+        "name": "Tester(FamiliesOfGeneralMappingsAndRanges)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsConstantTimeAccessGeneralMapping",
+            "Tester(IsConstantTimeAccessGeneralMapping)"
+        ],
+        "name": "IsConstantTimeAccessGeneralMapping",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsConstantTimeAccessGeneralMapping)"
+        ],
+        "name": "Tester(IsConstantTimeAccessGeneralMapping)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)"
+        ],
+        "name": "IsEndoGeneralMapping",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsEndoGeneralMapping)"
+        ],
+        "name": "Tester(IsEndoGeneralMapping)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsTotal",
+            "Tester(IsTotal)"
+        ],
+        "name": "IsTotal",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTotal)"
+        ],
+        "name": "Tester(IsTotal)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSingleValued",
+            "Tester(IsSingleValued)"
+        ],
+        "name": "IsSingleValued",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSingleValued)"
+        ],
+        "name": "Tester(IsSingleValued)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsInjective",
+            "Tester(IsInjective)"
+        ],
+        "name": "IsInjective",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsInjective)"
+        ],
+        "name": "Tester(IsInjective)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSurjective",
+            "Tester(IsSurjective)"
+        ],
+        "name": "IsSurjective",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSurjective)"
+        ],
+        "name": "Tester(IsSurjective)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(Range)"
+        ],
+        "name": "Tester(Range)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Source)"
+        ],
+        "name": "Tester(Source)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingRelation)"
+        ],
+        "name": "Tester(UnderlyingRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingGeneralMapping)"
+        ],
+        "name": "Tester(UnderlyingGeneralMapping)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IdentityMapping)"
+        ],
+        "name": "Tester(IdentityMapping)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InverseGeneralMapping)"
+        ],
+        "name": "Tester(InverseGeneralMapping)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ImagesSource)"
+        ],
+        "name": "Tester(ImagesSource)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PreImagesRange)"
+        ],
+        "name": "Tester(PreImagesRange)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsCompositionMappingRep"
+        ],
+        "name": "IsCompositionMappingRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsGeneralRestrictedMappingRep"
+        ],
+        "name": "IsGeneralRestrictedMappingRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(MappingGeneratorsImages)"
+        ],
+        "name": "Tester(MappingGeneratorsImages)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)"
+        ],
+        "name": "RespectsMultiplication",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(RespectsMultiplication)"
+        ],
+        "name": "Tester(RespectsMultiplication)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "RespectsOne",
+            "Tester(RespectsOne)"
+        ],
+        "name": "RespectsOne",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(RespectsOne)"
+        ],
+        "name": "Tester(RespectsOne)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "RespectsInverses",
+            "Tester(RespectsInverses)"
+        ],
+        "name": "RespectsInverses",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(RespectsInverses)"
+        ],
+        "name": "Tester(RespectsInverses)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(KernelOfMultiplicativeGeneralMapping)"
+        ],
+        "name": "Tester(KernelOfMultiplicativeGeneralMapping)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoKernelOfMultiplicativeGeneralMapping)"
+        ],
+        "name": "Tester(CoKernelOfMultiplicativeGeneralMapping)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "RespectsAddition",
+            "Tester(RespectsAddition)"
+        ],
+        "name": "RespectsAddition",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(RespectsAddition)"
+        ],
+        "name": "Tester(RespectsAddition)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "RespectsZero",
+            "Tester(RespectsZero)"
+        ],
+        "name": "RespectsZero",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(RespectsZero)"
+        ],
+        "name": "Tester(RespectsZero)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)"
+        ],
+        "name": "RespectsAdditiveInverses",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(RespectsAdditiveInverses)"
+        ],
+        "name": "Tester(RespectsAdditiveInverses)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(KernelOfAdditiveGeneralMapping)"
+        ],
+        "name": "Tester(KernelOfAdditiveGeneralMapping)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoKernelOfAdditiveGeneralMapping)"
+        ],
+        "name": "Tester(CoKernelOfAdditiveGeneralMapping)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)"
+        ],
+        "name": "RespectsScalarMultiplication",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(RespectsScalarMultiplication)"
+        ],
+        "name": "Tester(RespectsScalarMultiplication)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsFieldHomomorphism",
+            "Tester(IsFieldHomomorphism)"
+        ],
+        "name": "IsFieldHomomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFieldHomomorphism)"
+        ],
+        "name": "Tester(IsFieldHomomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "TransformsMultiplicationIntoAddition",
+            "Tester(TransformsMultiplicationIntoAddition)"
+        ],
+        "name": "TransformsMultiplicationIntoAddition",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(TransformsMultiplicationIntoAddition)"
+        ],
+        "name": "Tester(TransformsMultiplicationIntoAddition)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "TranformsOneIntoZero",
+            "Tester(TranformsOneIntoZero)"
+        ],
+        "name": "TranformsOneIntoZero",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(TranformsOneIntoZero)"
+        ],
+        "name": "Tester(TranformsOneIntoZero)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "TransformsInversesIntoAdditiveInverses",
+            "Tester(TransformsInversesIntoAdditiveInverses)"
+        ],
+        "name": "TransformsInversesIntoAdditiveInverses",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(TransformsInversesIntoAdditiveInverses)"
+        ],
+        "name": "Tester(TransformsInversesIntoAdditiveInverses)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "TransformsAdditionIntoMultiplication",
+            "Tester(TransformsAdditionIntoMultiplication)"
+        ],
+        "name": "TransformsAdditionIntoMultiplication",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(TransformsAdditionIntoMultiplication)"
+        ],
+        "name": "Tester(TransformsAdditionIntoMultiplication)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "TransformsZeroIntoOne",
+            "Tester(TransformsZeroIntoOne)"
+        ],
+        "name": "TransformsZeroIntoOne",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(TransformsZeroIntoOne)"
+        ],
+        "name": "Tester(TransformsZeroIntoOne)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "TransformsAdditiveInversesIntoInverses",
+            "Tester(TransformsAdditiveInversesIntoInverses)"
+        ],
+        "name": "TransformsAdditiveInversesIntoInverses",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(TransformsAdditiveInversesIntoInverses)"
+        ],
+        "name": "Tester(TransformsAdditiveInversesIntoInverses)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(Successors)"
+        ],
+        "name": "Tester(Successors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOfBinaryRelation)"
+        ],
+        "name": "Tester(DegreeOfBinaryRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)"
+        ],
+        "name": "IsReflexiveBinaryRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsReflexiveBinaryRelation)"
+        ],
+        "name": "Tester(IsReflexiveBinaryRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)"
+        ],
+        "name": "IsSymmetricBinaryRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSymmetricBinaryRelation)"
+        ],
+        "name": "Tester(IsSymmetricBinaryRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)"
+        ],
+        "name": "IsTransitiveBinaryRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTransitiveBinaryRelation)"
+        ],
+        "name": "Tester(IsTransitiveBinaryRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsAntisymmetricBinaryRelation",
+            "Tester(IsAntisymmetricBinaryRelation)"
+        ],
+        "name": "IsAntisymmetricBinaryRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAntisymmetricBinaryRelation)"
+        ],
+        "name": "Tester(IsAntisymmetricBinaryRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)"
+        ],
+        "name": "IsPreOrderBinaryRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPreOrderBinaryRelation)"
+        ],
+        "name": "Tester(IsPreOrderBinaryRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPartialOrderBinaryRelation",
+            "Tester(IsPartialOrderBinaryRelation)"
+        ],
+        "name": "IsPartialOrderBinaryRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPartialOrderBinaryRelation)"
+        ],
+        "name": "Tester(IsPartialOrderBinaryRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPartialOrderBinaryRelation",
+            "Tester(IsPartialOrderBinaryRelation)",
+            "IsLatticeOrderBinaryRelation",
+            "Tester(IsLatticeOrderBinaryRelation)"
+        ],
+        "name": "IsLatticeOrderBinaryRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLatticeOrderBinaryRelation)"
+        ],
+        "name": "Tester(IsLatticeOrderBinaryRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)"
+        ],
+        "name": "IsEquivalenceRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsEquivalenceRelation)"
+        ],
+        "name": "Tester(IsEquivalenceRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsHasseDiagram",
+            "Tester(IsHasseDiagram)"
+        ],
+        "name": "IsHasseDiagram",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsHasseDiagram)"
+        ],
+        "name": "Tester(IsHasseDiagram)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(PartialOrderOfHasseDiagram)"
+        ],
+        "name": "Tester(PartialOrderOfHasseDiagram)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EquivalenceRelationPartition)"
+        ],
+        "name": "Tester(EquivalenceRelationPartition)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfEquivalenceRelationPartition)"
+        ],
+        "name": "Tester(GeneratorsOfEquivalenceRelationPartition)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass"
+        ],
+        "name": "IsEquivalenceClass",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(EquivalenceClassRelation)"
+        ],
+        "name": "Tester(EquivalenceClassRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EquivalenceClasses)"
+        ],
+        "name": "Tester(EquivalenceClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma"
+        ],
+        "name": "IsMagma",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "Tester(MultiplicativeNeutralElement)"
+        ],
+        "name": "IsMagmaWithOne",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "Tester(MultiplicativeNeutralElement)"
+        ],
+        "name": "IsMagmaWithInversesIfNonzero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "Tester(MultiplicativeNeutralElement)"
+        ],
+        "name": "IsMagmaWithInverses",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(AsMagma)"
+        ],
+        "name": "Tester(AsMagma)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfMagma)"
+        ],
+        "name": "Tester(GeneratorsOfMagma)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfMagmaWithOne)"
+        ],
+        "name": "Tester(GeneratorsOfMagmaWithOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfMagmaWithInverses)"
+        ],
+        "name": "Tester(GeneratorsOfMagmaWithInverses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)"
+        ],
+        "name": "IsGeneratorsOfMagmaWithInverses",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGeneratorsOfMagmaWithInverses)"
+        ],
+        "name": "Tester(IsGeneratorsOfMagmaWithInverses)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(TrivialSubmagmaWithOne)"
+        ],
+        "name": "Tester(TrivialSubmagmaWithOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAssociative",
+            "Tester(IsAssociative)"
+        ],
+        "name": "IsAssociative",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAssociative)"
+        ],
+        "name": "Tester(IsAssociative)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCommutative",
+            "Tester(IsCommutative)"
+        ],
+        "name": "IsCommutative",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCommutative)"
+        ],
+        "name": "Tester(IsCommutative)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(MultiplicativeNeutralElement)"
+        ],
+        "name": "Tester(MultiplicativeNeutralElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Centre)"
+        ],
+        "name": "Tester(Centre)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Idempotents)"
+        ],
+        "name": "Tester(Idempotents)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CentralizerInParent)"
+        ],
+        "name": "Tester(CentralizerInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MagmaGeneratorsOfFamily)"
+        ],
+        "name": "Tester(MagmaGeneratorsOfFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfMagmaIdeal)"
+        ],
+        "name": "Tester(GeneratorsOfMagmaIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithZero"
+        ],
+        "name": "IsMultiplicativeElementWithZero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithZero)"
+        ],
+        "name": "CategoryCollections(IsMultiplicativeElementWithZero)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(MultiplicativeZero)"
+        ],
+        "name": "Tester(MultiplicativeZero)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithZero",
+            "IsMagmaWithZeroAdjoinedElementRep"
+        ],
+        "name": "IsMagmaWithZeroAdjoinedElementRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithZeroAdjoined"
+        ],
+        "name": "IsMagmaWithZeroAdjoined",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(InjectionZeroMagma)"
+        ],
+        "name": "Tester(InjectionZeroMagma)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MagmaWithZeroAdjoined)"
+        ],
+        "name": "Tester(MagmaWithZeroAdjoined)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingInjectionZeroMagma)"
+        ],
+        "name": "Tester(UnderlyingInjectionZeroMagma)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsLeftMagmaCongruence"
+        ],
+        "name": "IsLeftMagmaCongruence",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratingPairsOfLeftMagmaCongruence)"
+        ],
+        "name": "Tester(GeneratingPairsOfLeftMagmaCongruence)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PartialClosureOfCongruence)"
+        ],
+        "name": "Tester(PartialClosureOfCongruence)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsRightMagmaCongruence"
+        ],
+        "name": "IsRightMagmaCongruence",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratingPairsOfRightMagmaCongruence)"
+        ],
+        "name": "Tester(GeneratingPairsOfRightMagmaCongruence)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsLeftMagmaCongruence",
+            "IsRightMagmaCongruence",
+            "IsMagmaCongruence"
+        ],
+        "name": "IsMagmaCongruence",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GeneratingPairsOfMagmaCongruence)"
+        ],
+        "name": "Tester(GeneratingPairsOfMagmaCongruence)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass",
+            "IsCongruenceClass"
+        ],
+        "name": "IsCongruenceClass",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsLeftSemigroupCongruence",
+            "Tester(IsLeftSemigroupCongruence)"
+        ],
+        "name": "IsLeftSemigroupCongruence",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLeftSemigroupCongruence)"
+        ],
+        "name": "Tester(IsLeftSemigroupCongruence)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRightSemigroupCongruence",
+            "Tester(IsRightSemigroupCongruence)"
+        ],
+        "name": "IsRightSemigroupCongruence",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRightSemigroupCongruence)"
+        ],
+        "name": "Tester(IsRightSemigroupCongruence)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsLeftSemigroupCongruence",
+            "Tester(IsLeftSemigroupCongruence)",
+            "IsRightSemigroupCongruence",
+            "Tester(IsRightSemigroupCongruence)",
+            "IsSemigroupCongruence",
+            "Tester(IsSemigroupCongruence)"
+        ],
+        "name": "IsSemigroupCongruence",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSemigroupCongruence)"
+        ],
+        "name": "Tester(IsSemigroupCongruence)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsReesCongruence",
+            "Tester(IsReesCongruence)"
+        ],
+        "name": "IsReesCongruence",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsReesCongruence)"
+        ],
+        "name": "Tester(IsReesCongruence)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(AsSemigroup)"
+        ],
+        "name": "Tester(AsSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "IsGeneratorsOfSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGeneratorsOfSemigroup)"
+        ],
+        "name": "Tester(IsGeneratorsOfSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(CayleyGraphSemigroup)"
+        ],
+        "name": "Tester(CayleyGraphSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CayleyGraphDualSemigroup)"
+        ],
+        "name": "Tester(CayleyGraphDualSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsZeroGroup",
+            "Tester(IsZeroGroup)",
+            "IsZeroSimpleSemigroup",
+            "Tester(IsZeroSimpleSemigroup)"
+        ],
+        "name": "IsZeroGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZeroGroup)"
+        ],
+        "name": "Tester(IsZeroGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)"
+        ],
+        "name": "IsSimpleSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSimpleSemigroup)"
+        ],
+        "name": "Tester(IsSimpleSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsZeroSimpleSemigroup",
+            "Tester(IsZeroSimpleSemigroup)"
+        ],
+        "name": "IsZeroSimpleSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZeroSimpleSemigroup)"
+        ],
+        "name": "Tester(IsZeroSimpleSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ANonReesCongruenceOfSemigroup)"
+        ],
+        "name": "Tester(ANonReesCongruenceOfSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsReesCongruenceSemigroup",
+            "Tester(IsReesCongruenceSemigroup)"
+        ],
+        "name": "IsReesCongruenceSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsReesCongruenceSemigroup)"
+        ],
+        "name": "Tester(IsReesCongruenceSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)"
+        ],
+        "name": "IsRegularSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRegularSemigroup)"
+        ],
+        "name": "Tester(IsRegularSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)"
+        ],
+        "name": "IsInverseSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsInverseSemigroup)"
+        ],
+        "name": "Tester(IsInverseSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NilpotencyDegree)"
+        ],
+        "name": "Tester(NilpotencyDegree)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBand",
+            "Tester(IsBand)"
+        ],
+        "name": "IsBand",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBand)"
+        ],
+        "name": "Tester(IsBand)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBrandtSemigroup",
+            "Tester(IsBrandtSemigroup)"
+        ],
+        "name": "IsBrandtSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBrandtSemigroup)"
+        ],
+        "name": "Tester(IsBrandtSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCliffordSemigroup",
+            "Tester(IsCliffordSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)"
+        ],
+        "name": "IsCliffordSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCliffordSemigroup)"
+        ],
+        "name": "Tester(IsCliffordSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCommutativeSemigroup",
+            "Tester(IsCommutativeSemigroup)"
+        ],
+        "name": "IsCommutativeSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCommutativeSemigroup)"
+        ],
+        "name": "Tester(IsCommutativeSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)"
+        ],
+        "name": "IsCompletelyRegularSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCompletelyRegularSemigroup)"
+        ],
+        "name": "Tester(IsCompletelyRegularSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCompletelySimpleSemigroup",
+            "Tester(IsCompletelySimpleSemigroup)"
+        ],
+        "name": "IsCompletelySimpleSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCompletelySimpleSemigroup)"
+        ],
+        "name": "Tester(IsCompletelySimpleSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)"
+        ],
+        "name": "IsGroupAsSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupAsSemigroup)"
+        ],
+        "name": "Tester(IsGroupAsSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsIdempotentGenerated",
+            "Tester(IsIdempotentGenerated)",
+            "IsSemiband",
+            "Tester(IsSemiband)"
+        ],
+        "name": "IsIdempotentGenerated",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIdempotentGenerated)"
+        ],
+        "name": "Tester(IsIdempotentGenerated)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsLeftZeroSemigroup",
+            "Tester(IsLeftZeroSemigroup)"
+        ],
+        "name": "IsLeftZeroSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLeftZeroSemigroup)"
+        ],
+        "name": "Tester(IsLeftZeroSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMonogenicSemigroup",
+            "Tester(IsMonogenicSemigroup)"
+        ],
+        "name": "IsMonogenicSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMonogenicSemigroup)"
+        ],
+        "name": "Tester(IsMonogenicSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)"
+        ],
+        "name": "IsMonoidAsSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMonoidAsSemigroup)"
+        ],
+        "name": "Tester(IsMonoidAsSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNilpotentSemigroup",
+            "Tester(IsNilpotentSemigroup)"
+        ],
+        "name": "IsNilpotentSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNilpotentSemigroup)"
+        ],
+        "name": "Tester(IsNilpotentSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)"
+        ],
+        "name": "IsOrthodoxSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsOrthodoxSemigroup)"
+        ],
+        "name": "Tester(IsOrthodoxSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRectangularBand",
+            "Tester(IsRectangularBand)"
+        ],
+        "name": "IsRectangularBand",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRectangularBand)"
+        ],
+        "name": "Tester(IsRectangularBand)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRightZeroSemigroup",
+            "Tester(IsRightZeroSemigroup)"
+        ],
+        "name": "IsRightZeroSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRightZeroSemigroup)"
+        ],
+        "name": "Tester(IsRightZeroSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSemiband",
+            "Tester(IsSemiband)"
+        ],
+        "name": "IsSemiband",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSemiband)"
+        ],
+        "name": "Tester(IsSemiband)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsBand",
+            "Tester(IsBand)",
+            "IsCliffordSemigroup",
+            "Tester(IsCliffordSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsIdempotentGenerated",
+            "Tester(IsIdempotentGenerated)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsSemiband",
+            "Tester(IsSemiband)",
+            "IsSemilattice",
+            "Tester(IsSemilattice)"
+        ],
+        "name": "IsSemilattice",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSemilattice)"
+        ],
+        "name": "Tester(IsSemilattice)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsZeroSemigroup",
+            "Tester(IsZeroSemigroup)"
+        ],
+        "name": "IsZeroSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZeroSemigroup)"
+        ],
+        "name": "Tester(IsZeroSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsLeftSemigroupIdeal",
+            "Tester(IsLeftSemigroupIdeal)"
+        ],
+        "name": "IsLeftSemigroupIdeal",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLeftSemigroupIdeal)"
+        ],
+        "name": "Tester(IsLeftSemigroupIdeal)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRightSemigroupIdeal",
+            "Tester(IsRightSemigroupIdeal)"
+        ],
+        "name": "IsRightSemigroupIdeal",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRightSemigroupIdeal)"
+        ],
+        "name": "Tester(IsRightSemigroupIdeal)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSemigroupIdeal",
+            "Tester(IsSemigroupIdeal)"
+        ],
+        "name": "IsSemigroupIdeal",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSemigroupIdeal)"
+        ],
+        "name": "Tester(IsSemigroupIdeal)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ReesCongruenceOfSemigroupIdeal)"
+        ],
+        "name": "Tester(ReesCongruenceOfSemigroupIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsMonoid)"
+        ],
+        "name": "Tester(AsMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NameIsomorphismClass)"
+        ],
+        "name": "Tester(NameIsomorphismClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCyclic",
+            "Tester(IsCyclic)"
+        ],
+        "name": "IsCyclic",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCyclic)"
+        ],
+        "name": "Tester(IsCyclic)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsElementaryAbelian",
+            "Tester(IsElementaryAbelian)"
+        ],
+        "name": "IsElementaryAbelian",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsElementaryAbelian)"
+        ],
+        "name": "Tester(IsElementaryAbelian)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFinitelyGeneratedGroup",
+            "Tester(IsFinitelyGeneratedGroup)"
+        ],
+        "name": "IsFinitelyGeneratedGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFinitelyGeneratedGroup)"
+        ],
+        "name": "Tester(IsFinitelyGeneratedGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSubsetLocallyFiniteGroup",
+            "Tester(IsSubsetLocallyFiniteGroup)"
+        ],
+        "name": "IsSubsetLocallyFiniteGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSubsetLocallyFiniteGroup)"
+        ],
+        "name": "Tester(IsSubsetLocallyFiniteGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "CanEasilyTestMembership"
+        ],
+        "name": "CanEasilyTestMembership",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "CanEasilyComputeWithIndependentGensAbelianGroup"
+        ],
+        "name": "CanEasilyComputeWithIndependentGensAbelianGroup",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "CanComputeSize",
+            "CanComputeSizeAnySubgroup"
+        ],
+        "name": "CanComputeSizeAnySubgroup",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "KnowsHowToDecompose",
+            "Tester(KnowsHowToDecompose)"
+        ],
+        "name": "KnowsHowToDecompose",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(KnowsHowToDecompose)"
+        ],
+        "name": "Tester(KnowsHowToDecompose)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPGroup",
+            "Tester(IsPGroup)"
+        ],
+        "name": "IsPGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPGroup)"
+        ],
+        "name": "Tester(IsPGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(PrimePGroup)"
+        ],
+        "name": "Tester(PrimePGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PClassPGroup)"
+        ],
+        "name": "Tester(PClassPGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RankPGroup)"
+        ],
+        "name": "Tester(RankPGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNilpotentGroup",
+            "Tester(IsNilpotentGroup)",
+            "IsSupersolvableGroup",
+            "Tester(IsSupersolvableGroup)",
+            "IsSolvableGroup",
+            "Tester(IsSolvableGroup)",
+            "IsNilpotentByFinite",
+            "Tester(IsNilpotentByFinite)"
+        ],
+        "name": "IsNilpotentGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNilpotentGroup)"
+        ],
+        "name": "Tester(IsNilpotentGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPerfectGroup",
+            "Tester(IsPerfectGroup)"
+        ],
+        "name": "IsPerfectGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPerfectGroup)"
+        ],
+        "name": "Tester(IsPerfectGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSporadicSimpleGroup",
+            "Tester(IsSporadicSimpleGroup)"
+        ],
+        "name": "IsSporadicSimpleGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSporadicSimpleGroup)"
+        ],
+        "name": "Tester(IsSporadicSimpleGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSimpleGroup",
+            "Tester(IsSimpleGroup)"
+        ],
+        "name": "IsSimpleGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSimpleGroup)"
+        ],
+        "name": "Tester(IsSimpleGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsAlmostSimpleGroup",
+            "Tester(IsAlmostSimpleGroup)"
+        ],
+        "name": "IsAlmostSimpleGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAlmostSimpleGroup)"
+        ],
+        "name": "Tester(IsAlmostSimpleGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSupersolvableGroup",
+            "Tester(IsSupersolvableGroup)",
+            "IsSolvableGroup",
+            "Tester(IsSolvableGroup)"
+        ],
+        "name": "IsSupersolvableGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSupersolvableGroup)"
+        ],
+        "name": "Tester(IsSupersolvableGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMonomialGroup",
+            "Tester(IsMonomialGroup)",
+            "IsSolvableGroup",
+            "Tester(IsSolvableGroup)"
+        ],
+        "name": "IsMonomialGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMonomialGroup)"
+        ],
+        "name": "Tester(IsMonomialGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSolvableGroup",
+            "Tester(IsSolvableGroup)"
+        ],
+        "name": "IsSolvableGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSolvableGroup)"
+        ],
+        "name": "Tester(IsSolvableGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSolvableGroup",
+            "Tester(IsSolvableGroup)",
+            "IsPolycyclicGroup",
+            "Tester(IsPolycyclicGroup)"
+        ],
+        "name": "IsPolycyclicGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPolycyclicGroup)"
+        ],
+        "name": "Tester(IsPolycyclicGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(AbelianInvariants)"
+        ],
+        "name": "Tester(AbelianInvariants)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsInfiniteAbelianizationGroup)"
+        ],
+        "name": "Tester(IsInfiniteAbelianizationGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsGroup)"
+        ],
+        "name": "Tester(AsGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ChiefSeries)"
+        ],
+        "name": "Tester(ChiefSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CommutatorFactorGroup)"
+        ],
+        "name": "Tester(CommutatorFactorGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CompositionSeries)"
+        ],
+        "name": "Tester(CompositionSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConjugacyClasses)"
+        ],
+        "name": "Tester(ConjugacyClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConjugacyClassesMaximalSubgroups)"
+        ],
+        "name": "Tester(ConjugacyClassesMaximalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalSubgroups)"
+        ],
+        "name": "Tester(MaximalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalSubgroupClassReps)"
+        ],
+        "name": "Tester(MaximalSubgroupClassReps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PerfectResiduum)"
+        ],
+        "name": "Tester(PerfectResiduum)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RepresentativesPerfectSubgroups)"
+        ],
+        "name": "Tester(RepresentativesPerfectSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RepresentativesSimpleSubgroups)"
+        ],
+        "name": "Tester(RepresentativesSimpleSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConjugacyClassesPerfectSubgroups)"
+        ],
+        "name": "Tester(ConjugacyClassesPerfectSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConjugacyClassesSubgroups)"
+        ],
+        "name": "Tester(ConjugacyClassesSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LatticeSubgroups)"
+        ],
+        "name": "Tester(LatticeSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DerivedLength)"
+        ],
+        "name": "Tester(DerivedLength)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(HirschLength)"
+        ],
+        "name": "Tester(HirschLength)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DerivedSeriesOfGroup)"
+        ],
+        "name": "Tester(DerivedSeriesOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DerivedSubgroup)"
+        ],
+        "name": "Tester(DerivedSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalAbelianQuotient)"
+        ],
+        "name": "Tester(MaximalAbelianQuotient)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CommutatorLength)"
+        ],
+        "name": "Tester(CommutatorLength)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DimensionsLoewyFactors)"
+        ],
+        "name": "Tester(DimensionsLoewyFactors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ElementaryAbelianSeries)"
+        ],
+        "name": "Tester(ElementaryAbelianSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ElementaryAbelianSeriesLargeSteps)"
+        ],
+        "name": "Tester(ElementaryAbelianSeriesLargeSteps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Exponent)"
+        ],
+        "name": "Tester(Exponent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FittingSubgroup)"
+        ],
+        "name": "Tester(FittingSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PrefrattiniSubgroup)"
+        ],
+        "name": "Tester(PrefrattiniSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FrattiniSubgroup)"
+        ],
+        "name": "Tester(FrattiniSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InvariantForm)"
+        ],
+        "name": "Tester(InvariantForm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(JenningsSeries)"
+        ],
+        "name": "Tester(JenningsSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LowerCentralSeriesOfGroup)"
+        ],
+        "name": "Tester(LowerCentralSeriesOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NilpotencyClassOfGroup)"
+        ],
+        "name": "Tester(NilpotencyClassOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalNormalSubgroups)"
+        ],
+        "name": "Tester(MaximalNormalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalMaximalSubgroups)"
+        ],
+        "name": "Tester(NormalMaximalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimalNormalSubgroups)"
+        ],
+        "name": "Tester(MinimalNormalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalSubgroups)"
+        ],
+        "name": "Tester(NormalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrConjugacyClasses)"
+        ],
+        "name": "Tester(NrConjugacyClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedOmegas)"
+        ],
+        "name": "Tester(ComputedOmegas)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedAgemos)"
+        ],
+        "name": "Tester(ComputedAgemos)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RadicalGroup)"
+        ],
+        "name": "Tester(RadicalGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RationalClasses)"
+        ],
+        "name": "Tester(RationalClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsSmallest)"
+        ],
+        "name": "Tester(GeneratorsSmallest)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LargestElementGroup)"
+        ],
+        "name": "Tester(LargestElementGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimalGeneratingSet)"
+        ],
+        "name": "Tester(MinimalGeneratingSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SmallGeneratingSet)"
+        ],
+        "name": "Tester(SmallGeneratingSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SupersolvableResiduum)"
+        ],
+        "name": "Tester(SupersolvableResiduum)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComplementSystem)"
+        ],
+        "name": "Tester(ComplementSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SylowSystem)"
+        ],
+        "name": "Tester(SylowSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(HallSystem)"
+        ],
+        "name": "Tester(HallSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Socle)"
+        ],
+        "name": "Tester(Socle)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UpperCentralSeriesOfGroup)"
+        ],
+        "name": "Tester(UpperCentralSeriesOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoreInParent)"
+        ],
+        "name": "Tester(CoreInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndexInParent)"
+        ],
+        "name": "Tester(IndexInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndexInWholeGroup)"
+        ],
+        "name": "Tester(IndexInWholeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndependentGeneratorsOfAbelianGroup)"
+        ],
+        "name": "Tester(IndependentGeneratorsOfAbelianGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNormalInParent",
+            "Tester(IsNormalInParent)"
+        ],
+        "name": "IsNormalInParent",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNormalInParent)"
+        ],
+        "name": "Tester(IsNormalInParent)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ComputedIsPNilpotents)"
+        ],
+        "name": "Tester(ComputedIsPNilpotents)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedIsPSolvables)"
+        ],
+        "name": "Tester(ComputedIsPSolvables)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalClosureInParent)"
+        ],
+        "name": "Tester(NormalClosureInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalizerInParent)"
+        ],
+        "name": "Tester(NormalizerInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedPCentralSeriess)"
+        ],
+        "name": "Tester(ComputedPCentralSeriess)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedPRumps)"
+        ],
+        "name": "Tester(ComputedPRumps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedPCores)"
+        ],
+        "name": "Tester(ComputedPCores)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SubnormalSeriesInParent)"
+        ],
+        "name": "Tester(SubnormalSeriesInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedSylowSubgroups)"
+        ],
+        "name": "Tester(ComputedSylowSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedSylowComplements)"
+        ],
+        "name": "Tester(ComputedSylowComplements)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedHallSubgroups)"
+        ],
+        "name": "Tester(ComputedHallSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GrowthFunctionOfGroup)"
+        ],
+        "name": "Tester(GrowthFunctionOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ElementTestFunction)"
+        ],
+        "name": "Tester(ElementTestFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRightTransversal"
+        ],
+        "name": "IsRightTransversal",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CategoryCollections(IsRightTransversal)"
+        ],
+        "name": "CategoryCollections(IsRightTransversal)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(RightTransversalInParent)"
+        ],
+        "name": "Tester(RightTransversalInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismTypeInfoFiniteSimpleGroup)"
+        ],
+        "name": "Tester(IsomorphismTypeInfoFiniteSimpleGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismPcGroup)"
+        ],
+        "name": "Tester(IsomorphismPcGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismSpecialPcGroup)"
+        ],
+        "name": "Tester(IsomorphismSpecialPcGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismPermGroup)"
+        ],
+        "name": "Tester(IsomorphismPermGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismFpGroup)"
+        ],
+        "name": "Tester(IsomorphismFpGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PrimePowerComponents)"
+        ],
+        "name": "Tester(PrimePowerComponents)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsGroupOfFamily"
+        ],
+        "name": "IsGroupOfFamily",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "IsGeneratorsOfInverseSemigroup",
+            "Tester(IsGeneratorsOfInverseSemigroup)"
+        ],
+        "name": "IsGeneratorsOfInverseSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGeneratorsOfInverseSemigroup)"
+        ],
+        "name": "Tester(IsGeneratorsOfInverseSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfInverseMonoid)"
+        ],
+        "name": "Tester(GeneratorsOfInverseMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfInverseSemigroup)"
+        ],
+        "name": "Tester(GeneratorsOfInverseSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsInverseSemigroup)"
+        ],
+        "name": "Tester(AsInverseSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsInverseMonoid)"
+        ],
+        "name": "Tester(AsInverseMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ReverseNaturalPartialOrder)"
+        ],
+        "name": "Tester(ReverseNaturalPartialOrder)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalPartialOrder)"
+        ],
+        "name": "Tester(NaturalPartialOrder)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsNearAdditiveMagma"
+        ],
+        "name": "IsNearAdditiveMagma",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "IsGeneralizedDomain",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero"
+        ],
+        "name": "IsNearAdditiveMagmaWithZero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup"
+        ],
+        "name": "IsNearAdditiveGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)"
+        ],
+        "name": "IsAdditivelyCommutative",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAdditivelyCommutative)"
+        ],
+        "name": "Tester(IsAdditivelyCommutative)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfNearAdditiveMagma)"
+        ],
+        "name": "Tester(GeneratorsOfNearAdditiveMagma)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+        ],
+        "name": "Tester(GeneratorsOfNearAdditiveMagmaWithZero)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfNearAdditiveGroup)"
+        ],
+        "name": "Tester(GeneratorsOfNearAdditiveGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TrivialSubnearAdditiveMagmaWithZero)"
+        ],
+        "name": "Tester(TrivialSubnearAdditiveMagmaWithZero)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AdditiveNeutralElement)"
+        ],
+        "name": "Tester(AdditiveNeutralElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsAdditiveElement",
+            "IsGeneralizedDomain",
+            "IsExtASet",
+            "IsAssociativeAOpESum",
+            "IsTrivialAOpEZero",
+            "IsAdditiveCoset"
+        ],
+        "name": "IsAdditiveCoset",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsLDistributive",
+            "Tester(IsLDistributive)"
+        ],
+        "name": "IsLDistributive",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLDistributive)"
+        ],
+        "name": "Tester(IsLDistributive)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRDistributive",
+            "Tester(IsRDistributive)"
+        ],
+        "name": "IsRDistributive",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRDistributive)"
+        ],
+        "name": "Tester(IsRDistributive)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfSemiring)"
+        ],
+        "name": "Tester(GeneratorsOfSemiring)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfSemiringWithOne)"
+        ],
+        "name": "Tester(GeneratorsOfSemiringWithOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfSemiringWithZero)"
+        ],
+        "name": "Tester(GeneratorsOfSemiringWithZero)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfSemiringWithOneAndZero)"
+        ],
+        "name": "Tester(GeneratorsOfSemiringWithOneAndZero)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsSemiring)"
+        ],
+        "name": "Tester(AsSemiring)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsSemiringWithOne)"
+        ],
+        "name": "Tester(AsSemiringWithOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsSemiringWithZero)"
+        ],
+        "name": "Tester(AsSemiringWithZero)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsSemiringWithOneAndZero)"
+        ],
+        "name": "Tester(AsSemiringWithOneAndZero)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CentralIdempotentsOfSemiring)"
+        ],
+        "name": "Tester(CentralIdempotentsOfSemiring)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsNearRing)"
+        ],
+        "name": "Tester(AsNearRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsRing)"
+        ],
+        "name": "Tester(AsRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfRing)"
+        ],
+        "name": "Tester(GeneratorsOfRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfRingWithOne)"
+        ],
+        "name": "Tester(GeneratorsOfRingWithOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing"
+        ],
+        "name": "IsUniqueFactorizationRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing",
+            "IsEuclideanRing"
+        ],
+        "name": "IsEuclideanRing",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsAnticommutative",
+            "Tester(IsAnticommutative)"
+        ],
+        "name": "IsAnticommutative",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAnticommutative)"
+        ],
+        "name": "Tester(IsAnticommutative)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsIntegralRing",
+            "Tester(IsIntegralRing)"
+        ],
+        "name": "IsIntegralRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIntegralRing)"
+        ],
+        "name": "Tester(IsIntegralRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsJacobianRing",
+            "Tester(IsJacobianRing)"
+        ],
+        "name": "IsJacobianRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsJacobianRing)"
+        ],
+        "name": "Tester(IsJacobianRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsZeroSquaredRing",
+            "Tester(IsZeroSquaredRing)"
+        ],
+        "name": "IsZeroSquaredRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZeroSquaredRing)"
+        ],
+        "name": "Tester(IsZeroSquaredRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsZeroMultiplicationRing",
+            "Tester(IsZeroMultiplicationRing)"
+        ],
+        "name": "IsZeroMultiplicationRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZeroMultiplicationRing)"
+        ],
+        "name": "Tester(IsZeroMultiplicationRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(Units)"
+        ],
+        "name": "Tester(Units)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralizedCartanMatrix",
+            "Tester(IsGeneralizedCartanMatrix)"
+        ],
+        "name": "IsGeneralizedCartanMatrix",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGeneralizedCartanMatrix)"
+        ],
+        "name": "Tester(IsGeneralizedCartanMatrix)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(BaseMat)"
+        ],
+        "name": "Tester(BaseMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BaseOrthogonalSpaceMat)"
+        ],
+        "name": "Tester(BaseOrthogonalSpaceMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DefaultFieldOfMatrix)"
+        ],
+        "name": "Tester(DefaultFieldOfMatrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DepthOfUpperTriangularMatrix)"
+        ],
+        "name": "Tester(DepthOfUpperTriangularMatrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DeterminantMat)"
+        ],
+        "name": "Tester(DeterminantMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DimensionsMat)"
+        ],
+        "name": "Tester(DimensionsMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NullspaceMat)"
+        ],
+        "name": "Tester(NullspaceMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TriangulizedNullspaceMat)"
+        ],
+        "name": "Tester(TriangulizedNullspaceMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ProjectiveOrder)"
+        ],
+        "name": "Tester(ProjectiveOrder)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RankMat)"
+        ],
+        "name": "Tester(RankMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SemiEchelonMat)"
+        ],
+        "name": "Tester(SemiEchelonMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SemiEchelonMatTransformation)"
+        ],
+        "name": "Tester(SemiEchelonMatTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TransposedMatImmutable)"
+        ],
+        "name": "Tester(TransposedMatImmutable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMonomialMatrix",
+            "Tester(IsMonomialMatrix)"
+        ],
+        "name": "IsMonomialMatrix",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMonomialMatrix)"
+        ],
+        "name": "Tester(IsMonomialMatrix)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(JordanDecomposition)"
+        ],
+        "name": "Tester(JordanDecomposition)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CharacteristicPolynomial)"
+        ],
+        "name": "Tester(CharacteristicPolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BaseIntMat)"
+        ],
+        "name": "Tester(BaseIntMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NullspaceIntMat)"
+        ],
+        "name": "Tester(NullspaceIntMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AbelianInvariantsOfList)"
+        ],
+        "name": "Tester(AbelianInvariantsOfList)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MatrixByBlockMatrix)"
+        ],
+        "name": "Tester(MatrixByBlockMatrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTwoSidedIdealInParent",
+            "Tester(IsTwoSidedIdealInParent)",
+            "IsLeftIdealInParent",
+            "Tester(IsLeftIdealInParent)",
+            "IsRightIdealInParent",
+            "Tester(IsRightIdealInParent)"
+        ],
+        "name": "IsTwoSidedIdealInParent",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTwoSidedIdealInParent)"
+        ],
+        "name": "Tester(IsTwoSidedIdealInParent)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsLeftIdealInParent",
+            "Tester(IsLeftIdealInParent)"
+        ],
+        "name": "IsLeftIdealInParent",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLeftIdealInParent)"
+        ],
+        "name": "Tester(IsLeftIdealInParent)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRightIdealInParent",
+            "Tester(IsRightIdealInParent)"
+        ],
+        "name": "IsRightIdealInParent",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRightIdealInParent)"
+        ],
+        "name": "Tester(IsRightIdealInParent)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfTwoSidedIdeal)"
+        ],
+        "name": "Tester(GeneratorsOfTwoSidedIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfLeftIdeal)"
+        ],
+        "name": "Tester(GeneratorsOfLeftIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfRightIdeal)"
+        ],
+        "name": "Tester(GeneratorsOfRightIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LeftActingRingOfIdeal)"
+        ],
+        "name": "Tester(LeftActingRingOfIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RightActingRingOfIdeal)"
+        ],
+        "name": "Tester(RightActingRingOfIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule"
+        ],
+        "name": "IsFreeLeftModule",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsFiniteDimensional",
+            "Tester(IsFiniteDimensional)"
+        ],
+        "name": "IsFiniteDimensional",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFiniteDimensional)"
+        ],
+        "name": "Tester(IsFiniteDimensional)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFullRowModule",
+            "Tester(IsFullRowModule)",
+            "IsRowModule",
+            "Tester(IsRowModule)"
+        ],
+        "name": "IsFullRowModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullRowModule)"
+        ],
+        "name": "Tester(IsFullRowModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFullMatrixModule",
+            "Tester(IsFullMatrixModule)",
+            "IsMatrixModule",
+            "Tester(IsMatrixModule)"
+        ],
+        "name": "IsFullMatrixModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullMatrixModule)"
+        ],
+        "name": "Tester(IsFullMatrixModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis"
+        ],
+        "name": "IsHandledByNiceBasis",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(Dimension)"
+        ],
+        "name": "Tester(Dimension)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+        ],
+        "name": "Tester(GeneratorsOfLeftOperatorAdditiveGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfRightOperatorAdditiveGroup)"
+        ],
+        "name": "Tester(GeneratorsOfRightOperatorAdditiveGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRowModule",
+            "Tester(IsRowModule)"
+        ],
+        "name": "IsRowModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRowModule)"
+        ],
+        "name": "Tester(IsRowModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMatrixModule",
+            "Tester(IsMatrixModule)"
+        ],
+        "name": "IsMatrixModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMatrixModule)"
+        ],
+        "name": "Tester(IsMatrixModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(DimensionOfVectors)"
+        ],
+        "name": "Tester(DimensionOfVectors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsListOrCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsBasis"
+        ],
+        "name": "IsBasis",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsCanonicalBasis",
+            "Tester(IsCanonicalBasis)"
+        ],
+        "name": "IsCanonicalBasis",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCanonicalBasis)"
+        ],
+        "name": "Tester(IsCanonicalBasis)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCanonicalBasis",
+            "Tester(IsCanonicalBasis)",
+            "IsCanonicalBasisFullRowModule",
+            "Tester(IsCanonicalBasisFullRowModule)"
+        ],
+        "name": "IsCanonicalBasisFullRowModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCanonicalBasisFullRowModule)"
+        ],
+        "name": "Tester(IsCanonicalBasisFullRowModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCanonicalBasis",
+            "Tester(IsCanonicalBasis)",
+            "IsCanonicalBasisFullMatrixModule",
+            "Tester(IsCanonicalBasisFullMatrixModule)"
+        ],
+        "name": "IsCanonicalBasisFullMatrixModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCanonicalBasisFullMatrixModule)"
+        ],
+        "name": "Tester(IsCanonicalBasisFullMatrixModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsIntegralBasis",
+            "Tester(IsIntegralBasis)"
+        ],
+        "name": "IsIntegralBasis",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIntegralBasis)"
+        ],
+        "name": "Tester(IsIntegralBasis)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNormalBasis",
+            "Tester(IsNormalBasis)"
+        ],
+        "name": "IsNormalBasis",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNormalBasis)"
+        ],
+        "name": "Tester(IsNormalBasis)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSemiEchelonized",
+            "Tester(IsSemiEchelonized)"
+        ],
+        "name": "IsSemiEchelonized",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSemiEchelonized)"
+        ],
+        "name": "Tester(IsSemiEchelonized)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(BasisVectors)"
+        ],
+        "name": "Tester(BasisVectors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EnumeratorByBasis)"
+        ],
+        "name": "Tester(EnumeratorByBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StructureConstantsTable)"
+        ],
+        "name": "Tester(StructureConstantsTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingLeftModule)"
+        ],
+        "name": "Tester(UnderlyingLeftModule)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Basis)"
+        ],
+        "name": "Tester(Basis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SemiEchelonBasis)"
+        ],
+        "name": "Tester(SemiEchelonBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsGenericFiniteSpace"
+        ],
+        "name": "IsGenericFiniteSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsSpaceOfRationalFunctions"
+        ],
+        "name": "IsSpaceOfRationalFunctions",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsListOrCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsSmallList",
+            "Tester(IsSmallList)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsBasis",
+            "IsBasisByNiceBasis"
+        ],
+        "name": "IsBasisByNiceBasis",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(NiceBasis)"
+        ],
+        "name": "Tester(NiceBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NiceFreeLeftModule)"
+        ],
+        "name": "Tester(NiceFreeLeftModule)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NiceFreeLeftModuleInfo)"
+        ],
+        "name": "Tester(NiceFreeLeftModuleInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsMutableBasis"
+        ],
+        "name": "IsMutableBasis",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsGaussianSpace"
+        ],
+        "name": "IsGaussianSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalBasis)"
+        ],
+        "name": "Tester(CanonicalBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsNonGaussianRowSpace"
+        ],
+        "name": "IsNonGaussianRowSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsNonGaussianMatrixSpace"
+        ],
+        "name": "IsNonGaussianMatrixSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(NormedRowVectors)"
+        ],
+        "name": "Tester(NormedRowVectors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsSubspacesVectorSpace"
+        ],
+        "name": "IsSubspacesVectorSpace",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(Subspaces)"
+        ],
+        "name": "Tester(Subspaces)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrthogonalSpaceInFullRowSpace)"
+        ],
+        "name": "Tester(OrthogonalSpaceInFullRowSpace)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsVectorSpaceHomomorphism",
+            "Tester(IsVectorSpaceHomomorphism)"
+        ],
+        "name": "IsVectorSpaceHomomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsVectorSpaceHomomorphism)"
+        ],
+        "name": "Tester(IsVectorSpaceHomomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(AsLeftModuleGeneralMappingByImages)"
+        ],
+        "name": "Tester(AsLeftModuleGeneralMappingByImages)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFullHomModule",
+            "Tester(IsFullHomModule)"
+        ],
+        "name": "IsFullHomModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullHomModule)"
+        ],
+        "name": "Tester(IsFullHomModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPseudoCanonicalBasisFullHomModule",
+            "Tester(IsPseudoCanonicalBasisFullHomModule)"
+        ],
+        "name": "IsPseudoCanonicalBasisFullHomModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPseudoCanonicalBasisFullHomModule)"
+        ],
+        "name": "Tester(IsPseudoCanonicalBasisFullHomModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsFiniteDimensional",
+            "Tester(IsFiniteDimensional)",
+            "IsHandledByNiceBasis",
+            "IsLinearMappingsModule"
+        ],
+        "name": "IsLinearMappingsModule",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "IsSimpleAlgebra",
+            "Tester(IsSimpleAlgebra)"
+        ],
+        "name": "IsSimpleAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSimpleAlgebra)"
+        ],
+        "name": "Tester(IsSimpleAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfLeftOperatorRing)"
+        ],
+        "name": "Tester(GeneratorsOfLeftOperatorRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfLeftOperatorRingWithOne)"
+        ],
+        "name": "Tester(GeneratorsOfLeftOperatorRingWithOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PowerSubalgebraSeries)"
+        ],
+        "name": "Tester(PowerSubalgebraSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AdjointBasis)"
+        ],
+        "name": "Tester(AdjointBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndicesOfAdjointBasis)"
+        ],
+        "name": "Tester(IndicesOfAdjointBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RadicalOfAlgebra)"
+        ],
+        "name": "Tester(RadicalOfAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DirectSumDecomposition)"
+        ],
+        "name": "Tester(DirectSumDecomposition)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NullAlgebra)"
+        ],
+        "name": "Tester(NullAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieAlgebraByDomain)"
+        ],
+        "name": "Tester(LieAlgebraByDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "IsQuaternion"
+        ],
+        "name": "IsQuaternion",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsQuaternion)"
+        ],
+        "name": "CategoryCollections(IsQuaternion)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsQuaternion))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsQuaternion))",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LeviMalcevDecomposition)"
+        ],
+        "name": "Tester(LeviMalcevDecomposition)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Grading)"
+        ],
+        "name": "Tester(Grading)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsElementOfMagmaRingModuloRelations"
+        ],
+        "name": "IsElementOfMagmaRingModuloRelations",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsElementOfMagmaRingModuloRelations)"
+        ],
+        "name": "CategoryCollections(IsElementOfMagmaRingModuloRelations)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsElementOfMagmaRingModuloRelations)"
+        ],
+        "name": "CategoryFamily(IsElementOfMagmaRingModuloRelations)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsElementOfMagmaRingModuloRelations",
+            "IsElementOfFreeMagmaRing"
+        ],
+        "name": "IsElementOfFreeMagmaRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsElementOfMagmaRingModuloRelations)",
+            "CategoryCollections(IsElementOfFreeMagmaRing)"
+        ],
+        "name": "CategoryCollections(IsElementOfFreeMagmaRing)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsElementOfMagmaRingModuloRelations)",
+            "CategoryFamily(IsElementOfFreeMagmaRing)"
+        ],
+        "name": "CategoryFamily(IsElementOfFreeMagmaRing)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(CoefficientsAndMagmaElements)"
+        ],
+        "name": "Tester(CoefficientsAndMagmaElements)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ZeroCoefficient)"
+        ],
+        "name": "Tester(ZeroCoefficient)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsFreeLeftModule",
+            "IsMagmaRingModuloRelations"
+        ],
+        "name": "IsMagmaRingModuloRelations",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsFreeLeftModule",
+            "IsMagmaRingModuloRelations",
+            "IsFreeMagmaRing"
+        ],
+        "name": "IsFreeMagmaRing",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsGroupRing",
+            "Tester(IsGroupRing)"
+        ],
+        "name": "IsGroupRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupRing)"
+        ],
+        "name": "Tester(IsGroupRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingMagma)"
+        ],
+        "name": "Tester(UnderlyingMagma)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentationIdeal)"
+        ],
+        "name": "Tester(AugmentationIdeal)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsFreeLeftModule",
+            "IsMagmaRingModuloRelations",
+            "IsMagmaRingModuloSpanOfZero"
+        ],
+        "name": "IsMagmaRingModuloSpanOfZero",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsElementOfMagmaRingModuloRelations)",
+            "IsElementOfMagmaRingModuloSpanOfZeroFamily"
+        ],
+        "name": "IsElementOfMagmaRingModuloSpanOfZeroFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsSpaceOfElementsOfMagmaRing"
+        ],
+        "name": "IsSpaceOfElementsOfMagmaRing",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsElementOfFpAlgebra"
+        ],
+        "name": "IsElementOfFpAlgebra",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsElementOfFpAlgebra)"
+        ],
+        "name": "CategoryCollections(IsElementOfFpAlgebra)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsElementOfFpAlgebra)"
+        ],
+        "name": "CategoryFamily(IsElementOfFpAlgebra)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsFreeLeftModule",
+            "IsSubalgebraFpAlgebra"
+        ],
+        "name": "IsSubalgebraFpAlgebra",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsFullFpAlgebra",
+            "Tester(IsFullFpAlgebra)"
+        ],
+        "name": "IsFullFpAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullFpAlgebra)"
+        ],
+        "name": "Tester(IsFullFpAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(FreeGeneratorsOfFpAlgebra)"
+        ],
+        "name": "Tester(FreeGeneratorsOfFpAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RelatorsOfFpAlgebra)"
+        ],
+        "name": "Tester(RelatorsOfFpAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeAlgebraOfFpAlgebra)"
+        ],
+        "name": "Tester(FreeAlgebraOfFpAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNormalForm",
+            "Tester(IsNormalForm)"
+        ],
+        "name": "IsNormalForm",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNormalForm)"
+        ],
+        "name": "Tester(IsNormalForm)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NiceNormalFormByExtRepFunction)"
+        ],
+        "name": "Tester(NiceNormalFormByExtRepFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NiceAlgebraMonomorphism)"
+        ],
+        "name": "Tester(NiceAlgebraMonomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsFpAlgebraElementsSpace"
+        ],
+        "name": "IsFpAlgebraElementsSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "IsLieAbelian",
+            "Tester(IsLieAbelian)",
+            "IsLieNilpotent",
+            "Tester(IsLieNilpotent)",
+            "IsLieSolvable",
+            "Tester(IsLieSolvable)"
+        ],
+        "name": "IsLieAbelian",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieAbelian)"
+        ],
+        "name": "Tester(IsLieAbelian)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsLieNilpotent",
+            "Tester(IsLieNilpotent)",
+            "IsLieSolvable",
+            "Tester(IsLieSolvable)"
+        ],
+        "name": "IsLieNilpotent",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieNilpotent)"
+        ],
+        "name": "Tester(IsLieNilpotent)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRestrictedLieAlgebra",
+            "Tester(IsRestrictedLieAlgebra)"
+        ],
+        "name": "IsRestrictedLieAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRestrictedLieAlgebra)"
+        ],
+        "name": "Tester(IsRestrictedLieAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(LieDerivedSubalgebra)"
+        ],
+        "name": "Tester(LieDerivedSubalgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieDerivedSeries)"
+        ],
+        "name": "Tester(LieDerivedSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieSolvable",
+            "Tester(IsLieSolvable)"
+        ],
+        "name": "IsLieSolvable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieSolvable)"
+        ],
+        "name": "Tester(IsLieSolvable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(LieLowerCentralSeries)"
+        ],
+        "name": "Tester(LieLowerCentralSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieUpperCentralSeries)"
+        ],
+        "name": "Tester(LieUpperCentralSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieCentre)"
+        ],
+        "name": "Tester(LieCentre)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RightDerivations)"
+        ],
+        "name": "Tester(RightDerivations)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LeftDerivations)"
+        ],
+        "name": "Tester(LeftDerivations)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(KillingMatrix)"
+        ],
+        "name": "Tester(KillingMatrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CartanSubalgebra)"
+        ],
+        "name": "Tester(CartanSubalgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PthPowerImages)"
+        ],
+        "name": "Tester(PthPowerImages)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NonNilpotentElement)"
+        ],
+        "name": "Tester(NonNilpotentElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieNilRadical)"
+        ],
+        "name": "Tester(LieNilRadical)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieSolvableRadical)"
+        ],
+        "name": "Tester(LieSolvableRadical)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SemiSimpleType)"
+        ],
+        "name": "Tester(SemiSimpleType)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieCentralizerInParent)"
+        ],
+        "name": "Tester(LieCentralizerInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieNormalizerInParent)"
+        ],
+        "name": "Tester(LieNormalizerInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PowerS)"
+        ],
+        "name": "Tester(PowerS)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsRootSystem"
+        ],
+        "name": "IsRootSystem",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsRootSystem",
+            "IsRootSystemFromLieAlgebra"
+        ],
+        "name": "IsRootSystemFromLieAlgebra",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingLieAlgebra)"
+        ],
+        "name": "Tester(UnderlyingLieAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RootSystem)"
+        ],
+        "name": "Tester(RootSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PositiveRoots)"
+        ],
+        "name": "Tester(PositiveRoots)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NegativeRoots)"
+        ],
+        "name": "Tester(NegativeRoots)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PositiveRootVectors)"
+        ],
+        "name": "Tester(PositiveRootVectors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NegativeRootVectors)"
+        ],
+        "name": "Tester(NegativeRootVectors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SimpleSystem)"
+        ],
+        "name": "Tester(SimpleSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CartanMatrix)"
+        ],
+        "name": "Tester(CartanMatrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BilinearFormMat)"
+        ],
+        "name": "Tester(BilinearFormMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalGenerators)"
+        ],
+        "name": "Tester(CanonicalGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ChevalleyBasis)"
+        ],
+        "name": "Tester(ChevalleyBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UniversalEnvelopingAlgebra)"
+        ],
+        "name": "Tester(UniversalEnvelopingAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsElementOfMagmaRingModuloRelations)",
+            "IsFamilyElementOfFreeLieAlgebra"
+        ],
+        "name": "IsFamilyElementOfFreeLieAlgebra",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsFptoSCAMorphism"
+        ],
+        "name": "IsFptoSCAMorphism",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(JenningsLieAlgebra)"
+        ],
+        "name": "Tester(JenningsLieAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PCentralLieAlgebra)"
+        ],
+        "name": "Tester(PCentralLieAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)"
+        ],
+        "name": "Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsFamilyOverFullCoefficientsFamily"
+        ],
+        "name": "IsFamilyOverFullCoefficientsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsSCAlgebraObj"
+        ],
+        "name": "IsSCAlgebraObj",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsSCAlgebraObj)"
+        ],
+        "name": "CategoryCollections(IsSCAlgebraObj)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsSCAlgebraObj))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsSCAlgebraObj))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsSCAlgebraObj)"
+        ],
+        "name": "CategoryFamily(IsSCAlgebraObj)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsFullSCAlgebra",
+            "Tester(IsFullSCAlgebra)"
+        ],
+        "name": "IsFullSCAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullSCAlgebra)"
+        ],
+        "name": "Tester(IsFullSCAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCanonicalBasis",
+            "Tester(IsCanonicalBasis)",
+            "IsCanonicalBasisFullSCAlgebra",
+            "Tester(IsCanonicalBasisFullSCAlgebra)"
+        ],
+        "name": "IsCanonicalBasisFullSCAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCanonicalBasisFullSCAlgebra)"
+        ],
+        "name": "Tester(IsCanonicalBasisFullSCAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsSCAlgebraObjSpace"
+        ],
+        "name": "IsSCAlgebraObjSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismFpFLMLOR)"
+        ],
+        "name": "Tester(IsomorphismFpFLMLOR)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismMatrixFLMLOR)"
+        ],
+        "name": "Tester(IsomorphismMatrixFLMLOR)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismSCFLMLOR)"
+        ],
+        "name": "Tester(IsomorphismSCFLMLOR)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsJacobianElement",
+            "IsZeroSquaredElement",
+            "IsLieObject"
+        ],
+        "name": "IsLieObject",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsJacobianElement)",
+            "CategoryCollections(IsZeroSquaredElement)",
+            "CategoryCollections(IsLieObject)"
+        ],
+        "name": "CategoryCollections(IsLieObject)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsJacobianElement)",
+            "CategoryCollections(IsRestrictedJacobianElement)",
+            "CategoryCollections(IsZeroSquaredElement)",
+            "CategoryCollections(IsLieObject)",
+            "CategoryCollections((IsLieObject and IsRestrictedJacobianElement))"
+        ],
+        "name": "CategoryCollections((IsLieObject and IsRestrictedJacobianElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LieFamily)"
+        ],
+        "name": "Tester(LieFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingFamily)"
+        ],
+        "name": "Tester(UnderlyingFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieObject)"
+        ],
+        "name": "Tester(LieObject)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingRingElement)"
+        ],
+        "name": "Tester(UnderlyingRingElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsLieObjectsModule"
+        ],
+        "name": "IsLieObjectsModule",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsAlgebraModuleElement"
+        ],
+        "name": "IsAlgebraModuleElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsAlgebraModuleElement)"
+        ],
+        "name": "CategoryCollections(IsAlgebraModuleElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsAlgebraModuleElement)"
+        ],
+        "name": "CategoryFamily(IsAlgebraModuleElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsAlgebraModuleElement",
+            "IsLeftAlgebraModuleElement"
+        ],
+        "name": "IsLeftAlgebraModuleElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsAlgebraModuleElement)",
+            "CategoryCollections(IsLeftAlgebraModuleElement)"
+        ],
+        "name": "CategoryCollections(IsLeftAlgebraModuleElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsAlgebraModuleElement",
+            "IsRightAlgebraModuleElement"
+        ],
+        "name": "IsRightAlgebraModuleElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsAlgebraModuleElement)",
+            "CategoryCollections(IsRightAlgebraModuleElement)"
+        ],
+        "name": "CategoryCollections(IsRightAlgebraModuleElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsAlgebraModule",
+            "Tester(IsAlgebraModule)"
+        ],
+        "name": "IsAlgebraModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAlgebraModule)"
+        ],
+        "name": "Tester(IsAlgebraModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsLeftAlgebraModule",
+            "Tester(IsLeftAlgebraModule)"
+        ],
+        "name": "IsLeftAlgebraModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLeftAlgebraModule)"
+        ],
+        "name": "Tester(IsLeftAlgebraModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRightAlgebraModule",
+            "Tester(IsRightAlgebraModule)"
+        ],
+        "name": "IsRightAlgebraModule",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRightAlgebraModule)"
+        ],
+        "name": "Tester(IsRightAlgebraModule)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(LeftActingAlgebra)"
+        ],
+        "name": "Tester(LeftActingAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RightActingAlgebra)"
+        ],
+        "name": "Tester(RightActingAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfAlgebraModule)"
+        ],
+        "name": "Tester(GeneratorsOfAlgebraModule)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsListOrCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsBasis",
+            "IsBasisOfAlgebraModuleElementSpace"
+        ],
+        "name": "IsBasisOfAlgebraModuleElementSpace",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(AdjointModule)"
+        ],
+        "name": "Tester(AdjointModule)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FaithfulModule)"
+        ],
+        "name": "Tester(FaithfulModule)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMonomialElement"
+        ],
+        "name": "IsMonomialElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMonomialElement)"
+        ],
+        "name": "CategoryCollections(IsMonomialElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsMonomialElement)"
+        ],
+        "name": "CategoryFamily(IsMonomialElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMonomialElement",
+            "IsTensorElement"
+        ],
+        "name": "IsTensorElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMonomialElement)",
+            "CategoryCollections(IsTensorElement)"
+        ],
+        "name": "CategoryCollections(IsTensorElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMonomialElement",
+            "IsWedgeElement"
+        ],
+        "name": "IsWedgeElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMonomialElement)",
+            "CategoryCollections(IsWedgeElement)"
+        ],
+        "name": "CategoryCollections(IsWedgeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMonomialElement",
+            "IsSymmetricPowerElement"
+        ],
+        "name": "IsSymmetricPowerElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMonomialElement)",
+            "CategoryCollections(IsSymmetricPowerElement)"
+        ],
+        "name": "CategoryCollections(IsSymmetricPowerElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsDirectSumElement"
+        ],
+        "name": "IsDirectSumElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsDirectSumElement)"
+        ],
+        "name": "CategoryCollections(IsDirectSumElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsDirectSumElement)"
+        ],
+        "name": "CategoryFamily(IsDirectSumElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsSparseRowSpaceElement"
+        ],
+        "name": "IsSparseRowSpaceElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsSparseRowSpaceElement)"
+        ],
+        "name": "CategoryCollections(IsSparseRowSpaceElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsSparseRowSpaceElement)"
+        ],
+        "name": "CategoryFamily(IsSparseRowSpaceElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsDirectSumElementsSpace"
+        ],
+        "name": "IsDirectSumElementsSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsCochain"
+        ],
+        "name": "IsCochain",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsCochain)"
+        ],
+        "name": "CategoryCollections(IsCochain)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsWeylGroup",
+            "Tester(IsWeylGroup)"
+        ],
+        "name": "IsWeylGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsWeylGroup)"
+        ],
+        "name": "Tester(IsWeylGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(WeylGroup)"
+        ],
+        "name": "Tester(WeylGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SparseCartanMatrix)"
+        ],
+        "name": "Tester(SparseCartanMatrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LongestWeylWordPerm)"
+        ],
+        "name": "Tester(LongestWeylWordPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PositiveRootsAsWeights)"
+        ],
+        "name": "Tester(PositiveRootsAsWeights)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsUEALatticeElement"
+        ],
+        "name": "IsUEALatticeElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsUEALatticeElement)"
+        ],
+        "name": "CategoryCollections(IsUEALatticeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsUEALatticeElement)"
+        ],
+        "name": "CategoryFamily(IsUEALatticeElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LatticeGeneratorsInUEA)"
+        ],
+        "name": "Tester(LatticeGeneratorsInUEA)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsWeightRepElement"
+        ],
+        "name": "IsWeightRepElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsWeightRepElement)"
+        ],
+        "name": "CategoryCollections(IsWeightRepElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsWeightRepElement)"
+        ],
+        "name": "CategoryFamily(IsWeightRepElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsListOrCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsBasis",
+            "IsBasisOfWeightRepElementSpace"
+        ],
+        "name": "IsBasisOfWeightRepElementSpace",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsCochainsSpace"
+        ],
+        "name": "IsCochainsSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsSearchTable"
+        ],
+        "name": "IsSearchTable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsSearchTable",
+            "IsVectorSearchTable"
+        ],
+        "name": "IsVectorSearchTable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing",
+            "IsEuclideanRing",
+            "IsFreeLeftModule",
+            "IsIntegers"
+        ],
+        "name": "IsIntegers",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsPositiveIntegers"
+        ],
+        "name": "IsPositiveIntegers",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsNonnegativeIntegers"
+        ],
+        "name": "IsNonnegativeIntegers",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing",
+            "IsEuclideanRing",
+            "IsFreeLeftModule",
+            "IsFiniteDimensional",
+            "Tester(IsFiniteDimensional)",
+            "IsGaussianIntegers"
+        ],
+        "name": "IsGaussianIntegers",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(PrimeDivisors)"
+        ],
+        "name": "Tester(PrimeDivisors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsSCRingObj"
+        ],
+        "name": "IsSCRingObj",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsSCRingObj)"
+        ],
+        "name": "CategoryCollections(IsSCRingObj)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsSCRingObj))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsSCRingObj))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsSCRingObj)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsSCRingObj)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsSCRingObj)"
+        ],
+        "name": "CategoryFamily(IsSCRingObj)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(StandardGeneratorsSubringSCRing)"
+        ],
+        "name": "Tester(StandardGeneratorsSubringSCRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Subrings)"
+        ],
+        "name": "Tester(Subrings)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Ideals)"
+        ],
+        "name": "Tester(Ideals)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DirectSumInfo)"
+        ],
+        "name": "Tester(DirectSumInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction"
+        ],
+        "name": "IsPolynomialFunction",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsRationalFunction"
+        ],
+        "name": "IsRationalFunction",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsPolynomialFunction)"
+        ],
+        "name": "CategoryCollections(IsPolynomialFunction)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsPolynomialFunction)",
+            "CategoryCollections(IsRationalFunction)"
+        ],
+        "name": "CategoryCollections(IsRationalFunction)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsPolynomialFunctionsFamilyElement"
+        ],
+        "name": "IsPolynomialFunctionsFamilyElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsRationalFunction",
+            "IsPolynomialFunctionsFamilyElement",
+            "IsRationalFunctionsFamilyElement"
+        ],
+        "name": "IsRationalFunctionsFamilyElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsPolynomialFunctionsFamily"
+        ],
+        "name": "IsPolynomialFunctionsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsUFDFamily",
+            "Tester(IsUFDFamily)",
+            "IsPolynomialFunctionsFamily",
+            "IsRationalFunctionsFamily"
+        ],
+        "name": "IsRationalFunctionsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsRationalFunction",
+            "IsRationalFunctionOverField"
+        ],
+        "name": "IsRationalFunctionOverField",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(RationalFunctionsFamily)"
+        ],
+        "name": "Tester(RationalFunctionsFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoefficientsFamily)"
+        ],
+        "name": "Tester(CoefficientsFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NumeratorOfRationalFunction)"
+        ],
+        "name": "Tester(NumeratorOfRationalFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DenominatorOfRationalFunction)"
+        ],
+        "name": "Tester(DenominatorOfRationalFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "Tester(IsPolynomial)"
+        ],
+        "name": "IsPolynomial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPolynomial)"
+        ],
+        "name": "Tester(IsPolynomial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(AsPolynomial)"
+        ],
+        "name": "Tester(AsPolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnivariateRationalFunction",
+            "Tester(IsUnivariateRationalFunction)"
+        ],
+        "name": "IsUnivariateRationalFunction",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsUnivariateRationalFunction)"
+        ],
+        "name": "Tester(IsUnivariateRationalFunction)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsUnivariateRationalFunction",
+            "Tester(IsUnivariateRationalFunction)",
+            "IsLaurentPolynomial",
+            "Tester(IsLaurentPolynomial)"
+        ],
+        "name": "IsLaurentPolynomial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLaurentPolynomial)"
+        ],
+        "name": "Tester(IsLaurentPolynomial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsUnivariateRationalFunction",
+            "Tester(IsUnivariateRationalFunction)",
+            "IsConstantRationalFunction",
+            "Tester(IsConstantRationalFunction)"
+        ],
+        "name": "IsConstantRationalFunction",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsConstantRationalFunction)"
+        ],
+        "name": "Tester(IsConstantRationalFunction)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsRationalFunction",
+            "IsRationalFunctionDefaultRep"
+        ],
+        "name": "IsRationalFunctionDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsPolynomial",
+            "Tester(IsPolynomial)",
+            "IsPolynomialDefaultRep"
+        ],
+        "name": "IsPolynomialDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsUnivariateRationalFunction",
+            "Tester(IsUnivariateRationalFunction)",
+            "IsLaurentPolynomial",
+            "Tester(IsLaurentPolynomial)",
+            "IsLaurentPolynomialDefaultRep"
+        ],
+        "name": "IsLaurentPolynomialDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsUnivariateRationalFunction",
+            "Tester(IsUnivariateRationalFunction)",
+            "IsUnivariateRationalFunctionDefaultRep"
+        ],
+        "name": "IsUnivariateRationalFunctionDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(ExtRepNumeratorRatFun)"
+        ],
+        "name": "Tester(ExtRepNumeratorRatFun)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ExtRepDenominatorRatFun)"
+        ],
+        "name": "Tester(ExtRepDenominatorRatFun)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ExtRepPolynomialRatFun)"
+        ],
+        "name": "Tester(ExtRepPolynomialRatFun)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoefficientsOfLaurentPolynomial)"
+        ],
+        "name": "Tester(CoefficientsOfLaurentPolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndeterminateNumberOfUnivariateRationalFunction)"
+        ],
+        "name": "Tester(IndeterminateNumberOfUnivariateRationalFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndeterminateOfUnivariateRationalFunction)"
+        ],
+        "name": "Tester(IndeterminateOfUnivariateRationalFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoefficientsOfUnivariatePolynomial)"
+        ],
+        "name": "Tester(CoefficientsOfUnivariatePolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOfLaurentPolynomial)"
+        ],
+        "name": "Tester(DegreeOfLaurentPolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoefficientsOfUnivariateRationalFunction)"
+        ],
+        "name": "Tester(CoefficientsOfUnivariateRationalFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Derivative)"
+        ],
+        "name": "Tester(Derivative)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Discriminant)"
+        ],
+        "name": "Tester(Discriminant)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsRationalFunction",
+            "IsLaurentPolynomialsFamilyElement"
+        ],
+        "name": "IsLaurentPolynomialsFamilyElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsRationalFunction",
+            "IsUnivariatePolynomialsFamilyElement"
+        ],
+        "name": "IsUnivariatePolynomialsFamilyElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "Tester(OneImmutable)",
+            "IsCommutativeFamily",
+            "Tester(IsCommutativeFamily)",
+            "IsLaurentPolynomialsFamily"
+        ],
+        "name": "IsLaurentPolynomialsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsUnivariatePolynomialsFamily"
+        ],
+        "name": "IsUnivariatePolynomialsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(PrimeField)"
+        ],
+        "name": "Tester(PrimeField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPrimeField",
+            "Tester(IsPrimeField)"
+        ],
+        "name": "IsPrimeField",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPrimeField)"
+        ],
+        "name": "Tester(IsPrimeField)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(DefiningPolynomial)"
+        ],
+        "name": "Tester(DefiningPolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOverPrimeField)"
+        ],
+        "name": "Tester(DegreeOverPrimeField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfDivisionRing)"
+        ],
+        "name": "Tester(GeneratorsOfDivisionRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalBase)"
+        ],
+        "name": "Tester(NormalBase)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PrimitiveElement)"
+        ],
+        "name": "Tester(PrimitiveElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PrimitiveRoot)"
+        ],
+        "name": "Tester(PrimitiveRoot)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RootOfDefiningPolynomial)"
+        ],
+        "name": "Tester(RootOfDefiningPolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Subfields)"
+        ],
+        "name": "Tester(Subfields)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsNonTrivial",
+            "Tester(IsNonTrivial)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "IsCommutative",
+            "Tester(IsCommutative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing",
+            "IsEuclideanRing",
+            "IsIntegralRing",
+            "Tester(IsIntegralRing)",
+            "IsFreeLeftModule",
+            "IsFieldControlledByGaloisGroup"
+        ],
+        "name": "IsFieldControlledByGaloisGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(Conjugates)"
+        ],
+        "name": "Tester(Conjugates)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Norm)"
+        ],
+        "name": "Tester(Norm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Trace)"
+        ],
+        "name": "Tester(Trace)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GaloisGroup)"
+        ],
+        "name": "Tester(GaloisGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComplexConjugate)"
+        ],
+        "name": "Tester(ComplexConjugate)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RealPart)"
+        ],
+        "name": "Tester(RealPart)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ImaginaryPart)"
+        ],
+        "name": "Tester(ImaginaryPart)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FrobeniusAutomorphism)"
+        ],
+        "name": "Tester(FrobeniusAutomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsFieldElementsSpace"
+        ],
+        "name": "IsFieldElementsSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsZmodnZObj"
+        ],
+        "name": "IsZmodnZObj",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsZmodnZObj",
+            "IsZmodnZObjNonprime"
+        ],
+        "name": "IsZmodnZObjNonprime",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsAdditivelyCommutativeElement)",
+            "CategoryFamily(IsZmodnZObjNonprime)"
+        ],
+        "name": "CategoryFamily(IsZmodnZObjNonprime)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsAdditivelyCommutativeElement)",
+            "CategoryCollections(IsCommutativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsZmodnZObjNonprime)"
+        ],
+        "name": "CategoryCollections(IsZmodnZObjNonprime)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))",
+            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(ModulusOfZmodnZObj)"
+        ],
+        "name": "Tester(ModulusOfZmodnZObj)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZmodnZepsObj"
+        ],
+        "name": "IsZmodnZepsObj",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZmodnZepsObj)"
+        ],
+        "name": "CategoryCollections(IsZmodnZepsObj)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsZmodnZepsRep"
+        ],
+        "name": "IsZmodnZepsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(Cyclotomic)"
+        ],
+        "name": "Tester(Cyclotomic)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsRingOfIntegralCyclotomics)"
+        ],
+        "name": "Tester(IsRingOfIntegralCyclotomics)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GaloisMat)"
+        ],
+        "name": "Tester(GaloisMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RationalizedMat)"
+        ],
+        "name": "Tester(RationalizedMat)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField",
+            "Tester(IsNumberField)"
+        ],
+        "name": "IsNumberField",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNumberField)"
+        ],
+        "name": "Tester(IsNumberField)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNumberField",
+            "Tester(IsNumberField)",
+            "IsAbelianNumberField",
+            "Tester(IsAbelianNumberField)"
+        ],
+        "name": "IsAbelianNumberField",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAbelianNumberField)"
+        ],
+        "name": "Tester(IsAbelianNumberField)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNumberField",
+            "Tester(IsNumberField)",
+            "IsAbelianNumberField",
+            "Tester(IsAbelianNumberField)",
+            "IsCyclotomicField",
+            "Tester(IsCyclotomicField)"
+        ],
+        "name": "IsCyclotomicField",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCyclotomicField)"
+        ],
+        "name": "Tester(IsCyclotomicField)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GaloisStabilizer)"
+        ],
+        "name": "Tester(GaloisStabilizer)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsNonTrivial",
+            "Tester(IsNonTrivial)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsAdditivelyCommutativeElement)",
+            "CategoryCollections(IsCommutativeElement)",
+            "IsGeneralizedDomain",
+            "CategoryCollections(IsCyclotomic)",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "IsCommutative",
+            "Tester(IsCommutative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing",
+            "IsEuclideanRing",
+            "IsIntegralRing",
+            "Tester(IsIntegralRing)",
+            "IsFreeLeftModule",
+            "IsGaussianRationals"
+        ],
+        "name": "IsGaussianRationals",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(ExponentOfPowering)"
+        ],
+        "name": "Tester(ExponentOfPowering)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsCommutativeElement",
+            "IsPadicNumber"
+        ],
+        "name": "IsPadicNumber",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsCommutativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsPadicNumber)"
+        ],
+        "name": "CategoryCollections(IsPadicNumber)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(CategoryCollections(IsPadicNumber))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsPadicNumber))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsPadicNumber)"
+        ],
+        "name": "CategoryFamily(IsPadicNumber)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsCommutativeElement",
+            "IsPadicNumber",
+            "IsPurePadicNumber"
+        ],
+        "name": "IsPurePadicNumber",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsPadicNumber)",
+            "CategoryFamily(IsPurePadicNumber)"
+        ],
+        "name": "CategoryFamily(IsPurePadicNumber)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsCommutativeElement",
+            "IsPadicNumber",
+            "IsPadicExtensionNumber"
+        ],
+        "name": "IsPadicExtensionNumber",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsPadicNumber)",
+            "CategoryFamily(IsPadicExtensionNumber)"
+        ],
+        "name": "CategoryFamily(IsPadicExtensionNumber)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsPolynomialRing"
+        ],
+        "name": "IsPolynomialRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsFunctionField"
+        ],
+        "name": "IsFunctionField",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsPolynomialRing",
+            "IsUnivariatePolynomialRing"
+        ],
+        "name": "IsUnivariatePolynomialRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsPolynomialRing",
+            "IsFiniteFieldPolynomialRing"
+        ],
+        "name": "IsFiniteFieldPolynomialRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsPolynomialRing",
+            "IsAbelianNumberFieldPolynomialRing"
+        ],
+        "name": "IsAbelianNumberFieldPolynomialRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsPolynomialRing",
+            "IsAlgebraicExtensionPolynomialRing"
+        ],
+        "name": "IsAlgebraicExtensionPolynomialRing",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsPolynomialRing",
+            "IsAbelianNumberFieldPolynomialRing",
+            "IsRationalsPolynomialRing"
+        ],
+        "name": "IsRationalsPolynomialRing",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(CoefficientsRing)"
+        ],
+        "name": "Tester(CoefficientsRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndeterminatesOfPolynomialRing)"
+        ],
+        "name": "Tester(IndeterminatesOfPolynomialRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SplittingField)"
+        ],
+        "name": "Tester(SplittingField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IrrFacsPol)"
+        ],
+        "name": "Tester(IrrFacsPol)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimizedBombieriNorm)"
+        ],
+        "name": "Tester(MinimizedBombieriNorm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsAlgebraicElement"
+        ],
+        "name": "IsAlgebraicElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsZDFRE)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsAdditivelyCommutativeElement)",
+            "CategoryCollections(IsCommutativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsAlgebraicElement)"
+        ],
+        "name": "CategoryCollections(IsAlgebraicElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsZDFRE))",
+            "CategoryCollections(CategoryCollections(IsAssociativeElement))",
+            "CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))",
+            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(CategoryCollections(IsAlgebraicElement))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(IsAlgebraicElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))"
+        ],
+        "name": "CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))",
+            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))",
+            "CategoryFamily(IsAdditivelyCommutativeElement)",
+            "CategoryFamily(IsAlgebraicElement)"
+        ],
+        "name": "CategoryFamily(IsAlgebraicElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsNonTrivial",
+            "Tester(IsNonTrivial)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "IsCommutative",
+            "Tester(IsCommutative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing",
+            "IsEuclideanRing",
+            "IsIntegralRing",
+            "Tester(IsIntegralRing)",
+            "IsFreeLeftModule",
+            "IsAlgebraicExtension"
+        ],
+        "name": "IsAlgebraicExtension",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(AlgebraicElementsFamilies)"
+        ],
+        "name": "Tester(AlgebraicElementsFamilies)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DefectApproximation)"
+        ],
+        "name": "Tester(DefectApproximation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsCyclotomic",
+            "IsUnknown"
+        ],
+        "name": "IsUnknown",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsWord"
+        ],
+        "name": "IsWord",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsWord)"
+        ],
+        "name": "CategoryCollections(IsWord)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsWord",
+            "IsNonassocWord"
+        ],
+        "name": "IsNonassocWord",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsWord)",
+            "CategoryCollections(IsNonassocWord)"
+        ],
+        "name": "CategoryCollections(IsNonassocWord)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsWord)",
+            "CategoryCollections(IsNonassocWord)",
+            "CategoryCollections((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))"
+        ],
+        "name": "CategoryCollections((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsNonassocWord)"
+        ],
+        "name": "CategoryFamily(IsNonassocWord)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsNonassocWord)",
+            "CategoryFamily((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))"
+        ],
+        "name": "CategoryFamily((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsWord)",
+            "CategoryCollections((IsWord and IsAssociativeElement))"
+        ],
+        "name": "CategoryCollections((IsWord and IsAssociativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsWord)",
+            "CategoryCollections((IsWord and IsAssociativeElement))",
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+        ],
+        "name": "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsWord)",
+            "CategoryCollections((IsWord and IsAssociativeElement))",
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+        ],
+        "name": "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))"
+        ],
+        "name": "CategoryFamily((IsWord and IsAssociativeElement))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+        ],
+        "name": "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))",
+            "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+        ],
+        "name": "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsSyllableWordsFamily"
+        ],
+        "name": "IsSyllableWordsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsSyllableWordsFamily",
+            "Is8BitsFamily"
+        ],
+        "name": "Is8BitsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsSyllableWordsFamily",
+            "Is16BitsFamily"
+        ],
+        "name": "Is16BitsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsSyllableWordsFamily",
+            "Is32BitsFamily"
+        ],
+        "name": "Is32BitsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsSyllableWordsFamily",
+            "IsInfBitsFamily"
+        ],
+        "name": "IsInfBitsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsSyllableAssocWordRep"
+        ],
+        "name": "IsSyllableAssocWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsLetterAssocWordRep"
+        ],
+        "name": "IsLetterAssocWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsLetterAssocWordRep",
+            "IsBLetterAssocWordRep"
+        ],
+        "name": "IsBLetterAssocWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsLetterAssocWordRep",
+            "IsWLetterAssocWordRep"
+        ],
+        "name": "IsWLetterAssocWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsLetterWordsFamily"
+        ],
+        "name": "IsLetterWordsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsLetterWordsFamily",
+            "IsBLetterWordsFamily"
+        ],
+        "name": "IsBLetterWordsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily((IsWord and IsAssociativeElement))",
+            "IsLetterWordsFamily",
+            "IsWLetterWordsFamily"
+        ],
+        "name": "IsWLetterWordsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsFreeSemigroup",
+            "Tester(IsFreeSemigroup)"
+        ],
+        "name": "IsFreeSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFreeSemigroup)"
+        ],
+        "name": "Tester(IsFreeSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFreeMonoid",
+            "Tester(IsFreeMonoid)"
+        ],
+        "name": "IsFreeMonoid",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFreeMonoid)"
+        ],
+        "name": "Tester(IsFreeMonoid)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NumberSyllables)"
+        ],
+        "name": "Tester(NumberSyllables)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BaseDomain)"
+        ],
+        "name": "Tester(BaseDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RowLength)"
+        ],
+        "name": "Tester(RowLength)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsPositionalObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsRowVectorObj",
+            "IsPlistVectorRep"
+        ],
+        "name": "IsPlistVectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsPositionalObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMatrixObj",
+            "IsRowListMatrix",
+            "IsPlistMatrixRep"
+        ],
+        "name": "IsPlistMatrixRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsIntVector"
+        ],
+        "name": "IsIntVector",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsFFEVector"
+        ],
+        "name": "IsFFEVector",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsCheckingVector"
+        ],
+        "name": "IsCheckingVector",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsCheckingMatrix"
+        ],
+        "name": "IsCheckingMatrix",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsRewritingSystem"
+        ],
+        "name": "IsRewritingSystem",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsRewritingSystem",
+            "IsReducedConfluentRewritingSystem"
+        ],
+        "name": "IsReducedConfluentRewritingSystem",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsBuiltFromAdditiveMagmaWithInverses",
+            "Tester(IsBuiltFromAdditiveMagmaWithInverses)"
+        ],
+        "name": "IsBuiltFromAdditiveMagmaWithInverses",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBuiltFromAdditiveMagmaWithInverses)"
+        ],
+        "name": "Tester(IsBuiltFromAdditiveMagmaWithInverses)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)"
+        ],
+        "name": "IsBuiltFromMagma",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBuiltFromMagma)"
+        ],
+        "name": "Tester(IsBuiltFromMagma)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)",
+            "IsBuiltFromMagmaWithOne",
+            "Tester(IsBuiltFromMagmaWithOne)"
+        ],
+        "name": "IsBuiltFromMagmaWithOne",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBuiltFromMagmaWithOne)"
+        ],
+        "name": "Tester(IsBuiltFromMagmaWithOne)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)",
+            "IsBuiltFromMagmaWithOne",
+            "Tester(IsBuiltFromMagmaWithOne)",
+            "IsBuiltFromMagmaWithInverses",
+            "Tester(IsBuiltFromMagmaWithInverses)"
+        ],
+        "name": "IsBuiltFromMagmaWithInverses",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBuiltFromMagmaWithInverses)"
+        ],
+        "name": "Tester(IsBuiltFromMagmaWithInverses)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)",
+            "IsBuiltFromMagmaWithOne",
+            "Tester(IsBuiltFromMagmaWithOne)",
+            "IsBuiltFromMagmaWithInverses",
+            "Tester(IsBuiltFromMagmaWithInverses)",
+            "IsBuiltFromGroup",
+            "Tester(IsBuiltFromGroup)"
+        ],
+        "name": "IsBuiltFromGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBuiltFromGroup)"
+        ],
+        "name": "Tester(IsBuiltFromGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBuiltFromSemigroup",
+            "Tester(IsBuiltFromSemigroup)"
+        ],
+        "name": "IsBuiltFromSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBuiltFromSemigroup)"
+        ],
+        "name": "Tester(IsBuiltFromSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBuiltFromMonoid",
+            "Tester(IsBuiltFromMonoid)"
+        ],
+        "name": "IsBuiltFromMonoid",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBuiltFromMonoid)"
+        ],
+        "name": "Tester(IsBuiltFromMonoid)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(SemigroupOfRewritingSystem)"
+        ],
+        "name": "Tester(SemigroupOfRewritingSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MonoidOfRewritingSystem)"
+        ],
+        "name": "Tester(MonoidOfRewritingSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConfluentRws)"
+        ],
+        "name": "Tester(ConfluentRws)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsOfRws)"
+        ],
+        "name": "Tester(GeneratorsOfRws)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NumberGeneratorsOfRws)"
+        ],
+        "name": "Tester(NumberGeneratorsOfRws)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Rules)"
+        ],
+        "name": "Tester(Rules)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrderingOfRewritingSystem)"
+        ],
+        "name": "Tester(OrderingOfRewritingSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsConfluent",
+            "Tester(IsConfluent)"
+        ],
+        "name": "IsConfluent",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsConfluent)"
+        ],
+        "name": "Tester(IsConfluent)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsReduced",
+            "Tester(IsReduced)"
+        ],
+        "name": "IsReduced",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsReduced)"
+        ],
+        "name": "Tester(IsReduced)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsRewritingSystem",
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)",
+            "IsBuiltFromMagmaWithOne",
+            "Tester(IsBuiltFromMagmaWithOne)",
+            "IsBuiltFromMagmaWithInverses",
+            "Tester(IsBuiltFromMagmaWithInverses)",
+            "IsBuiltFromGroup",
+            "Tester(IsBuiltFromGroup)",
+            "IsPolycyclicCollector"
+        ],
+        "name": "IsPolycyclicCollector",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsRewritingSystem",
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)",
+            "IsBuiltFromMagmaWithOne",
+            "Tester(IsBuiltFromMagmaWithOne)",
+            "IsBuiltFromMagmaWithInverses",
+            "Tester(IsBuiltFromMagmaWithInverses)",
+            "IsBuiltFromGroup",
+            "Tester(IsBuiltFromGroup)",
+            "IsPolycyclicCollector",
+            "IsPowerConjugateCollector"
+        ],
+        "name": "IsPowerConjugateCollector",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsRewritingSystem",
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)",
+            "IsBuiltFromMagmaWithOne",
+            "Tester(IsBuiltFromMagmaWithOne)",
+            "IsBuiltFromMagmaWithInverses",
+            "Tester(IsBuiltFromMagmaWithInverses)",
+            "IsBuiltFromGroup",
+            "Tester(IsBuiltFromGroup)",
+            "IsPolycyclicCollector",
+            "IsPowerCommutatorCollector"
+        ],
+        "name": "IsPowerCommutatorCollector",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(RelativeOrders)"
+        ],
+        "name": "Tester(RelativeOrders)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsUpToDatePolycyclicCollector"
+        ],
+        "name": "IsUpToDatePolycyclicCollector",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsElementsFamilyByRws"
+        ],
+        "name": "IsElementsFamilyByRws",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMultiplicativeElementWithInverseByRws"
+        ],
+        "name": "IsMultiplicativeElementWithInverseByRws",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsElementFinitePolycyclicGroup"
+        ],
+        "name": "IsElementFinitePolycyclicGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "IsSubsetLocallyFiniteGroup",
+            "Tester(IsSubsetLocallyFiniteGroup)",
+            "CategoryCollections(IsElementFinitePolycyclicGroup)"
+        ],
+        "name": "CategoryCollections(IsElementFinitePolycyclicGroup)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsMultiplicativeElementWithInverseByRws",
+            "IsMultiplicativeElementWithInverseByPolycyclicCollector"
+        ],
+        "name": "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+        ],
+        "name": "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(DefiningPcgs)"
+        ],
+        "name": "Tester(DefiningPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsKernelPcWord"
+        ],
+        "name": "IsKernelPcWord",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsElementsFamilyByRws",
+            "IsElementsFamilyBy8BitsSingleCollector"
+        ],
+        "name": "IsElementsFamilyBy8BitsSingleCollector",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsElementsFamilyByRws",
+            "IsElementsFamilyBy16BitsSingleCollector"
+        ],
+        "name": "IsElementsFamilyBy16BitsSingleCollector",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsElementsFamilyByRws",
+            "IsElementsFamilyBy32BitsSingleCollector"
+        ],
+        "name": "IsElementsFamilyBy32BitsSingleCollector",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsMonomialOrdering"
+        ],
+        "name": "IsMonomialOrdering",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsMonomialOrdering",
+            "IsMonomialOrderingDefaultRep"
+        ],
+        "name": "IsMonomialOrderingDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(MonomialComparisonFunction)"
+        ],
+        "name": "Tester(MonomialComparisonFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MonomialExtrepComparisonFun)"
+        ],
+        "name": "Tester(MonomialExtrepComparisonFun)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OccuringVariableIndices)"
+        ],
+        "name": "Tester(OccuringVariableIndices)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StoredGroebnerBasis)"
+        ],
+        "name": "Tester(StoredGroebnerBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsNoImmediateMethodsObject",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsConstantTimeAccessList",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralPcgs"
+        ],
+        "name": "IsGeneralPcgs",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsNoImmediateMethodsObject",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsConstantTimeAccessList",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralPcgs",
+            "IsModuloPcgs"
+        ],
+        "name": "IsModuloPcgs",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsNoImmediateMethodsObject",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsConstantTimeAccessList",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralPcgs",
+            "IsModuloPcgs",
+            "IsPcgs"
+        ],
+        "name": "IsPcgs",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "IsPcgsFamily"
+        ],
+        "name": "IsPcgsFamily",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep"
+        ],
+        "name": "IsPcgsDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(PcGroupWithPcgs)"
+        ],
+        "name": "Tester(PcGroupWithPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GroupOfPcgs)"
+        ],
+        "name": "Tester(GroupOfPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OneOfPcgs)"
+        ],
+        "name": "Tester(OneOfPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PcSeries)"
+        ],
+        "name": "Tester(PcSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgsElementaryAbelianSeries",
+            "Tester(IsPcgsElementaryAbelianSeries)"
+        ],
+        "name": "IsPcgsElementaryAbelianSeries",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPcgsElementaryAbelianSeries)"
+        ],
+        "name": "Tester(IsPcgsElementaryAbelianSeries)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(PcgsElementaryAbelianSeries)"
+        ],
+        "name": "Tester(PcgsElementaryAbelianSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndicesEANormalSteps)"
+        ],
+        "name": "Tester(IndicesEANormalSteps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EANormalSeriesByPcgs)"
+        ],
+        "name": "Tester(EANormalSeriesByPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgsCentralSeries",
+            "Tester(IsPcgsCentralSeries)"
+        ],
+        "name": "IsPcgsCentralSeries",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPcgsCentralSeries)"
+        ],
+        "name": "Tester(IsPcgsCentralSeries)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(PcgsCentralSeries)"
+        ],
+        "name": "Tester(PcgsCentralSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndicesCentralNormalSteps)"
+        ],
+        "name": "Tester(IndicesCentralNormalSteps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CentralNormalSeriesByPcgs)"
+        ],
+        "name": "Tester(CentralNormalSeriesByPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgsPCentralSeriesPGroup",
+            "Tester(IsPcgsPCentralSeriesPGroup)"
+        ],
+        "name": "IsPcgsPCentralSeriesPGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPcgsPCentralSeriesPGroup)"
+        ],
+        "name": "Tester(IsPcgsPCentralSeriesPGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(PcgsPCentralSeriesPGroup)"
+        ],
+        "name": "Tester(PcgsPCentralSeriesPGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndicesPCentralNormalStepsPGroup)"
+        ],
+        "name": "Tester(IndicesPCentralNormalStepsPGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PCentralNormalSeriesByPcgsPGroup)"
+        ],
+        "name": "Tester(PCentralNormalSeriesByPcgsPGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgsChiefSeries",
+            "Tester(IsPcgsChiefSeries)"
+        ],
+        "name": "IsPcgsChiefSeries",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPcgsChiefSeries)"
+        ],
+        "name": "Tester(IsPcgsChiefSeries)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(PcgsChiefSeries)"
+        ],
+        "name": "Tester(PcgsChiefSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndicesChiefNormalSteps)"
+        ],
+        "name": "Tester(IndicesChiefNormalSteps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ChiefNormalSeriesByPcgs)"
+        ],
+        "name": "Tester(ChiefNormalSeriesByPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndicesNormalSteps)"
+        ],
+        "name": "Tester(IndicesNormalSteps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalSeriesByPcgs)"
+        ],
+        "name": "Tester(NormalSeriesByPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPrimeOrdersPcgs",
+            "Tester(IsPrimeOrdersPcgs)",
+            "IsFiniteOrdersPcgs",
+            "Tester(IsFiniteOrdersPcgs)"
+        ],
+        "name": "IsPrimeOrdersPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPrimeOrdersPcgs)"
+        ],
+        "name": "Tester(IsPrimeOrdersPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFiniteOrdersPcgs",
+            "Tester(IsFiniteOrdersPcgs)"
+        ],
+        "name": "IsFiniteOrdersPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFiniteOrdersPcgs)"
+        ],
+        "name": "Tester(IsFiniteOrdersPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(RefinedPcGroup)"
+        ],
+        "name": "Tester(RefinedPcGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismRefinedPcGroup)"
+        ],
+        "name": "Tester(IsomorphismRefinedPcGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsNoImmediateMethodsObject",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsConstantTimeAccessList",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralPcgs",
+            "IsModuloPcgs",
+            "IsPcgs",
+            "IsInducedPcgs"
+        ],
+        "name": "IsInducedPcgs",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LeadCoeffsIGS)"
+        ],
+        "name": "Tester(LeadCoeffsIGS)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ParentPcgs)"
+        ],
+        "name": "Tester(ParentPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalPcgs)"
+        ],
+        "name": "Tester(CanonicalPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCanonicalPcgs",
+            "Tester(IsCanonicalPcgs)"
+        ],
+        "name": "IsCanonicalPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCanonicalPcgs)"
+        ],
+        "name": "Tester(IsCanonicalPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsParentPcgsFamilyPcgs",
+            "Tester(IsParentPcgsFamilyPcgs)"
+        ],
+        "name": "IsParentPcgsFamilyPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsParentPcgsFamilyPcgs)"
+        ],
+        "name": "Tester(IsParentPcgsFamilyPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ElementaryAbelianSubseries)"
+        ],
+        "name": "Tester(ElementaryAbelianSubseries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCanonicalPcgs",
+            "Tester(IsCanonicalPcgs)",
+            "IsParentPcgsFamilyPcgs",
+            "Tester(IsParentPcgsFamilyPcgs)",
+            "IsFamilyPcgs",
+            "Tester(IsFamilyPcgs)"
+        ],
+        "name": "IsFamilyPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFamilyPcgs)"
+        ],
+        "name": "Tester(IsFamilyPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(DenominatorOfModuloPcgs)"
+        ],
+        "name": "Tester(DenominatorOfModuloPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NumeratorOfModuloPcgs)"
+        ],
+        "name": "Tester(NumeratorOfModuloPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumeratorParentPcgsFamilyPcgs",
+            "Tester(IsNumeratorParentPcgsFamilyPcgs)"
+        ],
+        "name": "IsNumeratorParentPcgsFamilyPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNumeratorParentPcgsFamilyPcgs)"
+        ],
+        "name": "Tester(IsNumeratorParentPcgsFamilyPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsFiniteOrdersPcgs",
+            "Tester(IsFiniteOrdersPcgs)",
+            "IsPcgsPermGroupRep"
+        ],
+        "name": "IsPcgsPermGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsFiniteOrdersPcgs",
+            "Tester(IsFiniteOrdersPcgs)",
+            "IsPcgsPermGroupRep",
+            "IsModuloPcgsPermGroupRep"
+        ],
+        "name": "IsModuloPcgsPermGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsPcgsElementaryAbelianSeries",
+            "Tester(IsPcgsElementaryAbelianSeries)",
+            "IsSpecialPcgs",
+            "Tester(IsSpecialPcgs)"
+        ],
+        "name": "IsSpecialPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSpecialPcgs)"
+        ],
+        "name": "Tester(IsSpecialPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(SpecialPcgs)"
+        ],
+        "name": "Tester(SpecialPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LGHeads)"
+        ],
+        "name": "Tester(LGHeads)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LGTails)"
+        ],
+        "name": "Tester(LGTails)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LGWeights)"
+        ],
+        "name": "Tester(LGWeights)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LGLayers)"
+        ],
+        "name": "Tester(LGLayers)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LGFirst)"
+        ],
+        "name": "Tester(LGFirst)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LGLength)"
+        ],
+        "name": "Tester(LGLength)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InducedPcgsWrtSpecialPcgs)"
+        ],
+        "name": "Tester(InducedPcgsWrtSpecialPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalPcgsWrtSpecialPcgs)"
+        ],
+        "name": "Tester(CanonicalPcgsWrtSpecialPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInducedPcgsWrtSpecialPcgs",
+            "Tester(IsInducedPcgsWrtSpecialPcgs)"
+        ],
+        "name": "IsInducedPcgsWrtSpecialPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsInducedPcgsWrtSpecialPcgs)"
+        ],
+        "name": "Tester(IsInducedPcgsWrtSpecialPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCanonicalPcgsWrtSpecialPcgs",
+            "Tester(IsCanonicalPcgsWrtSpecialPcgs)"
+        ],
+        "name": "IsCanonicalPcgsWrtSpecialPcgs",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCanonicalPcgsWrtSpecialPcgs)"
+        ],
+        "name": "Tester(IsCanonicalPcgsWrtSpecialPcgs)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalPcgsWrtFamilyPcgs)"
+        ],
+        "name": "Tester(CanonicalPcgsWrtFamilyPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalPcgsWrtHomePcgs)"
+        ],
+        "name": "Tester(CanonicalPcgsWrtHomePcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FamilyPcgs)"
+        ],
+        "name": "Tester(FamilyPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(HomePcgs)"
+        ],
+        "name": "Tester(HomePcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InducedPcgsWrtFamilyPcgs)"
+        ],
+        "name": "Tester(InducedPcgsWrtFamilyPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedInducedPcgses)"
+        ],
+        "name": "Tester(ComputedInducedPcgses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InducedPcgsWrtHomePcgs)"
+        ],
+        "name": "Tester(InducedPcgsWrtHomePcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Pcgs)"
+        ],
+        "name": "Tester(Pcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneralizedPcgs)"
+        ],
+        "name": "Tester(GeneralizedPcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CanComputeSize",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "CanComputeSizeAnySubgroup",
+            "IsSolvableGroup",
+            "Tester(IsSolvableGroup)",
+            "CanEasilyComputePcgs"
+        ],
+        "name": "CanEasilyComputePcgs",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(OmegaSeries)"
+        ],
+        "name": "Tester(OmegaSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalizerInHomePcgs)"
+        ],
+        "name": "Tester(NormalizerInHomePcgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MultiplicationTable)"
+        ],
+        "name": "Tester(MultiplicationTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AllBlocks)"
+        ],
+        "name": "Tester(AllBlocks)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TransitiveIdentification)"
+        ],
+        "name": "Tester(TransitiveIdentification)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PrimitiveIdentification)"
+        ],
+        "name": "Tester(PrimitiveIdentification)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ONanScottType)"
+        ],
+        "name": "Tester(ONanScottType)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SocleTypePrimitiveGroup)"
+        ],
+        "name": "Tester(SocleTypePrimitiveGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TwoClosure)"
+        ],
+        "name": "Tester(TwoClosure)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages"
+        ],
+        "name": "IsGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages"
+        ],
+        "name": "IsPreimagesByAsGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+        ],
+        "name": "IsGroupGeneralMappingByAsGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(AsGroupGeneralMappingByImages)"
+        ],
+        "name": "Tester(AsGroupGeneralMappingByImages)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MappingOfWhichItIsAsGGMBI)"
+        ],
+        "name": "Tester(MappingOfWhichItIsAsGGMBI)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalHomomorphismByNormalSubgroupNCInParent)"
+        ],
+        "name": "Tester(NaturalHomomorphismByNormalSubgroupNCInParent)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsConjugatorIsomorphism",
+            "Tester(IsConjugatorIsomorphism)"
+        ],
+        "name": "IsConjugatorIsomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsConjugatorIsomorphism)"
+        ],
+        "name": "Tester(IsConjugatorIsomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsConjugatorIsomorphism",
+            "Tester(IsConjugatorIsomorphism)",
+            "IsInnerAutomorphism",
+            "Tester(IsInnerAutomorphism)"
+        ],
+        "name": "IsInnerAutomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsInnerAutomorphism)"
+        ],
+        "name": "Tester(IsInnerAutomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ConjugatorOfConjugatorIsomorphism)"
+        ],
+        "name": "Tester(ConjugatorOfConjugatorIsomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ImagesSmallestGenerators)"
+        ],
+        "name": "Tester(ImagesSmallestGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RegularActionHomomorphism)"
+        ],
+        "name": "Tester(RegularActionHomomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsGroupGeneralMappingByPcgs"
+        ],
+        "name": "IsGroupGeneralMappingByPcgs",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsGroupGeneralMappingByPcgs",
+            "IsPcGroupGeneralMappingByImages"
+        ],
+        "name": "IsPcGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsToPcGroupGeneralMappingByImages"
+        ],
+        "name": "IsToPcGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsNaturalHomomorphismPcGroupRep"
+        ],
+        "name": "IsNaturalHomomorphismPcGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsGroupGeneralMappingByPcgs",
+            "IsPcGroupGeneralMappingByImages",
+            "IsToPcGroupGeneralMappingByImages",
+            "IsPcgsToPcgsGeneralMappingByImages"
+        ],
+        "name": "IsPcgsToPcgsGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(DirectProductInfo)"
+        ],
+        "name": "Tester(DirectProductInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SubdirectProductInfo)"
+        ],
+        "name": "Tester(SubdirectProductInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SemidirectProductInfo)"
+        ],
+        "name": "Tester(SemidirectProductInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(WreathProductInfo)"
+        ],
+        "name": "Tester(WreathProductInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeProductInfo)"
+        ],
+        "name": "Tester(FreeProductInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsWreathProductElement"
+        ],
+        "name": "IsWreathProductElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsWreathProductElement)"
+        ],
+        "name": "CategoryCollections(IsWreathProductElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsWreathProductElement",
+            "IsWreathProductElementDefaultRep"
+        ],
+        "name": "IsWreathProductElementDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPermGroupGeneralMapping"
+        ],
+        "name": "IsPermGroupGeneralMapping",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsPermGroupGeneralMapping",
+            "IsPermGroupGeneralMappingByImages"
+        ],
+        "name": "IsPermGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsToPermGroupGeneralMappingByImages"
+        ],
+        "name": "IsToPermGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsNaturalSymmetricGroup",
+            "Tester(IsNaturalSymmetricGroup)",
+            "IsSymmetricGroup",
+            "Tester(IsSymmetricGroup)"
+        ],
+        "name": "IsNaturalSymmetricGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNaturalSymmetricGroup)"
+        ],
+        "name": "Tester(IsNaturalSymmetricGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNaturalAlternatingGroup",
+            "Tester(IsNaturalAlternatingGroup)",
+            "IsAlternatingGroup",
+            "Tester(IsAlternatingGroup)"
+        ],
+        "name": "IsNaturalAlternatingGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNaturalAlternatingGroup)"
+        ],
+        "name": "Tester(IsNaturalAlternatingGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsAlternatingGroup",
+            "Tester(IsAlternatingGroup)"
+        ],
+        "name": "IsAlternatingGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAlternatingGroup)"
+        ],
+        "name": "Tester(IsAlternatingGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSymmetricGroup",
+            "Tester(IsSymmetricGroup)"
+        ],
+        "name": "IsSymmetricGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSymmetricGroup)"
+        ],
+        "name": "Tester(IsSymmetricGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(SymmetricParentGroup)"
+        ],
+        "name": "Tester(SymmetricParentGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AlternatingSubgroup)"
+        ],
+        "name": "Tester(AlternatingSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrbitStabilizingParentGroup)"
+        ],
+        "name": "Tester(OrbitStabilizingParentGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DirectFactorsOfGroup)"
+        ],
+        "name": "Tester(DirectFactorsOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SemidirectFactorsOfGroup)"
+        ],
+        "name": "Tester(SemidirectFactorsOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DecompositionTypesOfGroup)"
+        ],
+        "name": "Tester(DecompositionTypesOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsDihedralGroup",
+            "Tester(IsDihedralGroup)"
+        ],
+        "name": "IsDihedralGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsDihedralGroup)"
+        ],
+        "name": "Tester(IsDihedralGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(DihedralGenerators)"
+        ],
+        "name": "Tester(DihedralGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuaternionGroup",
+            "Tester(IsQuaternionGroup)"
+        ],
+        "name": "IsQuaternionGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsQuaternionGroup)"
+        ],
+        "name": "Tester(IsQuaternionGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(QuaternionGenerators)"
+        ],
+        "name": "Tester(QuaternionGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuasiDihedralGroup",
+            "Tester(IsQuasiDihedralGroup)"
+        ],
+        "name": "IsQuasiDihedralGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsQuasiDihedralGroup)"
+        ],
+        "name": "Tester(IsQuasiDihedralGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(QuasiDihedralGenerators)"
+        ],
+        "name": "Tester(QuasiDihedralGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPSL",
+            "Tester(IsPSL)"
+        ],
+        "name": "IsPSL",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPSL)"
+        ],
+        "name": "Tester(IsPSL)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ParametersOfGroupViewedAsPSL)"
+        ],
+        "name": "Tester(ParametersOfGroupViewedAsPSL)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ParametersOfGroupViewedAsSL)"
+        ],
+        "name": "Tester(ParametersOfGroupViewedAsSL)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ParametersOfGroupViewedAsGL)"
+        ],
+        "name": "Tester(ParametersOfGroupViewedAsGL)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AlternatingDegree)"
+        ],
+        "name": "Tester(AlternatingDegree)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SymmetricDegree)"
+        ],
+        "name": "Tester(SymmetricDegree)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PSLDegree)"
+        ],
+        "name": "Tester(PSLDegree)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PSLUnderlyingField)"
+        ],
+        "name": "Tester(PSLUnderlyingField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SLDegree)"
+        ],
+        "name": "Tester(SLDegree)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SLUnderlyingField)"
+        ],
+        "name": "Tester(SLUnderlyingField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GLDegree)"
+        ],
+        "name": "Tester(GLDegree)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GLUnderlyingField)"
+        ],
+        "name": "Tester(GLUnderlyingField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StructureDescription)"
+        ],
+        "name": "Tester(StructureDescription)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsQuotientSystem"
+        ],
+        "name": "IsQuotientSystem",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsPQuotientSystem",
+            "Tester(IsPQuotientSystem)"
+        ],
+        "name": "IsPQuotientSystem",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPQuotientSystem)"
+        ],
+        "name": "Tester(IsPQuotientSystem)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNilpQuotientSystem",
+            "Tester(IsNilpQuotientSystem)"
+        ],
+        "name": "IsNilpQuotientSystem",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNilpQuotientSystem)"
+        ],
+        "name": "Tester(IsNilpQuotientSystem)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet"
+        ],
+        "name": "IsExternalSet",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset"
+        ],
+        "name": "IsExternalSubset",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit"
+        ],
+        "name": "IsExternalOrbit",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSetByPcgs"
+        ],
+        "name": "IsExternalSetByPcgs",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSetDefaultRep"
+        ],
+        "name": "IsExternalSetDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSetByActorsRep"
+        ],
+        "name": "IsExternalSetByActorsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(ActingDomain)"
+        ],
+        "name": "Tester(ActingDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(HomeEnumerator)"
+        ],
+        "name": "Tester(HomeEnumerator)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism"
+        ],
+        "name": "IsActionHomomorphism",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsActionHomomorphismByActors"
+        ],
+        "name": "IsActionHomomorphismByActors",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsActionHomomorphismSubset"
+        ],
+        "name": "IsActionHomomorphismSubset",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(ActionKernelExternalSet)"
+        ],
+        "name": "Tester(ActionKernelExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsActionHomomorphismByBase"
+        ],
+        "name": "IsActionHomomorphismByBase",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsConstituentHomomorphism"
+        ],
+        "name": "IsConstituentHomomorphism",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsBlocksHomomorphism"
+        ],
+        "name": "IsBlocksHomomorphism",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsLinearActionHomomorphism"
+        ],
+        "name": "IsLinearActionHomomorphism",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsProjectiveActionHomomorphism"
+        ],
+        "name": "IsProjectiveActionHomomorphism",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(LinearActionBasis)"
+        ],
+        "name": "Tester(LinearActionBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FunctionAction)"
+        ],
+        "name": "Tester(FunctionAction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StabilizerOfExternalSet)"
+        ],
+        "name": "Tester(StabilizerOfExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalRepresentativeOfExternalSet)",
+            "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
+        ],
+        "name": "Tester(CanonicalRepresentativeOfExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)",
+            "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
+        ],
+        "name": "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
+        ],
+        "name": "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ActorOfExternalSet)"
+        ],
+        "name": "Tester(ActorOfExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ActionHomomorphismAttr)"
+        ],
+        "name": "Tester(ActionHomomorphismAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SurjectiveActionHomomorphismAttr)"
+        ],
+        "name": "Tester(SurjectiveActionHomomorphismAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingExternalSet)"
+        ],
+        "name": "Tester(UnderlyingExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ExternalSet)"
+        ],
+        "name": "Tester(ExternalSet)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Orbits)"
+        ],
+        "name": "Tester(Orbits)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrbitsDomain)"
+        ],
+        "name": "Tester(OrbitsDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrbitLengths)"
+        ],
+        "name": "Tester(OrbitLengths)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrbitLengthsDomain)"
+        ],
+        "name": "Tester(OrbitLengthsDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ExternalOrbits)"
+        ],
+        "name": "Tester(ExternalOrbits)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ExternalOrbitsStabilizers)"
+        ],
+        "name": "Tester(ExternalOrbitsStabilizers)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Transitivity)"
+        ],
+        "name": "Tester(Transitivity)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BlocksAttr)"
+        ],
+        "name": "Tester(BlocksAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalBlocksAttr)"
+        ],
+        "name": "Tester(MaximalBlocksAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RepresentativesMinimalBlocksAttr)"
+        ],
+        "name": "Tester(RepresentativesMinimalBlocksAttr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Earns)"
+        ],
+        "name": "Tester(Earns)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransitive",
+            "Tester(IsTransitive)"
+        ],
+        "name": "IsTransitive",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTransitive)"
+        ],
+        "name": "Tester(IsTransitive)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPrimitive",
+            "Tester(IsPrimitive)"
+        ],
+        "name": "IsPrimitive",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPrimitive)"
+        ],
+        "name": "Tester(IsPrimitive)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPrimitiveAffine",
+            "Tester(IsPrimitiveAffine)"
+        ],
+        "name": "IsPrimitiveAffine",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPrimitiveAffine)"
+        ],
+        "name": "Tester(IsPrimitiveAffine)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSemiRegular",
+            "Tester(IsSemiRegular)"
+        ],
+        "name": "IsSemiRegular",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSemiRegular)"
+        ],
+        "name": "Tester(IsSemiRegular)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRegular",
+            "Tester(IsRegular)"
+        ],
+        "name": "IsRegular",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRegular)"
+        ],
+        "name": "Tester(IsRegular)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(RankAction)"
+        ],
+        "name": "Tester(RankAction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StabChainMutable)"
+        ],
+        "name": "Tester(StabChainMutable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StabChainImmutable)"
+        ],
+        "name": "Tester(StabChainImmutable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StabChainOptions)"
+        ],
+        "name": "Tester(StabChainOptions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BaseOfGroup)"
+        ],
+        "name": "Tester(BaseOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimalStabChain)"
+        ],
+        "name": "Tester(MinimalStabChain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsPerm",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsFiniteOrderElement",
+            "IsPermOnEnumerator"
+        ],
+        "name": "IsPermOnEnumerator",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit",
+            "IsExternalOrbitByStabilizerRep"
+        ],
+        "name": "IsExternalOrbitByStabilizerRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit",
+            "IsConjugacyClassGroupRep"
+        ],
+        "name": "IsConjugacyClassGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit",
+            "IsExternalOrbitByStabilizerRep",
+            "IsConjugacyClassGroupRep",
+            "IsConjugacyClassPermGroupRep"
+        ],
+        "name": "IsConjugacyClassPermGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsRationalClassGroupRep"
+        ],
+        "name": "IsRationalClassGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsRationalClassGroupRep",
+            "IsRationalClassPermGroupRep"
+        ],
+        "name": "IsRationalClassPermGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(DecomposedRationalClass)"
+        ],
+        "name": "Tester(DecomposedRationalClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StoredPermliftSeries)"
+        ],
+        "name": "Tester(StoredPermliftSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedAscendingChains)"
+        ],
+        "name": "Tester(ComputedAscendingChains)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsExtRSet",
+            "IsDoubleCoset"
+        ],
+        "name": "IsDoubleCoset",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LeftActingGroup)"
+        ],
+        "name": "Tester(LeftActingGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RightActingGroup)"
+        ],
+        "name": "Tester(RightActingGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RepresentativesContainedRightCosets)"
+        ],
+        "name": "Tester(RepresentativesContainedRightCosets)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit",
+            "IsRightCoset"
+        ],
+        "name": "IsRightCoset",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(NaturalHomomorphismsPool)"
+        ],
+        "name": "Tester(NaturalHomomorphismsPool)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SocleComplement)"
+        ],
+        "name": "Tester(SocleComplement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SocleDimensions)"
+        ],
+        "name": "Tester(SocleDimensions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ModuleOfExtension)"
+        ],
+        "name": "Tester(ModuleOfExtension)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OmegaAndLowerPCentralSeries)"
+        ],
+        "name": "Tester(OmegaAndLowerPCentralSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SchurCover)"
+        ],
+        "name": "Tester(SchurCover)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EpimorphismSchurCover)"
+        ],
+        "name": "Tester(EpimorphismSchurCover)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AbelianInvariantsMultiplier)"
+        ],
+        "name": "Tester(AbelianInvariantsMultiplier)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Epicentre)"
+        ],
+        "name": "Tester(Epicentre)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCentralFactor",
+            "Tester(IsCentralFactor)"
+        ],
+        "name": "IsCentralFactor",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCentralFactor)"
+        ],
+        "name": "Tester(IsCentralFactor)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit",
+            "IsConjugacyClassSubgroupsRep"
+        ],
+        "name": "IsConjugacyClassSubgroupsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit",
+            "IsExternalOrbitByStabilizerRep",
+            "IsConjugacyClassSubgroupsRep",
+            "IsConjugacyClassSubgroupsByStabilizerRep"
+        ],
+        "name": "IsConjugacyClassSubgroupsByStabilizerRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsLatticeSubgroupsRep"
+        ],
+        "name": "IsLatticeSubgroupsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(Zuppos)"
+        ],
+        "name": "Tester(Zuppos)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalSubgroupsLattice)"
+        ],
+        "name": "Tester(MaximalSubgroupsLattice)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimalSupergroupsLattice)"
+        ],
+        "name": "Tester(MinimalSupergroupsLattice)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TomDataAlmostSimpleRecognition)"
+        ],
+        "name": "Tester(TomDataAlmostSimpleRecognition)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFrattiniFree",
+            "Tester(IsFrattiniFree)"
+        ],
+        "name": "IsFrattiniFree",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFrattiniFree)"
+        ],
+        "name": "Tester(IsFrattiniFree)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsStraightLineProgram"
+        ],
+        "name": "IsStraightLineProgram",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LinesOfStraightLineProgram)"
+        ],
+        "name": "Tester(LinesOfStraightLineProgram)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrInputsOfStraightLineProgram)"
+        ],
+        "name": "Tester(NrInputsOfStraightLineProgram)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "StraightLineProgramElmRankFilter"
+        ],
+        "name": "StraightLineProgramElmRankFilter",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "StraightLineProgramElmRankFilter",
+            "IsStraightLineProgElm"
+        ],
+        "name": "IsStraightLineProgElm",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(StraightLineProgElmType)"
+        ],
+        "name": "Tester(StraightLineProgElmType)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SlotUsagePattern)"
+        ],
+        "name": "Tester(SlotUsagePattern)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LargestNrSlots)"
+        ],
+        "name": "Tester(LargestNrSlots)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsObjWithMemoryRankFilter"
+        ],
+        "name": "IsObjWithMemoryRankFilter",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsObjWithMemoryRankFilter",
+            "IsObjWithMemory"
+        ],
+        "name": "IsObjWithMemory",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(TypeOfObjWithMemory)"
+        ],
+        "name": "Tester(TypeOfObjWithMemory)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsSubgroupFgGroup"
+        ],
+        "name": "IsSubgroupFgGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsSubgroupFgGroup",
+            "IsSubgroupFpGroup"
+        ],
+        "name": "IsSubgroupFpGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsElementOfFpGroup"
+        ],
+        "name": "IsElementOfFpGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsElementOfFpGroup)"
+        ],
+        "name": "CategoryCollections(IsElementOfFpGroup)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsElementOfFpGroup)"
+        ],
+        "name": "CategoryFamily(IsElementOfFpGroup)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(FpElmEqualityMethod)"
+        ],
+        "name": "Tester(FpElmEqualityMethod)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FpElmComparisonMethod)"
+        ],
+        "name": "Tester(FpElmComparisonMethod)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FpElementNFFunction)"
+        ],
+        "name": "Tester(FpElementNFFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CosetTableInWholeGroup)"
+        ],
+        "name": "Tester(CosetTableInWholeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CosetTableNormalClosureInWholeGroup)"
+        ],
+        "name": "Tester(CosetTableNormalClosureInWholeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsSubgroupFgGroup",
+            "IsSubgroupFpGroup",
+            "IsSubgroupOfWholeGroupByQuotientRep"
+        ],
+        "name": "IsSubgroupOfWholeGroupByQuotientRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(AsSubgroupOfWholeGroupByQuotient)"
+        ],
+        "name": "Tester(AsSubgroupOfWholeGroupByQuotient)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeGeneratorsOfFpGroup)"
+        ],
+        "name": "Tester(FreeGeneratorsOfFpGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RelatorsOfFpGroup)"
+        ],
+        "name": "Tester(RelatorsOfFpGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeGroupOfFpGroup)"
+        ],
+        "name": "Tester(FreeGroupOfFpGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndicesInvolutaryGenerators)"
+        ],
+        "name": "Tester(IndicesInvolutaryGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StoredExcludedOrders)"
+        ],
+        "name": "Tester(StoredExcludedOrders)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FPFaithHom)"
+        ],
+        "name": "Tester(FPFaithHom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentedCosetTableMtcInWholeGroup)"
+        ],
+        "name": "Tester(AugmentedCosetTableMtcInWholeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentedCosetTableRrsInWholeGroup)"
+        ],
+        "name": "Tester(AugmentedCosetTableRrsInWholeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentedCosetTableNormalClosureInWholeGroup)"
+        ],
+        "name": "Tester(AugmentedCosetTableNormalClosureInWholeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsPresentation"
+        ],
+        "name": "IsPresentation",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(PrimaryGeneratorWords)"
+        ],
+        "name": "Tester(PrimaryGeneratorWords)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TietzeOrigin)"
+        ],
+        "name": "Tester(TietzeOrigin)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TzOptions)"
+        ],
+        "name": "Tester(TzOptions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "Extrarankfilter"
+        ],
+        "name": "Extrarankfilter",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "Extrarankfilter",
+            "IsFromFpGroupGeneralMapping"
+        ],
+        "name": "IsFromFpGroupGeneralMapping",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "Extrarankfilter",
+            "IsFromFpGroupGeneralMapping",
+            "IsFromFpGroupGeneralMappingByImages"
+        ],
+        "name": "IsFromFpGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "Extrarankfilter",
+            "IsFromFpGroupGeneralMapping",
+            "IsFromFpGroupGeneralMappingByImages",
+            "IsFromFpGroupStdGensGeneralMappingByImages"
+        ],
+        "name": "IsFromFpGroupStdGensGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsToFpGroupGeneralMappingByImages"
+        ],
+        "name": "IsToFpGroupGeneralMappingByImages",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsWordDecompHomomorphism",
+            "Tester(IsWordDecompHomomorphism)"
+        ],
+        "name": "IsWordDecompHomomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsWordDecompHomomorphism)"
+        ],
+        "name": "Tester(IsWordDecompHomomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(CosetTableFpHom)"
+        ],
+        "name": "Tester(CosetTableFpHom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismSimplifiedFpGroup)"
+        ],
+        "name": "Tester(IsomorphismSimplifiedFpGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EpimorphismFromFreeGroup)"
+        ],
+        "name": "Tester(EpimorphismFromFreeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsCanonicalBasisIntegersRep"
+        ],
+        "name": "IsCanonicalBasisIntegersRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(NiceMonomorphism)"
+        ],
+        "name": "Tester(NiceMonomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsNiceMonomorphism"
+        ],
+        "name": "IsNiceMonomorphism",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "IsCanonicalNiceMonomorphism",
+            "Tester(IsCanonicalNiceMonomorphism)"
+        ],
+        "name": "IsCanonicalNiceMonomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCanonicalNiceMonomorphism)"
+        ],
+        "name": "Tester(IsCanonicalNiceMonomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalNiceMonomorphism)"
+        ],
+        "name": "Tester(CanonicalNiceMonomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NiceObject)"
+        ],
+        "name": "Tester(NiceObject)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CanEasilyTestMembership",
+            "IsHandledByNiceMonomorphism",
+            "Tester(IsHandledByNiceMonomorphism)"
+        ],
+        "name": "IsHandledByNiceMonomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsHandledByNiceMonomorphism)"
+        ],
+        "name": "Tester(IsHandledByNiceMonomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(SeedFaithfulAction)"
+        ],
+        "name": "Tester(SeedFaithfulAction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AutomorphismGroup)"
+        ],
+        "name": "Tester(AutomorphismGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfAutomorphisms",
+            "Tester(IsGroupOfAutomorphisms)"
+        ],
+        "name": "IsGroupOfAutomorphisms",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupOfAutomorphisms)"
+        ],
+        "name": "Tester(IsGroupOfAutomorphisms)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFinite",
+            "Tester(IsFinite)",
+            "CanEasilyTestMembership",
+            "IsHandledByNiceMonomorphism",
+            "Tester(IsHandledByNiceMonomorphism)",
+            "IsGroupOfAutomorphisms",
+            "Tester(IsGroupOfAutomorphisms)",
+            "IsGroupOfAutomorphismsFiniteGroup",
+            "Tester(IsGroupOfAutomorphismsFiniteGroup)"
+        ],
+        "name": "IsGroupOfAutomorphismsFiniteGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupOfAutomorphismsFiniteGroup)"
+        ],
+        "name": "Tester(IsGroupOfAutomorphismsFiniteGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(AutomorphismDomain)"
+        ],
+        "name": "Tester(AutomorphismDomain)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfAutomorphisms",
+            "Tester(IsGroupOfAutomorphisms)",
+            "IsAutomorphismGroup",
+            "Tester(IsAutomorphismGroup)"
+        ],
+        "name": "IsAutomorphismGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAutomorphismGroup)"
+        ],
+        "name": "Tester(IsAutomorphismGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(InnerAutomorphismsAutomorphismGroup)"
+        ],
+        "name": "Tester(InnerAutomorphismsAutomorphismGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DefaultFieldOfMatrixGroup)"
+        ],
+        "name": "Tester(DefaultFieldOfMatrixGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DimensionOfMatrixGroup)"
+        ],
+        "name": "Tester(DimensionOfMatrixGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FieldOfMatrixGroup)"
+        ],
+        "name": "Tester(FieldOfMatrixGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TransposedMatrixGroup)"
+        ],
+        "name": "Tester(TransposedMatrixGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralLinearGroup",
+            "Tester(IsGeneralLinearGroup)"
+        ],
+        "name": "IsGeneralLinearGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGeneralLinearGroup)"
+        ],
+        "name": "Tester(IsGeneralLinearGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsGeneralLinearGroup",
+            "Tester(IsGeneralLinearGroup)",
+            "IsNaturalGL",
+            "Tester(IsNaturalGL)"
+        ],
+        "name": "IsNaturalGL",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNaturalGL)"
+        ],
+        "name": "Tester(IsNaturalGL)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSpecialLinearGroup",
+            "Tester(IsSpecialLinearGroup)"
+        ],
+        "name": "IsSpecialLinearGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSpecialLinearGroup)"
+        ],
+        "name": "Tester(IsSpecialLinearGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSpecialLinearGroup",
+            "Tester(IsSpecialLinearGroup)",
+            "IsNaturalSL",
+            "Tester(IsNaturalSL)",
+            "IsSubgroupSL",
+            "Tester(IsSubgroupSL)"
+        ],
+        "name": "IsNaturalSL",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNaturalSL)"
+        ],
+        "name": "Tester(IsNaturalSL)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSubgroupSL",
+            "Tester(IsSubgroupSL)"
+        ],
+        "name": "IsSubgroupSL",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSubgroupSL)"
+        ],
+        "name": "Tester(IsSubgroupSL)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(InvariantBilinearForm)"
+        ],
+        "name": "Tester(InvariantBilinearForm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFullSubgroupGLorSLRespectingBilinearForm",
+            "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"
+        ],
+        "name": "IsFullSubgroupGLorSLRespectingBilinearForm",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"
+        ],
+        "name": "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(InvariantSesquilinearForm)"
+        ],
+        "name": "Tester(InvariantSesquilinearForm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFullSubgroupGLorSLRespectingSesquilinearForm",
+            "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"
+        ],
+        "name": "IsFullSubgroupGLorSLRespectingSesquilinearForm",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"
+        ],
+        "name": "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(InvariantQuadraticForm)"
+        ],
+        "name": "Tester(InvariantQuadraticForm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFullSubgroupGLorSLRespectingQuadraticForm",
+            "Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"
+        ],
+        "name": "IsFullSubgroupGLorSLRespectingQuadraticForm",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"
+        ],
+        "name": "Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsFiniteOrderElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsCompletelySimpleSemigroup",
+            "Tester(IsCompletelySimpleSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsFinitelyGeneratedGroup",
+            "Tester(IsFinitelyGeneratedGroup)",
+            "IsSubsetLocallyFiniteGroup",
+            "Tester(IsSubsetLocallyFiniteGroup)",
+            "CanComputeFittingFree",
+            "IsNilpotentByFinite",
+            "Tester(IsNilpotentByFinite)"
+        ],
+        "name": "CanComputeFittingFree",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(FittingFreeLiftSetup)"
+        ],
+        "name": "Tester(FittingFreeLiftSetup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RecogDecompinfoHomomorphism)"
+        ],
+        "name": "Tester(RecogDecompinfoHomomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DirectFactorsFittingFreeSocle)"
+        ],
+        "name": "Tester(DirectFactorsFittingFreeSocle)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ChiefSeriesTF)"
+        ],
+        "name": "Tester(ChiefSeriesTF)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRationalMatrixGroup",
+            "Tester(IsRationalMatrixGroup)"
+        ],
+        "name": "IsRationalMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRationalMatrixGroup)"
+        ],
+        "name": "Tester(IsRationalMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsRationalMatrixGroup",
+            "Tester(IsRationalMatrixGroup)",
+            "IsIntegerMatrixGroup",
+            "Tester(IsIntegerMatrixGroup)"
+        ],
+        "name": "IsIntegerMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIntegerMatrixGroup)"
+        ],
+        "name": "Tester(IsIntegerMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ZClassRepsQClass)"
+        ],
+        "name": "Tester(ZClassRepsQClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalizerInGLnZ)"
+        ],
+        "name": "Tester(NormalizerInGLnZ)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CentralizerInGLnZ)"
+        ],
+        "name": "Tester(CentralizerInGLnZ)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBravaisGroup",
+            "Tester(IsBravaisGroup)"
+        ],
+        "name": "IsBravaisGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBravaisGroup)"
+        ],
+        "name": "Tester(IsBravaisGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(BravaisGroup)"
+        ],
+        "name": "Tester(BravaisGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BravaisSubgroups)"
+        ],
+        "name": "Tester(BravaisSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BravaisSupergroups)"
+        ],
+        "name": "Tester(BravaisSupergroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalizerInGLnZBravaisGroup)"
+        ],
+        "name": "Tester(NormalizerInGLnZBravaisGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InvariantLattice)"
+        ],
+        "name": "Tester(InvariantLattice)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsPerfectLibraryGroup"
+        ],
+        "name": "IsPerfectLibraryGroup",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(PerfectIdentification)"
+        ],
+        "name": "Tester(PerfectIdentification)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DataAboutSimpleGroup)"
+        ],
+        "name": "Tester(DataAboutSimpleGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsImfMatrixGroup"
+        ],
+        "name": "IsImfMatrixGroup",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(ImfRecord)"
+        ],
+        "name": "Tester(ImfRecord)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsOrdering"
+        ],
+        "name": "IsOrdering",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(OrderingsFamily)"
+        ],
+        "name": "Tester(OrderingsFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsWellFoundedOrdering",
+            "Tester(IsWellFoundedOrdering)"
+        ],
+        "name": "IsWellFoundedOrdering",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsWellFoundedOrdering)"
+        ],
+        "name": "Tester(IsWellFoundedOrdering)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsTotalOrdering",
+            "Tester(IsTotalOrdering)"
+        ],
+        "name": "IsTotalOrdering",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTotalOrdering)"
+        ],
+        "name": "Tester(IsTotalOrdering)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(FamilyForOrdering)"
+        ],
+        "name": "Tester(FamilyForOrdering)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LessThanFunction)"
+        ],
+        "name": "Tester(LessThanFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LessThanOrEqualFunction)"
+        ],
+        "name": "Tester(LessThanOrEqualFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrderingOnFamilyOfAssocWords",
+            "Tester(IsOrderingOnFamilyOfAssocWords)"
+        ],
+        "name": "IsOrderingOnFamilyOfAssocWords",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsOrderingOnFamilyOfAssocWords)"
+        ],
+        "name": "Tester(IsOrderingOnFamilyOfAssocWords)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(LetterRepWordsLessFunc)"
+        ],
+        "name": "Tester(LetterRepWordsLessFunc)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTranslationInvariantOrdering",
+            "Tester(IsTranslationInvariantOrdering)"
+        ],
+        "name": "IsTranslationInvariantOrdering",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTranslationInvariantOrdering)"
+        ],
+        "name": "Tester(IsTranslationInvariantOrdering)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(OrderingOnGenerators)"
+        ],
+        "name": "Tester(OrderingOnGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsShortLexOrdering",
+            "Tester(IsShortLexOrdering)"
+        ],
+        "name": "IsShortLexOrdering",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsShortLexOrdering)"
+        ],
+        "name": "Tester(IsShortLexOrdering)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(WeightOfGenerators)"
+        ],
+        "name": "Tester(WeightOfGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsWeightLexOrdering",
+            "Tester(IsWeightLexOrdering)"
+        ],
+        "name": "IsWeightLexOrdering",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsWeightLexOrdering)"
+        ],
+        "name": "Tester(IsWeightLexOrdering)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBasicWreathProductOrdering",
+            "Tester(IsBasicWreathProductOrdering)"
+        ],
+        "name": "IsBasicWreathProductOrdering",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBasicWreathProductOrdering)"
+        ],
+        "name": "Tester(IsBasicWreathProductOrdering)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsWreathProductOrdering",
+            "Tester(IsWreathProductOrdering)"
+        ],
+        "name": "IsWreathProductOrdering",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsWreathProductOrdering)"
+        ],
+        "name": "Tester(IsWreathProductOrdering)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(LevelsOfGenerators)"
+        ],
+        "name": "Tester(LevelsOfGenerators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LargestImageOfMovedPoint)"
+        ],
+        "name": "Tester(LargestImageOfMovedPoint)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SmallestImageOfMovedPoint)"
+        ],
+        "name": "Tester(SmallestImageOfMovedPoint)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RankOfTransformation)"
+        ],
+        "name": "Tester(RankOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsPermutation)"
+        ],
+        "name": "Tester(AsPermutation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsTransformation)"
+        ],
+        "name": "Tester(AsTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PermutationOfImage)"
+        ],
+        "name": "Tester(PermutationOfImage)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOfTransformationCollection)"
+        ],
+        "name": "Tester(DegreeOfTransformationCollection)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FlatKernelOfTransformation)"
+        ],
+        "name": "Tester(FlatKernelOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ImageSetOfTransformation)"
+        ],
+        "name": "Tester(ImageSetOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndexPeriodOfTransformation)"
+        ],
+        "name": "Tester(IndexPeriodOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(KernelOfTransformation)"
+        ],
+        "name": "Tester(KernelOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SmallestIdempotentPower)"
+        ],
+        "name": "Tester(SmallestIdempotentPower)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComponentRepsOfTransformation)"
+        ],
+        "name": "Tester(ComponentRepsOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrComponentsOfTransformation)"
+        ],
+        "name": "Tester(NrComponentsOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComponentsOfTransformation)"
+        ],
+        "name": "Tester(ComponentsOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CyclesOfTransformation)"
+        ],
+        "name": "Tester(CyclesOfTransformation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LeftOne)"
+        ],
+        "name": "Tester(LeftOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RightOne)"
+        ],
+        "name": "Tester(RightOne)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DomainOfPartialPerm)"
+        ],
+        "name": "Tester(DomainOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ImageListOfPartialPerm)"
+        ],
+        "name": "Tester(ImageListOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ImageSetOfPartialPerm)"
+        ],
+        "name": "Tester(ImageSetOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IndexPeriodOfPartialPerm)"
+        ],
+        "name": "Tester(IndexPeriodOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComponentRepsOfPartialPerm)"
+        ],
+        "name": "Tester(ComponentRepsOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrComponentsOfPartialPerm)"
+        ],
+        "name": "Tester(NrComponentsOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComponentsOfPartialPerm)"
+        ],
+        "name": "Tester(ComponentsOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FixedPointsOfPartialPerm)"
+        ],
+        "name": "Tester(FixedPointsOfPartialPerm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrFixedPoints)"
+        ],
+        "name": "Tester(NrFixedPoints)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOfPartialPermCollection)"
+        ],
+        "name": "Tester(DegreeOfPartialPermCollection)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CodegreeOfPartialPermCollection)"
+        ],
+        "name": "Tester(CodegreeOfPartialPermCollection)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RankOfPartialPermCollection)"
+        ],
+        "name": "Tester(RankOfPartialPermCollection)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DomainOfPartialPermCollection)"
+        ],
+        "name": "Tester(DomainOfPartialPermCollection)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ImageOfPartialPermCollection)"
+        ],
+        "name": "Tester(ImageOfPartialPermCollection)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TransformationRepresentation)"
+        ],
+        "name": "Tester(TransformationRepresentation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsElementOfFpSemigroup"
+        ],
+        "name": "IsElementOfFpSemigroup",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsElementOfFpSemigroup)"
+        ],
+        "name": "CategoryCollections(IsElementOfFpSemigroup)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsElementOfFpSemigroup)"
+        ],
+        "name": "CategoryFamily(IsElementOfFpSemigroup)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(FreeGeneratorsOfFpSemigroup)"
+        ],
+        "name": "Tester(FreeGeneratorsOfFpSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeSemigroupOfFpSemigroup)"
+        ],
+        "name": "Tester(FreeSemigroupOfFpSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RelationsOfFpSemigroup)"
+        ],
+        "name": "Tester(RelationsOfFpSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismFpSemigroup)"
+        ],
+        "name": "Tester(IsomorphismFpSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsAssociativeElement",
+            "IsElementOfFpMonoid"
+        ],
+        "name": "IsElementOfFpMonoid",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsElementOfFpMonoid)"
+        ],
+        "name": "CategoryCollections(IsElementOfFpMonoid)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsElementOfFpMonoid)"
+        ],
+        "name": "CategoryFamily(IsElementOfFpMonoid)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(FreeGeneratorsOfFpMonoid)"
+        ],
+        "name": "Tester(FreeGeneratorsOfFpMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeMonoidOfFpMonoid)"
+        ],
+        "name": "Tester(FreeMonoidOfFpMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RelationsOfFpMonoid)"
+        ],
+        "name": "Tester(RelationsOfFpMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismFpMonoid)"
+        ],
+        "name": "Tester(IsomorphismFpMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ReducedConfluentRewritingSystem)"
+        ],
+        "name": "Tester(ReducedConfluentRewritingSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeMonoidOfRewritingSystem)"
+        ],
+        "name": "Tester(FreeMonoidOfRewritingSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FamilyForRewritingSystem)"
+        ],
+        "name": "Tester(FamilyForRewritingSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeSemigroupOfRewritingSystem)"
+        ],
+        "name": "Tester(FreeSemigroupOfRewritingSystem)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsRewritingSystem",
+            "IsKnuthBendixRewritingSystem"
+        ],
+        "name": "IsKnuthBendixRewritingSystem",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(TzRules)"
+        ],
+        "name": "Tester(TzRules)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CosetTableOfFpSemigroup)"
+        ],
+        "name": "Tester(CosetTableOfFpSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsAssociativeElement",
+            "IsMonoidByAdjoiningIdentityElt"
+        ],
+        "name": "IsMonoidByAdjoiningIdentityElt",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsMonoidByAdjoiningIdentity"
+        ],
+        "name": "IsMonoidByAdjoiningIdentity",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(AdjoinedIdentityFamily)"
+        ],
+        "name": "Tester(AdjoinedIdentityFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingSemigroupFamily)"
+        ],
+        "name": "Tester(UnderlyingSemigroupFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AdjoinedIdentityDefaultType)"
+        ],
+        "name": "Tester(AdjoinedIdentityDefaultType)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsMonoidByAdjoiningIdentityEltRep"
+        ],
+        "name": "IsMonoidByAdjoiningIdentityEltRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(MonoidByAdjoiningIdentity)"
+        ],
+        "name": "Tester(MonoidByAdjoiningIdentity)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)"
+        ],
+        "name": "Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MonoidByAdjoiningIdentityElt)"
+        ],
+        "name": "Tester(MonoidByAdjoiningIdentityElt)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)"
+        ],
+        "name": "Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsGreensRelation"
+        ],
+        "name": "IsGreensRelation",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsGreensRelation",
+            "IsGreensRRelation"
+        ],
+        "name": "IsGreensRRelation",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsGreensRelation",
+            "IsGreensLRelation"
+        ],
+        "name": "IsGreensLRelation",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsGreensRelation",
+            "IsGreensJRelation"
+        ],
+        "name": "IsGreensJRelation",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsGreensRelation",
+            "IsGreensHRelation"
+        ],
+        "name": "IsGreensHRelation",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsEndoGeneralMapping",
+            "Tester(IsEndoGeneralMapping)",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsReflexiveBinaryRelation",
+            "Tester(IsReflexiveBinaryRelation)",
+            "IsSymmetricBinaryRelation",
+            "Tester(IsSymmetricBinaryRelation)",
+            "IsTransitiveBinaryRelation",
+            "Tester(IsTransitiveBinaryRelation)",
+            "IsPreOrderBinaryRelation",
+            "Tester(IsPreOrderBinaryRelation)",
+            "IsEquivalenceRelation",
+            "Tester(IsEquivalenceRelation)",
+            "IsGreensRelation",
+            "IsGreensDRelation"
+        ],
+        "name": "IsGreensDRelation",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsFiniteSemigroupGreensRelation",
+            "Tester(IsFiniteSemigroupGreensRelation)"
+        ],
+        "name": "IsFiniteSemigroupGreensRelation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFiniteSemigroupGreensRelation)"
+        ],
+        "name": "Tester(IsFiniteSemigroupGreensRelation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GreensRRelation)"
+        ],
+        "name": "Tester(GreensRRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensLRelation)"
+        ],
+        "name": "Tester(GreensLRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensJRelation)"
+        ],
+        "name": "Tester(GreensJRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensDRelation)"
+        ],
+        "name": "Tester(GreensDRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensHRelation)"
+        ],
+        "name": "Tester(GreensHRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AssociatedConcreteSemigroup)"
+        ],
+        "name": "Tester(AssociatedConcreteSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AssociatedFpSemigroup)"
+        ],
+        "name": "Tester(AssociatedFpSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass",
+            "IsGreensClass"
+        ],
+        "name": "IsGreensClass",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass",
+            "IsGreensClass",
+            "IsGreensRClass"
+        ],
+        "name": "IsGreensRClass",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass",
+            "IsGreensClass",
+            "IsGreensLClass"
+        ],
+        "name": "IsGreensLClass",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass",
+            "IsGreensClass",
+            "IsGreensJClass"
+        ],
+        "name": "IsGreensJClass",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass",
+            "IsGreensClass",
+            "IsGreensHClass"
+        ],
+        "name": "IsGreensHClass",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsEquivalenceClass",
+            "IsGreensClass",
+            "IsGreensDClass"
+        ],
+        "name": "IsGreensDClass",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(GreensRClasses)"
+        ],
+        "name": "Tester(GreensRClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensLClasses)"
+        ],
+        "name": "Tester(GreensLClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensJClasses)"
+        ],
+        "name": "Tester(GreensJClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensDClasses)"
+        ],
+        "name": "Tester(GreensDClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GreensHClasses)"
+        ],
+        "name": "Tester(GreensHClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RClassOfHClass)"
+        ],
+        "name": "Tester(RClassOfHClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LClassOfHClass)"
+        ],
+        "name": "Tester(LClassOfHClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DClassOfHClass)"
+        ],
+        "name": "Tester(DClassOfHClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DClassOfLClass)"
+        ],
+        "name": "Tester(DClassOfLClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DClassOfRClass)"
+        ],
+        "name": "Tester(DClassOfRClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GroupHClassOfGreensDClass)"
+        ],
+        "name": "Tester(GroupHClassOfGreensDClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRegularDClass",
+            "Tester(IsRegularDClass)"
+        ],
+        "name": "IsRegularDClass",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRegularDClass)"
+        ],
+        "name": "Tester(IsRegularDClass)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsGroupHClass",
+            "Tester(IsGroupHClass)"
+        ],
+        "name": "IsGroupHClass",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupHClass)"
+        ],
+        "name": "Tester(IsGroupHClass)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(EggBoxOfDClass)"
+        ],
+        "name": "Tester(EggBoxOfDClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InternalRepGreensRelation)"
+        ],
+        "name": "Tester(InternalRepGreensRelation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CanonicalGreensClass)"
+        ],
+        "name": "Tester(CanonicalGreensClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "IsSemigroupGeneralMappingRep"
+        ],
+        "name": "IsSemigroupGeneralMappingRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsSemigroupHomomorphismByImagesRep"
+        ],
+        "name": "IsSemigroupHomomorphismByImagesRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsFpSemigpReducedElt",
+            "Tester(IsFpSemigpReducedElt)"
+        ],
+        "name": "IsFpSemigpReducedElt",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFpSemigpReducedElt)"
+        ],
+        "name": "Tester(IsFpSemigpReducedElt)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFpMonoidReducedElt",
+            "Tester(IsFpMonoidReducedElt)"
+        ],
+        "name": "IsFpMonoidReducedElt",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFpMonoidReducedElt)"
+        ],
+        "name": "Tester(IsFpMonoidReducedElt)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFullTransformationSemigroup",
+            "Tester(IsFullTransformationSemigroup)"
+        ],
+        "name": "IsFullTransformationSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFullTransformationSemigroup)"
+        ],
+        "name": "Tester(IsFullTransformationSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOfTransformationSemigroup)"
+        ],
+        "name": "Tester(DegreeOfTransformationSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismTransformationSemigroup)"
+        ],
+        "name": "Tester(IsomorphismTransformationSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismTransformationMonoid)"
+        ],
+        "name": "Tester(IsomorphismTransformationMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AntiIsomorphismTransformationSemigroup)"
+        ],
+        "name": "Tester(AntiIsomorphismTransformationSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsReesMatrixSemigroupElement"
+        ],
+        "name": "IsReesMatrixSemigroupElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsReesZeroMatrixSemigroupElement"
+        ],
+        "name": "IsReesZeroMatrixSemigroupElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsReesMatrixSemigroupElement)"
+        ],
+        "name": "CategoryCollections(IsReesMatrixSemigroupElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+        ],
+        "name": "CategoryCollections(IsReesZeroMatrixSemigroupElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "IsReesMatrixSemigroup",
+            "Tester(IsReesMatrixSemigroup)"
+        ],
+        "name": "IsReesMatrixSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsReesMatrixSemigroup)"
+        ],
+        "name": "Tester(IsReesMatrixSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsReesZeroMatrixSemigroup",
+            "Tester(IsReesZeroMatrixSemigroup)"
+        ],
+        "name": "IsReesZeroMatrixSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsReesZeroMatrixSemigroup)"
+        ],
+        "name": "Tester(IsReesZeroMatrixSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(Matrix)"
+        ],
+        "name": "Tester(Matrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Rows)"
+        ],
+        "name": "Tester(Rows)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Columns)"
+        ],
+        "name": "Tester(Columns)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingSemigroup)"
+        ],
+        "name": "Tester(UnderlyingSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AssociatedReesMatrixSemigroupOfDClass)"
+        ],
+        "name": "Tester(AssociatedReesMatrixSemigroupOfDClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismReesMatrixSemigroup)"
+        ],
+        "name": "Tester(IsomorphismReesMatrixSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismReesZeroMatrixSemigroup)"
+        ],
+        "name": "Tester(IsomorphismReesZeroMatrixSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ReesMatrixSemigroupOfFamily)"
+        ],
+        "name": "Tester(ReesMatrixSemigroupOfFamily)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TypeReesMatrixSemigroupElements)"
+        ],
+        "name": "Tester(TypeReesMatrixSemigroupElements)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "IsQuotientSemigroup"
+        ],
+        "name": "IsQuotientSemigroup",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(QuotientSemigroupPreimage)"
+        ],
+        "name": "Tester(QuotientSemigroupPreimage)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(QuotientSemigroupCongruence)"
+        ],
+        "name": "Tester(QuotientSemigroupCongruence)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(QuotientSemigroupHomomorphism)"
+        ],
+        "name": "Tester(QuotientSemigroupHomomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOfPartialPermSemigroup)"
+        ],
+        "name": "Tester(DegreeOfPartialPermSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CodegreeOfPartialPermSemigroup)"
+        ],
+        "name": "Tester(CodegreeOfPartialPermSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RankOfPartialPermSemigroup)"
+        ],
+        "name": "Tester(RankOfPartialPermSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsSymmetricInverseSemigroup",
+            "Tester(IsSymmetricInverseSemigroup)"
+        ],
+        "name": "IsSymmetricInverseSemigroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSymmetricInverseSemigroup)"
+        ],
+        "name": "Tester(IsSymmetricInverseSemigroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismPartialPermSemigroup)"
+        ],
+        "name": "Tester(IsomorphismPartialPermSemigroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismPartialPermMonoid)"
+        ],
+        "name": "Tester(IsomorphismPartialPermMonoid)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsNearlyCharacterTable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsNearlyCharacterTable",
+            "IsCharacterTable"
+        ],
+        "name": "IsCharacterTable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsNearlyCharacterTable",
+            "IsCharacterTable",
+            "IsOrdinaryTable"
+        ],
+        "name": "IsOrdinaryTable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsNearlyCharacterTable",
+            "IsCharacterTable",
+            "IsBrauerTable"
+        ],
+        "name": "IsBrauerTable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsNearlyCharacterTable",
+            "IsCharacterTableInProgress"
+        ],
+        "name": "IsCharacterTableInProgress",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingGroup)"
+        ],
+        "name": "Tester(UnderlyingGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IdentificationOfConjugacyClasses)"
+        ],
+        "name": "Tester(IdentificationOfConjugacyClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CharacterDegrees)"
+        ],
+        "name": "Tester(CharacterDegrees)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Irr)"
+        ],
+        "name": "Tester(Irr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LinearCharacters)"
+        ],
+        "name": "Tester(LinearCharacters)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IBr)"
+        ],
+        "name": "Tester(IBr)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrdinaryCharacterTable)"
+        ],
+        "name": "Tester(OrdinaryCharacterTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAlmostSimpleCharacterTable",
+            "Tester(IsAlmostSimpleCharacterTable)"
+        ],
+        "name": "IsAlmostSimpleCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAlmostSimpleCharacterTable)"
+        ],
+        "name": "Tester(IsAlmostSimpleCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMonomialCharacterTable",
+            "Tester(IsMonomialCharacterTable)"
+        ],
+        "name": "IsMonomialCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMonomialCharacterTable)"
+        ],
+        "name": "Tester(IsMonomialCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNilpotentCharacterTable",
+            "Tester(IsNilpotentCharacterTable)"
+        ],
+        "name": "IsNilpotentCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNilpotentCharacterTable)"
+        ],
+        "name": "Tester(IsNilpotentCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPerfectCharacterTable",
+            "Tester(IsPerfectCharacterTable)"
+        ],
+        "name": "IsPerfectCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPerfectCharacterTable)"
+        ],
+        "name": "Tester(IsPerfectCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSimpleCharacterTable",
+            "Tester(IsSimpleCharacterTable)"
+        ],
+        "name": "IsSimpleCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSimpleCharacterTable)"
+        ],
+        "name": "Tester(IsSimpleCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSolvableCharacterTable",
+            "Tester(IsSolvableCharacterTable)"
+        ],
+        "name": "IsSolvableCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSolvableCharacterTable)"
+        ],
+        "name": "Tester(IsSolvableCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSporadicSimpleCharacterTable",
+            "Tester(IsSporadicSimpleCharacterTable)"
+        ],
+        "name": "IsSporadicSimpleCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSporadicSimpleCharacterTable)"
+        ],
+        "name": "Tester(IsSporadicSimpleCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSupersolvableCharacterTable",
+            "Tester(IsSupersolvableCharacterTable)"
+        ],
+        "name": "IsSupersolvableCharacterTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSupersolvableCharacterTable)"
+        ],
+        "name": "Tester(IsSupersolvableCharacterTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(OrdersClassRepresentatives)"
+        ],
+        "name": "Tester(OrdersClassRepresentatives)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SizesCentralizers)"
+        ],
+        "name": "Tester(SizesCentralizers)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SizesConjugacyClasses)"
+        ],
+        "name": "Tester(SizesConjugacyClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AutomorphismsOfTable)"
+        ],
+        "name": "Tester(AutomorphismsOfTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingCharacteristic)"
+        ],
+        "name": "Tester(UnderlyingCharacteristic)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassNames)"
+        ],
+        "name": "Tester(ClassNames)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CharacterNames)"
+        ],
+        "name": "Tester(CharacterNames)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassParameters)"
+        ],
+        "name": "Tester(ClassParameters)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CharacterParameters)"
+        ],
+        "name": "Tester(CharacterParameters)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Identifier)"
+        ],
+        "name": "Tester(Identifier)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InverseClasses)"
+        ],
+        "name": "Tester(InverseClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RealClasses)"
+        ],
+        "name": "Tester(RealClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassRoots)"
+        ],
+        "name": "Tester(ClassRoots)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfNormalSubgroups)"
+        ],
+        "name": "Tester(ClassPositionsOfNormalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfMaximalNormalSubgroups)"
+        ],
+        "name": "Tester(ClassPositionsOfMaximalNormalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfMinimalNormalSubgroups)"
+        ],
+        "name": "Tester(ClassPositionsOfMinimalNormalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfCentre)"
+        ],
+        "name": "Tester(ClassPositionsOfCentre)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfDirectProductDecompositions)"
+        ],
+        "name": "Tester(ClassPositionsOfDirectProductDecompositions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfDerivedSubgroup)"
+        ],
+        "name": "Tester(ClassPositionsOfDerivedSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfElementaryAbelianSeries)"
+        ],
+        "name": "Tester(ClassPositionsOfElementaryAbelianSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfFittingSubgroup)"
+        ],
+        "name": "Tester(ClassPositionsOfFittingSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfSolvableRadical)"
+        ],
+        "name": "Tester(ClassPositionsOfSolvableRadical)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfLowerCentralSeries)"
+        ],
+        "name": "Tester(ClassPositionsOfLowerCentralSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfUpperCentralSeries)"
+        ],
+        "name": "Tester(ClassPositionsOfUpperCentralSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfSolvableResiduum)"
+        ],
+        "name": "Tester(ClassPositionsOfSolvableResiduum)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfSupersolvableResiduum)"
+        ],
+        "name": "Tester(ClassPositionsOfSupersolvableResiduum)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedPrimeBlockss)"
+        ],
+        "name": "Tester(ComputedPrimeBlockss)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BlocksInfo)"
+        ],
+        "name": "Tester(BlocksInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DecompositionMatrix)"
+        ],
+        "name": "Tester(DecompositionMatrix)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedIsPSolvableCharacterTables)"
+        ],
+        "name": "Tester(ComputedIsPSolvableCharacterTables)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedIndicators)"
+        ],
+        "name": "Tester(ComputedIndicators)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedBrauerTables)"
+        ],
+        "name": "Tester(ComputedBrauerTables)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DisplayOptions)"
+        ],
+        "name": "Tester(DisplayOptions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FactorsOfDirectProduct)"
+        ],
+        "name": "Tester(FactorsOfDirectProduct)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CharacterTableIsoclinic)"
+        ],
+        "name": "Tester(CharacterTableIsoclinic)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SourceOfIsoclinicTable)"
+        ],
+        "name": "Tester(SourceOfIsoclinicTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPermutation)"
+        ],
+        "name": "Tester(ClassPermutation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalSubgroupClassesInfo)"
+        ],
+        "name": "Tester(NormalSubgroupClassesInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsLibraryCharacterTableRep"
+        ],
+        "name": "IsLibraryCharacterTableRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsNearlyCharacterTable",
+            "IsGenericCharacterTableRep"
+        ],
+        "name": "IsGenericCharacterTableRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "IsNearAdditiveElement",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "IsNearAdditiveElementWithZero",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "IsNearAdditiveElementWithInverse",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "IsAdditiveElement",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "IsMultiplicativeElement",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsMultiplicativeElementWithOne",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsMultiplicativeElementWithInverse",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedRowVector",
+            "IsAssociativeElement",
+            "IsCommutativeElement",
+            "IsClassFunction"
+        ],
+        "name": "IsClassFunction",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingCharacterTable)"
+        ],
+        "name": "Tester(UnderlyingCharacterTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ValuesOfClassFunction)"
+        ],
+        "name": "Tester(ValuesOfClassFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GlobalPartitionOfClasses)"
+        ],
+        "name": "Tester(GlobalPartitionOfClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TrivialCharacter)"
+        ],
+        "name": "Tester(TrivialCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalCharacter)"
+        ],
+        "name": "Tester(NaturalCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCharacter",
+            "Tester(IsCharacter)"
+        ],
+        "name": "IsCharacter",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCharacter)"
+        ],
+        "name": "Tester(IsCharacter)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsVirtualCharacter",
+            "Tester(IsVirtualCharacter)"
+        ],
+        "name": "IsVirtualCharacter",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsVirtualCharacter)"
+        ],
+        "name": "Tester(IsVirtualCharacter)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsIrreducibleCharacter",
+            "Tester(IsIrreducibleCharacter)"
+        ],
+        "name": "IsIrreducibleCharacter",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIrreducibleCharacter)"
+        ],
+        "name": "Tester(IsIrreducibleCharacter)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(CentreOfCharacter)"
+        ],
+        "name": "Tester(CentreOfCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConstituentsOfCharacter)"
+        ],
+        "name": "Tester(ConstituentsOfCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DegreeOfCharacter)"
+        ],
+        "name": "Tester(DegreeOfCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(KernelOfCharacter)"
+        ],
+        "name": "Tester(KernelOfCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassPositionsOfKernel)"
+        ],
+        "name": "Tester(ClassPositionsOfKernel)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CentralCharacter)"
+        ],
+        "name": "Tester(CentralCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DeterminantOfCharacter)"
+        ],
+        "name": "Tester(DeterminantOfCharacter)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BrauerCharacterValue)"
+        ],
+        "name": "Tester(BrauerCharacterValue)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsClassFunctionsSpace"
+        ],
+        "name": "IsClassFunctionsSpace",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(ComputedPowerMaps)"
+        ],
+        "name": "Tester(ComputedPowerMaps)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FusionConjugacyClassesOp)"
+        ],
+        "name": "Tester(FusionConjugacyClassesOp)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedClassFusions)"
+        ],
+        "name": "Tester(ComputedClassFusions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NamesOfFusionSources)"
+        ],
+        "name": "Tester(NamesOfFusionSources)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BaumClausenInfo)"
+        ],
+        "name": "Tester(BaumClausenInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IrreducibleRepresentations)"
+        ],
+        "name": "Tester(IrreducibleRepresentations)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IrrBaumClausen)"
+        ],
+        "name": "Tester(IrrBaumClausen)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IrrConlon)"
+        ],
+        "name": "Tester(IrrConlon)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MolienSeriesInfo)"
+        ],
+        "name": "Tester(MolienSeriesInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Alpha)"
+        ],
+        "name": "Tester(Alpha)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Delta)"
+        ],
+        "name": "Tester(Delta)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBergerCondition",
+            "Tester(IsBergerCondition)"
+        ],
+        "name": "IsBergerCondition",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBergerCondition)"
+        ],
+        "name": "Tester(IsBergerCondition)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPrimitiveCharacter",
+            "Tester(IsPrimitiveCharacter)"
+        ],
+        "name": "IsPrimitiveCharacter",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPrimitiveCharacter)"
+        ],
+        "name": "Tester(IsPrimitiveCharacter)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(TestQuasiPrimitive)"
+        ],
+        "name": "Tester(TestQuasiPrimitive)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuasiPrimitive",
+            "Tester(IsQuasiPrimitive)"
+        ],
+        "name": "IsQuasiPrimitive",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsQuasiPrimitive)"
+        ],
+        "name": "Tester(IsQuasiPrimitive)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsInducedFromNormalSubgroup",
+            "Tester(IsInducedFromNormalSubgroup)"
+        ],
+        "name": "IsInducedFromNormalSubgroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsInducedFromNormalSubgroup)"
+        ],
+        "name": "Tester(IsInducedFromNormalSubgroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMonomialCharacter",
+            "Tester(IsMonomialCharacter)"
+        ],
+        "name": "IsMonomialCharacter",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMonomialCharacter)"
+        ],
+        "name": "Tester(IsMonomialCharacter)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMonomialNumber",
+            "Tester(IsMonomialNumber)"
+        ],
+        "name": "IsMonomialNumber",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMonomialNumber)"
+        ],
+        "name": "Tester(IsMonomialNumber)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(TestMonomialQuick)"
+        ],
+        "name": "Tester(TestMonomialQuick)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TestMonomial)"
+        ],
+        "name": "Tester(TestMonomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TestSubnormallyMonomial)"
+        ],
+        "name": "Tester(TestSubnormallyMonomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubnormallyMonomial",
+            "Tester(IsSubnormallyMonomial)"
+        ],
+        "name": "IsSubnormallyMonomial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSubnormallyMonomial)"
+        ],
+        "name": "Tester(IsSubnormallyMonomial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(TestRelativelySM)"
+        ],
+        "name": "Tester(TestRelativelySM)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRelativelySM",
+            "Tester(IsRelativelySM)"
+        ],
+        "name": "IsRelativelySM",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsRelativelySM)"
+        ],
+        "name": "Tester(IsRelativelySM)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMinimalNonmonomial",
+            "Tester(IsMinimalNonmonomial)"
+        ],
+        "name": "IsMinimalNonmonomial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMinimalNonmonomial)"
+        ],
+        "name": "Tester(IsMinimalNonmonomial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(DixonRecord)"
+        ],
+        "name": "Tester(DixonRecord)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IrrDixonSchneider)"
+        ],
+        "name": "Tester(IrrDixonSchneider)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TableOfMarks)"
+        ],
+        "name": "Tester(TableOfMarks)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsTableOfMarks"
+        ],
+        "name": "IsTableOfMarks",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(PermutationTom)"
+        ],
+        "name": "Tester(PermutationTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MarksTom)"
+        ],
+        "name": "Tester(MarksTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SubsTom)"
+        ],
+        "name": "Tester(SubsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrSubsTom)"
+        ],
+        "name": "Tester(NrSubsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrdersTom)"
+        ],
+        "name": "Tester(OrdersTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LengthsTom)"
+        ],
+        "name": "Tester(LengthsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassTypesTom)"
+        ],
+        "name": "Tester(ClassTypesTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ClassNamesTom)"
+        ],
+        "name": "Tester(ClassNamesTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FusionsTom)"
+        ],
+        "name": "Tester(FusionsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IdempotentsTom)"
+        ],
+        "name": "Tester(IdempotentsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IdempotentsTomInfo)"
+        ],
+        "name": "Tester(IdempotentsTomInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MatTom)"
+        ],
+        "name": "Tester(MatTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MoebiusTom)"
+        ],
+        "name": "Tester(MoebiusTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(WeightsTom)"
+        ],
+        "name": "Tester(WeightsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAbelianTom",
+            "Tester(IsAbelianTom)"
+        ],
+        "name": "IsAbelianTom",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAbelianTom)"
+        ],
+        "name": "Tester(IsAbelianTom)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsCyclicTom",
+            "Tester(IsCyclicTom)"
+        ],
+        "name": "IsCyclicTom",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsCyclicTom)"
+        ],
+        "name": "Tester(IsCyclicTom)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNilpotentTom",
+            "Tester(IsNilpotentTom)"
+        ],
+        "name": "IsNilpotentTom",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNilpotentTom)"
+        ],
+        "name": "Tester(IsNilpotentTom)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPerfectTom",
+            "Tester(IsPerfectTom)"
+        ],
+        "name": "IsPerfectTom",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPerfectTom)"
+        ],
+        "name": "Tester(IsPerfectTom)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSolvableTom",
+            "Tester(IsSolvableTom)"
+        ],
+        "name": "IsSolvableTom",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSolvableTom)"
+        ],
+        "name": "Tester(IsSolvableTom)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(DerivedSubgroupsTomPossible)"
+        ],
+        "name": "Tester(DerivedSubgroupsTomPossible)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DerivedSubgroupsTomUnique)"
+        ],
+        "name": "Tester(DerivedSubgroupsTomUnique)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalizersTom)"
+        ],
+        "name": "Tester(NormalizersTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CyclicExtensionsTom)"
+        ],
+        "name": "Tester(CyclicExtensionsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedCyclicExtensionsTom)"
+        ],
+        "name": "Tester(ComputedCyclicExtensionsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalSubgroupsTom)"
+        ],
+        "name": "Tester(MaximalSubgroupsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GeneratorsSubgroupsTom)"
+        ],
+        "name": "Tester(GeneratorsSubgroupsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StraightLineProgramsTom)"
+        ],
+        "name": "Tester(StraightLineProgramsTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsTableOfMarksWithGens"
+        ],
+        "name": "IsTableOfMarksWithGens",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsString",
+            "IsListOrCollection",
+            "IsConstantTimeAccessList",
+            "IsUnicodeString"
+        ],
+        "name": "IsUnicodeString",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsInt",
+            "IsRat",
+            "IsCyc",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsChar",
+            "IsCyclotomic",
+            "IsUnicodeCharacter"
+        ],
+        "name": "IsUnicodeCharacter",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsObjToBePrinted"
+        ],
+        "name": "IsObjToBePrinted",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsFile"
+        ],
+        "name": "IsFile",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(ProcessID)"
+        ],
+        "name": "Tester(ProcessID)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IO_Result"
+        ],
+        "name": "IO_Result",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsRandomSource",
+            "IsRealRandomSource"
+        ],
+        "name": "IsRealRandomSource",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsBackgroundJob"
+        ],
+        "name": "IsBackgroundJob",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsBackgroundJob",
+            "IsBackgroundJobByFork"
+        ],
+        "name": "IsBackgroundJobByFork",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsWorkerFarm"
+        ],
+        "name": "IsWorkerFarm",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsWorkerFarm",
+            "IsWorkerFarmByFork"
+        ],
+        "name": "IsWorkerFarmByFork",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsIOHubCat"
+        ],
+        "name": "IsIOHubCat",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsIOHubCat",
+            "IsIOHub"
+        ],
+        "name": "IsIOHub",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsPositionalObjectRep",
+            "IsListOrCollection",
+            "IsConstantTimeAccessList",
+            "IsEmptyRowVectorRep"
+        ],
+        "name": "IsEmptyRowVectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsTable",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(CategoryCollections(IsExtAElement))",
+            "IsNearAdditiveElement",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElement))",
+            "IsNearAdditiveElementWithZero",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+            "IsNearAdditiveElementWithInverse",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "IsAdditiveElement",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "IsMultiplicativeElement",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsGeneralizedRowVector",
+            "IsNullMapMatrix"
+        ],
+        "name": "IsNullMapMatrix",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsBlockMatrixRep"
+        ],
+        "name": "IsBlockMatrixRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "Tester(Range)",
+            "Tester(Source)",
+            "IsDefaultGeneralMappingRep"
+        ],
+        "name": "IsDefaultGeneralMappingRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsMappingByFunctionRep"
+        ],
+        "name": "IsMappingByFunctionRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "IsMappingByFunctionRep",
+            "IsMappingByFunctionWithInverseRep"
+        ],
+        "name": "IsMappingByFunctionWithInverseRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsNonSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsMappingByFunctionRep",
+            "IsNonSPMappingByFunctionRep"
+        ],
+        "name": "IsNonSPMappingByFunctionRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsNonSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "IsMappingByFunctionRep",
+            "IsMappingByFunctionWithInverseRep",
+            "IsNonSPMappingByFunctionRep",
+            "IsNonSPMappingByFunctionWithInverseRep"
+        ],
+        "name": "IsNonSPMappingByFunctionWithInverseRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsMappingByFunctionRep",
+            "IsSPMappingByFunctionRep"
+        ],
+        "name": "IsSPMappingByFunctionRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "IsMappingByFunctionRep",
+            "IsMappingByFunctionWithInverseRep",
+            "IsSPMappingByFunctionRep",
+            "IsSPMappingByFunctionWithInverseRep"
+        ],
+        "name": "IsSPMappingByFunctionWithInverseRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsNonSPGeneralMapping",
+            "IsInverseGeneralMappingRep"
+        ],
+        "name": "IsInverseGeneralMappingRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsBinaryRelationDefaultRep"
+        ],
+        "name": "IsBinaryRelationDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsBinaryRelationOnPointsRep"
+        ],
+        "name": "IsBinaryRelationOnPointsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsEquivalenceRelationDefaultRep"
+        ],
+        "name": "IsEquivalenceRelationDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsEquivalenceClassDefaultRep"
+        ],
+        "name": "IsEquivalenceClassDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRightTransversal",
+            "IsRightTransversalRep"
+        ],
+        "name": "IsRightTransversalRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsAdditiveCosetDefaultRep"
+        ],
+        "name": "IsAdditiveCosetDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsRelativeBasisDefaultRep"
+        ],
+        "name": "IsRelativeBasisDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsBasisWithReplacedLeftModuleRep"
+        ],
+        "name": "IsBasisWithReplacedLeftModuleRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsMutableBasisByImmutableBasisRep"
+        ],
+        "name": "IsMutableBasisByImmutableBasisRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsMutableBasisViaNiceMutableBasisRep"
+        ],
+        "name": "IsMutableBasisViaNiceMutableBasisRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsSubspacesVectorSpaceDefaultRep"
+        ],
+        "name": "IsSubspacesVectorSpaceDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsSemiEchelonBasisOfGaussianRowSpaceRep"
+        ],
+        "name": "IsSemiEchelonBasisOfGaussianRowSpaceRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsSubspacesVectorSpaceDefaultRep",
+            "IsSubspacesFullRowSpaceDefaultRep"
+        ],
+        "name": "IsSubspacesFullRowSpaceDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsMutableBasisOfGaussianRowSpaceRep"
+        ],
+        "name": "IsMutableBasisOfGaussianRowSpaceRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsSemiEchelonBasisOfGaussianMatrixSpaceRep"
+        ],
+        "name": "IsSemiEchelonBasisOfGaussianMatrixSpaceRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsMutableBasisOfGaussianMatrixSpaceRep"
+        ],
+        "name": "IsMutableBasisOfGaussianMatrixSpaceRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsLinearGeneralMappingByImagesDefaultRep"
+        ],
+        "name": "IsLinearGeneralMappingByImagesDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsLinearMappingByMatrixDefaultRep"
+        ],
+        "name": "IsLinearMappingByMatrixDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsMagmaRingObjDefaultRep"
+        ],
+        "name": "IsMagmaRingObjDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsCanonicalBasis",
+            "Tester(IsCanonicalBasis)",
+            "IsCanonicalBasisFreeMagmaRingRep"
+        ],
+        "name": "IsCanonicalBasisFreeMagmaRingRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "IsEmbeddingRingMagmaRing"
+        ],
+        "name": "IsEmbeddingRingMagmaRing",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "IsEmbeddingMagmaMagmaRing"
+        ],
+        "name": "IsEmbeddingMagmaMagmaRing",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsAlgebraGeneralMappingByImagesDefaultRep"
+        ],
+        "name": "IsAlgebraGeneralMappingByImagesDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsAlgebraGeneralMappingByImagesDefaultRep",
+            "IsPolynomialRingDefaultGeneratorMapping"
+        ],
+        "name": "IsPolynomialRingDefaultGeneratorMapping",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsOperationAlgebraHomomorphismDefaultRep"
+        ],
+        "name": "IsOperationAlgebraHomomorphismDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsAlgebraHomomorphismFromFpRep"
+        ],
+        "name": "IsAlgebraHomomorphismFromFpRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis",
+            "IsSpaceOfUEAElements"
+        ],
+        "name": "IsSpaceOfUEAElements",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsDenseCoeffVectorRep"
+        ],
+        "name": "IsDenseCoeffVectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsLieEmbeddingRep"
+        ],
+        "name": "IsLieEmbeddingRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsMutableBasisViaUnderlyingMutableBasisRep"
+        ],
+        "name": "IsMutableBasisViaUnderlyingMutableBasisRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsMonomialElementRep"
+        ],
+        "name": "IsMonomialElementRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsBasisOfMonomialSpaceRep"
+        ],
+        "name": "IsBasisOfMonomialSpaceRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsBasisOfSparseRowSpaceRep"
+        ],
+        "name": "IsBasisOfSparseRowSpaceRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsPackedElementDefaultRep",
+            "IsZeroCochainRep"
+        ],
+        "name": "IsZeroCochainRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsSearchTable",
+            "IsVectorSearchTable",
+            "IsVectorSearchTableDefaultRep"
+        ],
+        "name": "IsVectorSearchTableDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "IsRingGeneralMappingByImagesDefaultRep"
+        ],
+        "name": "IsRingGeneralMappingByImagesDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "IsRingGeneralMappingByImagesDefaultRep",
+            "IsSCRingGeneralMappingByImagesDefaultRep"
+        ],
+        "name": "IsSCRingGeneralMappingByImagesDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsNonTrivial",
+            "Tester(IsNonTrivial)",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "IsCommutative",
+            "Tester(IsCommutative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsUniqueFactorizationRing",
+            "IsEuclideanRing",
+            "IsIntegralRing",
+            "Tester(IsIntegralRing)",
+            "IsFreeLeftModule",
+            "IsAlgebraicExtension",
+            "IsAlgebraicExtensionDefaultRep"
+        ],
+        "name": "IsAlgebraicExtensionDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsAlgebraicElement",
+            "IsAlgBFRep"
+        ],
+        "name": "IsAlgBFRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsAssociativeElement",
+            "IsAdditivelyCommutativeElement",
+            "IsCommutativeElement",
+            "IsAlgebraicElement",
+            "IsKroneckerConstRep"
+        ],
+        "name": "IsKroneckerConstRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsBasis",
+            "IsCanonicalBasis",
+            "Tester(IsCanonicalBasis)",
+            "IsCanonicalBasisAlgebraicExtension"
+        ],
+        "name": "IsCanonicalBasisAlgebraicExtension",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsUnknownDefaultRep"
+        ],
+        "name": "IsUnknownDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsBasisFiniteFieldRep"
+        ],
+        "name": "IsBasisFiniteFieldRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsFieldHomomorphism",
+            "Tester(IsFieldHomomorphism)",
+            "IsFrobeniusAutomorphism"
+        ],
+        "name": "IsFrobeniusAutomorphism",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsModulusRep"
+        ],
+        "name": "IsModulusRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsCoeffsModConwayPolRep"
+        ],
+        "name": "IsCoeffsModConwayPolRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsCanonicalBasisRationals"
+        ],
+        "name": "IsCanonicalBasisRationals",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsCanonicalBasisGaussianIntegersRep"
+        ],
+        "name": "IsCanonicalBasisGaussianIntegersRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsCanonicalBasisAbelianNumberFieldRep"
+        ],
+        "name": "IsCanonicalBasisAbelianNumberFieldRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsCanonicalBasisAbelianNumberFieldRep",
+            "IsCanonicalBasisCyclotomicFieldRep"
+        ],
+        "name": "IsCanonicalBasisCyclotomicFieldRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsANFAutomorphismRep"
+        ],
+        "name": "IsANFAutomorphismRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsLockedRepresentationVector"
+        ],
+        "name": "IsLockedRepresentationVector",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsBracketRep"
+        ],
+        "name": "IsBracketRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsSyllableAssocWordRep",
+            "Is8BitsAssocWord"
+        ],
+        "name": "Is8BitsAssocWord",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsSyllableAssocWordRep",
+            "Is16BitsAssocWord"
+        ],
+        "name": "Is16BitsAssocWord",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsSyllableAssocWordRep",
+            "Is32BitsAssocWord"
+        ],
+        "name": "Is32BitsAssocWord",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsAssociativeElement",
+            "IsWord",
+            "IsSyllableAssocWordRep",
+            "IsInfBitsAssocWord"
+        ],
+        "name": "IsInfBitsAssocWord",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsInfiniteListOfNamesRep"
+        ],
+        "name": "IsInfiniteListOfNamesRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsInfiniteListOfGeneratorsRep"
+        ],
+        "name": "IsInfiniteListOfGeneratorsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsSingleCollectorRep"
+        ],
+        "name": "IsSingleCollectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsSingleCollectorRep",
+            "Is8BitsSingleCollectorRep"
+        ],
+        "name": "Is8BitsSingleCollectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsSingleCollectorRep",
+            "Is16BitsSingleCollectorRep"
+        ],
+        "name": "Is16BitsSingleCollectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsSingleCollectorRep",
+            "Is32BitsSingleCollectorRep"
+        ],
+        "name": "Is32BitsSingleCollectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDefaultRhsTypeSingleCollector"
+        ],
+        "name": "IsDefaultRhsTypeSingleCollector",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsSingleCollectorRep",
+            "IsCombinatorialCollectorRep"
+        ],
+        "name": "IsCombinatorialCollectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep",
+            "IsNBitsPcWordRep"
+        ],
+        "name": "IsNBitsPcWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep",
+            "IsKernelPcWord",
+            "IsNBitsPcWordRep",
+            "Is8BitsPcWordRep"
+        ],
+        "name": "Is8BitsPcWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep",
+            "IsKernelPcWord",
+            "IsNBitsPcWordRep",
+            "Is16BitsPcWordRep"
+        ],
+        "name": "Is16BitsPcWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsDataObjectRep",
+            "IsKernelPcWord",
+            "IsNBitsPcWordRep",
+            "Is32BitsPcWordRep"
+        ],
+        "name": "Is32BitsPcWordRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsDeepThoughtCollectorRep"
+        ],
+        "name": "IsDeepThoughtCollectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsEnumeratorByPcgsRep"
+        ],
+        "name": "IsEnumeratorByPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsFiniteOrdersPcgs",
+            "Tester(IsFiniteOrdersPcgs)",
+            "IsPcgsByPcgsRep"
+        ],
+        "name": "IsPcgsByPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsInducedPcgsRep"
+        ],
+        "name": "IsInducedPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsInducedPcgsRep",
+            "IsSubsetInducedPcgsRep"
+        ],
+        "name": "IsSubsetInducedPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsInducedPcgsRep",
+            "IsSubsetInducedPcgsRep",
+            "IsTailInducedPcgsRep"
+        ],
+        "name": "IsTailInducedPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsModuloPcgsRep"
+        ],
+        "name": "IsModuloPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsModuloPcgsRep",
+            "IsModuloTailPcgsRep"
+        ],
+        "name": "IsModuloTailPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsModuloPcgsRep",
+            "IsModuloTailPcgsRep",
+            "IsSubsetInducedNumeratorModuloTailPcgsRep"
+        ],
+        "name": "IsSubsetInducedNumeratorModuloTailPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsModuloPcgsRep",
+            "IsModuloTailPcgsRep",
+            "IsModuloTailPcgsByListRep"
+        ],
+        "name": "IsModuloTailPcgsByListRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsModuloPcgsRep",
+            "IsNumeratorParentForExponentsRep"
+        ],
+        "name": "IsNumeratorParentForExponentsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsModuloPcgsRep",
+            "IsNumeratorParentLayersForExponentsRep"
+        ],
+        "name": "IsNumeratorParentLayersForExponentsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsUnsortedPcgsRep"
+        ],
+        "name": "IsUnsortedPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsUnsortedPcgsRep",
+            "IsSortedPcgsRep"
+        ],
+        "name": "IsSortedPcgsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "CanEasilyCompareElements",
+            "Tester(CanEasilyCompareElements)",
+            "CanEasilySortElements",
+            "Tester(CanEasilySortElements)",
+            "CanComputeSize",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "CategoryCollections(IsFiniteOrderElement)",
+            "IsGeneralizedDomain",
+            "CategoryCollections(IsPerm)",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsCompletelySimpleSemigroup",
+            "Tester(IsCompletelySimpleSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsFinitelyGeneratedGroup",
+            "Tester(IsFinitelyGeneratedGroup)",
+            "IsSubsetLocallyFiniteGroup",
+            "Tester(IsSubsetLocallyFiniteGroup)",
+            "CanEasilyTestMembership",
+            "CanComputeSizeAnySubgroup",
+            "KnowsHowToDecompose",
+            "Tester(KnowsHowToDecompose)",
+            "CanComputeFittingFree",
+            "IsMemberPcSeriesPermGroup",
+            "IsNilpotentByFinite",
+            "Tester(IsNilpotentByFinite)"
+        ],
+        "name": "IsMemberPcSeriesPermGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPositionalObjectRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsMagmaByMultiplicationTableObj"
+        ],
+        "name": "IsMagmaByMultiplicationTableObj",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPcgsDefaultRep",
+            "IsPcgsDirectProductRep"
+        ],
+        "name": "IsPcgsDirectProductRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsActionHomomorphismByBase",
+            "IsBlocksOfActionHomomorphism"
+        ],
+        "name": "IsBlocksOfActionHomomorphism",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsEmbeddingDirectProductPermGroup"
+        ],
+        "name": "IsEmbeddingDirectProductPermGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsEmbeddingWreathProductPermGroup"
+        ],
+        "name": "IsEmbeddingWreathProductPermGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsEmbeddingWreathProductPermGroup",
+            "IsEmbeddingImprimitiveWreathProductPermGroup"
+        ],
+        "name": "IsEmbeddingImprimitiveWreathProductPermGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages",
+            "IsEmbeddingWreathProductPermGroup",
+            "IsEmbeddingProductActionWreathProductPermGroup"
+        ],
+        "name": "IsEmbeddingProductActionWreathProductPermGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsProjectionDirectProductPermGroup"
+        ],
+        "name": "IsProjectionDirectProductPermGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsProjectionSubdirectProductPermGroup"
+        ],
+        "name": "IsProjectionSubdirectProductPermGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsEmbeddingDirectProductMatrixGroup"
+        ],
+        "name": "IsEmbeddingDirectProductMatrixGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsProjectionDirectProductMatrixGroup"
+        ],
+        "name": "IsProjectionDirectProductMatrixGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsEmbeddingImprimitiveWreathProductMatrixGroup"
+        ],
+        "name": "IsEmbeddingImprimitiveWreathProductMatrixGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPerm",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsFiniteOrderElement",
+            "IsSlicedPerm"
+        ],
+        "name": "IsSlicedPerm",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsPerm",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsFiniteOrderElement",
+            "IsSlicedPermInv"
+        ],
+        "name": "IsSlicedPermInv",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsGeneralizedDomain",
+            "IsExternalSet",
+            "IsExternalSubset",
+            "IsExternalOrbit",
+            "IsRightCoset",
+            "IsRightCosetDefaultRep"
+        ],
+        "name": "IsRightCosetDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsExtRSet",
+            "IsDoubleCoset",
+            "IsDoubleCosetDefaultRep"
+        ],
+        "name": "IsDoubleCosetDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRightTransversal",
+            "IsRightTransversalRep",
+            "IsRightTransversalViaCosetsRep"
+        ],
+        "name": "IsRightTransversalViaCosetsRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRightTransversal",
+            "IsRightTransversalRep",
+            "IsFactoredTransversalRep"
+        ],
+        "name": "IsFactoredTransversalRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRightTransversal",
+            "IsRightTransversalRep",
+            "IsRightTransversalPermGroupRep"
+        ],
+        "name": "IsRightTransversalPermGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRightTransversal",
+            "IsRightTransversalRep",
+            "IsRightTransversalPcGroupRep"
+        ],
+        "name": "IsRightTransversalPcGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsEnumeratorByNiceomorphismRep"
+        ],
+        "name": "IsEnumeratorByNiceomorphismRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsPreimagesByAsGroupGeneralMappingByImages",
+            "IsActionHomomorphism",
+            "IsActionHomomorphismByBase",
+            "IsActionHomomorphismAutomGroup"
+        ],
+        "name": "IsActionHomomorphismAutomGroup",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "IsTotal",
+            "Tester(IsTotal)",
+            "IsSingleValued",
+            "Tester(IsSingleValued)",
+            "IsInjective",
+            "Tester(IsInjective)",
+            "IsSurjective",
+            "Tester(IsSurjective)",
+            "IsBlowUpIsomorphism"
+        ],
+        "name": "IsBlowUpIsomorphism",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsRightTransversal",
+            "IsRightTransversalRep",
+            "IsRightTransversalFpGroupRep"
+        ],
+        "name": "IsRightTransversalFpGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsPresentationDefaultRep"
+        ],
+        "name": "IsPresentationDefaultRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsNoImmediateMethodsObject",
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsFinite",
+            "Tester(IsFinite)",
+            "IsConstantTimeAccessList",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralPcgs",
+            "IsModuloPcgs",
+            "IsPcgsDefaultRep",
+            "IsModuloPcgsFpGroupRep"
+        ],
+        "name": "IsModuloPcgsFpGroupRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsTransformationRepOfEndo"
+        ],
+        "name": "IsTransformationRepOfEndo",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsKnuthBendixRewritingSystemRep"
+        ],
+        "name": "IsKnuthBendixRewritingSystemRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsFreeLeftModule",
+            "IsFloatPseudoField"
+        ],
+        "name": "IsFloatPseudoField",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsExtAElement",
+            "IsNearAdditiveElement",
+            "IsNearAdditiveElementWithZero",
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsZDFRE",
+            "IsPolynomialFunction",
+            "IsRationalFunction",
+            "IsFloatRationalFunction"
+        ],
+        "name": "IsFloatRationalFunction",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsFreeLeftModule",
+            "IsFloatPseudoField",
+            "IsIEEE754PseudoField"
+        ],
+        "name": "IsIEEE754PseudoField",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(IdGroup)"
+        ],
+        "name": "Tester(IdGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Gap3CatalogueIdGroup)"
+        ],
+        "name": "Tester(Gap3CatalogueIdGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FrattinifactorSize)"
+        ],
+        "name": "Tester(FrattinifactorSize)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FrattinifactorId)"
+        ],
+        "name": "Tester(FrattinifactorId)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GaloisType)"
+        ],
+        "name": "Tester(GaloisType)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SimsNo)"
+        ],
+        "name": "Tester(SimsNo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimalBlockDimension)"
+        ],
+        "name": "Tester(MinimalBlockDimension)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPrimitiveMatrixGroup",
+            "Tester(IsPrimitiveMatrixGroup)"
+        ],
+        "name": "IsPrimitiveMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPrimitiveMatrixGroup)"
+        ],
+        "name": "Tester(IsPrimitiveMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsPrimGrpIterRep"
+        ],
+        "name": "IsPrimGrpIterRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "IsPGAutomorphismRep"
+        ],
+        "name": "IsPGAutomorphismRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(IrrFacsAlgExtPol)"
+        ],
+        "name": "Tester(IrrFacsAlgExtPol)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsList",
+            "IsDenseList",
+            "IsHomogeneousList",
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsBasis",
+            "IsBasisOfMatrixField"
+        ],
+        "name": "IsBasisOfMatrixField",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsUnitGroup",
+            "Tester(IsUnitGroup)"
+        ],
+        "name": "IsUnitGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsUnitGroup)"
+        ],
+        "name": "Tester(IsUnitGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsUnitGroupIsomorphism",
+            "Tester(IsUnitGroupIsomorphism)"
+        ],
+        "name": "IsUnitGroupIsomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsUnitGroupIsomorphism)"
+        ],
+        "name": "Tester(IsUnitGroupIsomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNumberFieldByMatrices",
+            "Tester(IsNumberFieldByMatrices)"
+        ],
+        "name": "IsNumberFieldByMatrices",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNumberFieldByMatrices)"
+        ],
+        "name": "Tester(IsNumberFieldByMatrices)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsMultGroupByFieldElemsIsomorphism",
+            "Tester(IsMultGroupByFieldElemsIsomorphism)"
+        ],
+        "name": "IsMultGroupByFieldElemsIsomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMultGroupByFieldElemsIsomorphism)"
+        ],
+        "name": "Tester(IsMultGroupByFieldElemsIsomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(IntegerDefiningPolynomial)"
+        ],
+        "name": "Tester(IntegerDefiningPolynomial)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IntegerPrimitiveElement)"
+        ],
+        "name": "Tester(IntegerPrimitiveElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(EquationOrderBasis)"
+        ],
+        "name": "Tester(EquationOrderBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MaximalOrderBasis)"
+        ],
+        "name": "Tester(MaximalOrderBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnitGroup)"
+        ],
+        "name": "Tester(UnitGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FieldOfUnitGroup)"
+        ],
+        "name": "Tester(FieldOfUnitGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsCopyable",
+            "IsRewritingSystem",
+            "IsBuiltFromMagma",
+            "Tester(IsBuiltFromMagma)",
+            "IsBuiltFromMagmaWithOne",
+            "Tester(IsBuiltFromMagmaWithOne)",
+            "IsBuiltFromMagmaWithInverses",
+            "Tester(IsBuiltFromMagmaWithInverses)",
+            "IsBuiltFromGroup",
+            "Tester(IsBuiltFromGroup)",
+            "IsPolycyclicCollector",
+            "IsPowerConjugateCollector",
+            "IsFromTheLeftCollectorRep"
+        ],
+        "name": "IsFromTheLeftCollectorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsWeightedCollector",
+            "Tester(IsWeightedCollector)"
+        ],
+        "name": "IsWeightedCollector",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsWeightedCollector)"
+        ],
+        "name": "Tester(IsWeightedCollector)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPolynomialCollector",
+            "Tester(IsPolynomialCollector)"
+        ],
+        "name": "IsPolynomialCollector",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPolynomialCollector)"
+        ],
+        "name": "Tester(IsPolynomialCollector)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "UseLibraryCollector",
+            "Tester(UseLibraryCollector)"
+        ],
+        "name": "UseLibraryCollector",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(UseLibraryCollector)"
+        ],
+        "name": "Tester(UseLibraryCollector)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPolycyclicPresentation",
+            "Tester(IsPolycyclicPresentation)"
+        ],
+        "name": "IsPolycyclicPresentation",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPolycyclicPresentation)"
+        ],
+        "name": "Tester(IsPolycyclicPresentation)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsPcpElement"
+        ],
+        "name": "IsPcpElement",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsFamily",
+            "CategoryFamily(IsPcpElement)"
+        ],
+        "name": "CategoryFamily(IsPcpElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "CategoryCollections(IsPcpElement)"
+        ],
+        "name": "CategoryCollections(IsPcpElement)",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsPcpElementRep"
+        ],
+        "name": "IsPcpElementRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(TailOfElm)"
+        ],
+        "name": "Tester(TailOfElm)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RelativeOrderPcp)"
+        ],
+        "name": "Tester(RelativeOrderPcp)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RelativeIndex)"
+        ],
+        "name": "Tester(RelativeIndex)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FactorOrder)"
+        ],
+        "name": "Tester(FactorOrder)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Igs)"
+        ],
+        "name": "Tester(Igs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Ngs)"
+        ],
+        "name": "Tester(Ngs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Cgs)"
+        ],
+        "name": "Tester(Cgs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsPcp"
+        ],
+        "name": "IsPcp",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsPcpRep"
+        ],
+        "name": "IsPcpRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "Extrarankfilter"
+        ],
+        "name": "Extrarankfilter",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "Extrarankfilter",
+            "IsFromPcpGHBI"
+        ],
+        "name": "IsFromPcpGHBI",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "Extrarankfilter"
+        ],
+        "name": "Extrarankfilter",
+        "type": "GAP_Filter"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "IsSPGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsOne",
+            "Tester(RespectsOne)",
+            "RespectsInverses",
+            "Tester(RespectsInverses)",
+            "IsGroupGeneralMappingByImages",
+            "Extrarankfilter",
+            "IsToPcpGHBI"
+        ],
+        "name": "IsToPcpGHBI",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(EfaSeries)"
+        ],
+        "name": "Tester(EfaSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PcpsOfEfaSeries)"
+        ],
+        "name": "Tester(PcpsOfEfaSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismPcpGroup)"
+        ],
+        "name": "Tester(IsomorphismPcpGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PcpGroupByEfaSeries)"
+        ],
+        "name": "Tester(PcpGroupByEfaSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsHomomorphismIntoMatrixGroup",
+            "Tester(IsHomomorphismIntoMatrixGroup)"
+        ],
+        "name": "IsHomomorphismIntoMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsHomomorphismIntoMatrixGroup)"
+        ],
+        "name": "Tester(IsHomomorphismIntoMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(SemiSimpleEfaSeries)"
+        ],
+        "name": "Tester(SemiSimpleEfaSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FCCentre)"
+        ],
+        "name": "Tester(FCCentre)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNilpotentByFinite",
+            "Tester(IsNilpotentByFinite)"
+        ],
+        "name": "IsNilpotentByFinite",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNilpotentByFinite)"
+        ],
+        "name": "Tester(IsNilpotentByFinite)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ComputedMaximalSubgroupClassesByIndexs)"
+        ],
+        "name": "Tester(ComputedMaximalSubgroupClassesByIndexs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedLowIndexSubgroupClassess)"
+        ],
+        "name": "Tester(ComputedLowIndexSubgroupClassess)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedLowIndexNormalSubgroupss)"
+        ],
+        "name": "Tester(ComputedLowIndexNormalSubgroupss)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SchurExtension)"
+        ],
+        "name": "Tester(SchurExtension)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SchurExtensionEpimorphism)"
+        ],
+        "name": "Tester(SchurExtensionEpimorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NonAbelianTensorSquare)"
+        ],
+        "name": "Tester(NonAbelianTensorSquare)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NonAbelianExteriorSquare)"
+        ],
+        "name": "Tester(NonAbelianExteriorSquare)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TorsionSubgroup)"
+        ],
+        "name": "Tester(TorsionSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalTorsionSubgroup)"
+        ],
+        "name": "Tester(NormalTorsionSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FiniteSubgroupClasses)"
+        ],
+        "name": "Tester(FiniteSubgroupClasses)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTorsionFree",
+            "Tester(IsTorsionFree)"
+        ],
+        "name": "IsTorsionFree",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTorsionFree)"
+        ],
+        "name": "Tester(IsTorsionFree)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFreeAbelian",
+            "Tester(IsFreeAbelian)"
+        ],
+        "name": "IsFreeAbelian",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFreeAbelian)"
+        ],
+        "name": "Tester(IsFreeAbelian)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsClass"
+        ],
+        "name": "IsClass",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(MemberFunction)"
+        ],
+        "name": "Tester(MemberFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedIsMembers)"
+        ],
+        "name": "Tester(ComputedIsMembers)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass",
+            "Tester(IsGroupClass)"
+        ],
+        "name": "IsGroupClass",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupClass)"
+        ],
+        "name": "Tester(IsGroupClass)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(GroupClass)"
+        ],
+        "name": "Tester(GroupClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "ContainsTrivialGroup",
+            "Tester(ContainsTrivialGroup)"
+        ],
+        "name": "ContainsTrivialGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(ContainsTrivialGroup)"
+        ],
+        "name": "Tester(ContainsTrivialGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSubgroupClosed",
+            "Tester(IsSubgroupClosed)",
+            "IsNormalSubgroupClosed",
+            "Tester(IsNormalSubgroupClosed)"
+        ],
+        "name": "IsSubgroupClosed",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSubgroupClosed)"
+        ],
+        "name": "Tester(IsSubgroupClosed)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNormalSubgroupClosed",
+            "Tester(IsNormalSubgroupClosed)"
+        ],
+        "name": "IsNormalSubgroupClosed",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNormalSubgroupClosed)"
+        ],
+        "name": "Tester(IsNormalSubgroupClosed)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsQuotientClosed",
+            "Tester(IsQuotientClosed)"
+        ],
+        "name": "IsQuotientClosed",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsQuotientClosed)"
+        ],
+        "name": "Tester(IsQuotientClosed)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsResiduallyClosed",
+            "Tester(IsResiduallyClosed)",
+            "IsDirectProductClosed",
+            "Tester(IsDirectProductClosed)"
+        ],
+        "name": "IsResiduallyClosed",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsResiduallyClosed)"
+        ],
+        "name": "Tester(IsResiduallyClosed)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNormalProductClosed",
+            "Tester(IsNormalProductClosed)",
+            "IsDirectProductClosed",
+            "Tester(IsDirectProductClosed)"
+        ],
+        "name": "IsNormalProductClosed",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNormalProductClosed)"
+        ],
+        "name": "Tester(IsNormalProductClosed)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsDirectProductClosed",
+            "Tester(IsDirectProductClosed)"
+        ],
+        "name": "IsDirectProductClosed",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsDirectProductClosed)"
+        ],
+        "name": "Tester(IsDirectProductClosed)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "ContainsTrivialGroup",
+            "Tester(ContainsTrivialGroup)",
+            "IsQuotientClosed",
+            "Tester(IsQuotientClosed)",
+            "IsDirectProductClosed",
+            "Tester(IsDirectProductClosed)",
+            "IsSchunckClass",
+            "Tester(IsSchunckClass)",
+            "IsSaturated",
+            "Tester(IsSaturated)"
+        ],
+        "name": "IsSchunckClass",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSchunckClass)"
+        ],
+        "name": "Tester(IsSchunckClass)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSaturated",
+            "Tester(IsSaturated)"
+        ],
+        "name": "IsSaturated",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSaturated)"
+        ],
+        "name": "Tester(IsSaturated)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(FittingClass)"
+        ],
+        "name": "Tester(FittingClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InjectorFunction)"
+        ],
+        "name": "Tester(InjectorFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RadicalFunction)"
+        ],
+        "name": "Tester(RadicalFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPrimitiveSolvableGroup",
+            "Tester(IsPrimitiveSolvableGroup)"
+        ],
+        "name": "IsPrimitiveSolvableGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPrimitiveSolvableGroup)"
+        ],
+        "name": "Tester(IsPrimitiveSolvableGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(SchunckClass)"
+        ],
+        "name": "Tester(SchunckClass)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Boundary)"
+        ],
+        "name": "Tester(Boundary)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ProjectorFunction)"
+        ],
+        "name": "Tester(ProjectorFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BoundaryFunction)"
+        ],
+        "name": "Tester(BoundaryFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrdinaryFormation)"
+        ],
+        "name": "Tester(OrdinaryFormation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SaturatedFormation)"
+        ],
+        "name": "Tester(SaturatedFormation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FittingFormation)"
+        ],
+        "name": "Tester(FittingFormation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SaturatedFittingFormation)"
+        ],
+        "name": "Tester(SaturatedFittingFormation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ResidualFunction)"
+        ],
+        "name": "Tester(ResidualFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LocalDefinitionFunction)"
+        ],
+        "name": "Tester(LocalDefinitionFunction)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedProjectors)"
+        ],
+        "name": "Tester(ComputedProjectors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedCoveringSubgroups)"
+        ],
+        "name": "Tester(ComputedCoveringSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedInjectors)"
+        ],
+        "name": "Tester(ComputedInjectors)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedRadicals)"
+        ],
+        "name": "Tester(ComputedRadicals)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedResiduals)"
+        ],
+        "name": "Tester(ComputedResiduals)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CharacteristicSubgroups)"
+        ],
+        "name": "Tester(CharacteristicSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalGeneratorsOfNilpotentResidual)"
+        ],
+        "name": "Tester(NormalGeneratorsOfNilpotentResidual)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PrimePowerGensPcSequence)"
+        ],
+        "name": "Tester(PrimePowerGensPcSequence)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NilpotentProjector)"
+        ],
+        "name": "Tester(NilpotentProjector)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SupersolvableProjector)"
+        ],
+        "name": "Tester(SupersolvableProjector)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SolvableSocle)"
+        ],
+        "name": "Tester(SolvableSocle)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SocleComponents)"
+        ],
+        "name": "Tester(SocleComponents)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SolvableSocleComponents)"
+        ],
+        "name": "Tester(SolvableSocleComponents)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedPSocleComponentss)"
+        ],
+        "name": "Tester(ComputedPSocleComponentss)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedPSocles)"
+        ],
+        "name": "Tester(ComputedPSocles)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AbelianMinimalNormalSubgroups)"
+        ],
+        "name": "Tester(AbelianMinimalNormalSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsClass",
+            "IsClassByPropertyRep"
+        ],
+        "name": "IsClassByPropertyRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsClass",
+            "IsClassByComplementRep"
+        ],
+        "name": "IsClassByComplementRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsClass",
+            "IsClassByIntersectionRep"
+        ],
+        "name": "IsClassByIntersectionRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsClass",
+            "IsClassByUnionRep"
+        ],
+        "name": "IsClassByUnionRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsClass",
+            "IsGroupClass",
+            "Tester(IsGroupClass)",
+            "IsGroupClassByListRep"
+        ],
+        "name": "IsGroupClassByListRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsClass",
+            "IsGroupClass",
+            "Tester(IsGroupClass)",
+            "ContainsTrivialGroup",
+            "Tester(ContainsTrivialGroup)",
+            "IsNormalSubgroupClosed",
+            "Tester(IsNormalSubgroupClosed)",
+            "IsNormalProductClosed",
+            "Tester(IsNormalProductClosed)",
+            "IsDirectProductClosed",
+            "Tester(IsDirectProductClosed)",
+            "IsFittingProductRep"
+        ],
+        "name": "IsFittingProductRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "CategoryCollections(CategoryCollections(IsExtLElement))",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(CategoryCollections(IsExtRElement))",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsClass",
+            "IsClassByPropertyRep",
+            "IsFittingSetRep"
+        ],
+        "name": "IsFittingSetRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsClass",
+            "IsGroupClass",
+            "Tester(IsGroupClass)",
+            "ContainsTrivialGroup",
+            "Tester(ContainsTrivialGroup)",
+            "IsQuotientClosed",
+            "Tester(IsQuotientClosed)",
+            "IsResiduallyClosed",
+            "Tester(IsResiduallyClosed)",
+            "IsDirectProductClosed",
+            "Tester(IsDirectProductClosed)",
+            "IsFormationProductRep"
+        ],
+        "name": "IsFormationProductRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsBBoxProgram"
+        ],
+        "name": "IsBBoxProgram",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsStraightLineDecision"
+        ],
+        "name": "IsStraightLineDecision",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(LinesOfStraightLineDecision)"
+        ],
+        "name": "Tester(LinesOfStraightLineDecision)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NrInputsOfStraightLineDecision)"
+        ],
+        "name": "Tester(NrInputsOfStraightLineDecision)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsBBoxProgram)"
+        ],
+        "name": "Tester(AsBBoxProgram)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsStraightLineProgram)"
+        ],
+        "name": "Tester(AsStraightLineProgram)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AsStraightLineDecision)"
+        ],
+        "name": "Tester(AsStraightLineDecision)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Maxes)"
+        ],
+        "name": "Tester(Maxes)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AtlasRepInfoRecord)"
+        ],
+        "name": "Tester(AtlasRepInfoRecord)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CASInfo)"
+        ],
+        "name": "Tester(CASInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConstructionInfoCharacterTable)"
+        ],
+        "name": "Tester(ConstructionInfoCharacterTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FusionToTom)"
+        ],
+        "name": "Tester(FusionToTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ProjectivesInfo)"
+        ],
+        "name": "Tester(ProjectivesInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ExtensionInfoCharacterTable)"
+        ],
+        "name": "Tester(ExtensionInfoCharacterTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GroupInfoForCharacterTable)"
+        ],
+        "name": "Tester(GroupInfoForCharacterTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "KnowsSomeGroupInfo",
+            "Tester(KnowsSomeGroupInfo)"
+        ],
+        "name": "KnowsSomeGroupInfo",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(KnowsSomeGroupInfo)"
+        ],
+        "name": "Tester(KnowsSomeGroupInfo)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsNontrivialDirectProduct",
+            "Tester(IsNontrivialDirectProduct)"
+        ],
+        "name": "IsNontrivialDirectProduct",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNontrivialDirectProduct)"
+        ],
+        "name": "Tester(IsNontrivialDirectProduct)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "KnowsDeligneLusztigNames",
+            "Tester(KnowsDeligneLusztigNames)"
+        ],
+        "name": "KnowsDeligneLusztigNames",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(KnowsDeligneLusztigNames)"
+        ],
+        "name": "Tester(KnowsDeligneLusztigNames)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsDuplicateTable",
+            "Tester(IsDuplicateTable)"
+        ],
+        "name": "IsDuplicateTable",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsDuplicateTable)"
+        ],
+        "name": "Tester(IsDuplicateTable)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(IdentifierOfMainTable)"
+        ],
+        "name": "Tester(IdentifierOfMainTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IdentifiersOfDuplicateTables)"
+        ],
+        "name": "Tester(IdentifiersOfDuplicateTables)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DeligneLusztigNames)"
+        ],
+        "name": "Tester(DeligneLusztigNames)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DeligneLusztigName)"
+        ],
+        "name": "Tester(DeligneLusztigName)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FingerprintOfCharacterTable)"
+        ],
+        "name": "Tester(FingerprintOfCharacterTable)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SpinSymIngredients)"
+        ],
+        "name": "Tester(SpinSymIngredients)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsNearlyCharacterTable",
+            "IsCharacterTable",
+            "IsSpinSymTable"
+        ],
+        "name": "IsSpinSymTable",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsLibTomRep"
+        ],
+        "name": "IsLibTomRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(NamesLibTom)"
+        ],
+        "name": "Tester(NamesLibTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NotifiedFusionsOfLibTom)"
+        ],
+        "name": "Tester(NotifiedFusionsOfLibTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FusionsOfLibTom)"
+        ],
+        "name": "Tester(FusionsOfLibTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NotifiedFusionsToLibTom)"
+        ],
+        "name": "Tester(NotifiedFusionsToLibTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FusionsToLibTom)"
+        ],
+        "name": "Tester(FusionsToLibTom)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(StandardGeneratorsInfo)"
+        ],
+        "name": "Tester(StandardGeneratorsInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsInvAutomatonCategory"
+        ],
+        "name": "IsInvAutomatonCategory",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(FGA_States)"
+        ],
+        "name": "Tester(FGA_States)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FGA_GeneratorsLetterRep)"
+        ],
+        "name": "Tester(FGA_GeneratorsLetterRep)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeGeneratorsOfGroup)"
+        ],
+        "name": "Tester(FreeGeneratorsOfGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RankOfFreeGroup)"
+        ],
+        "name": "Tester(RankOfFreeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CanComputeSize",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "CategoryCollections(IsAssociativeElement)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsGeneratorsOfMagmaWithInverses",
+            "Tester(IsGeneratorsOfMagmaWithInverses)",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsGeneratorsOfSemigroup",
+            "Tester(IsGeneratorsOfSemigroup)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "IsFinitelyGeneratedGroup",
+            "Tester(IsFinitelyGeneratedGroup)",
+            "CanEasilyTestMembership",
+            "CanComputeSizeAnySubgroup",
+            "CategoryCollections(IsWord)",
+            "CategoryCollections((IsWord and IsAssociativeElement))",
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))",
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsSubgroupFgGroup",
+            "IsSubgroupFpGroup",
+            "IsTorsionFree",
+            "Tester(IsTorsionFree)",
+            "Tester(FreeGroupAutomaton)"
+        ],
+        "name": "Tester(FreeGroupAutomaton)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FreeGroupExtendedAutomaton)"
+        ],
+        "name": "Tester(FreeGroupExtendedAutomaton)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalizerInWholeGroup)"
+        ],
+        "name": "Tester(NormalizerInWholeGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FGA_Source)"
+        ],
+        "name": "Tester(FGA_Source)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FGA_Image)"
+        ],
+        "name": "Tester(FGA_Image)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsGroupOfAutomorphisms",
+            "Tester(IsGroupOfAutomorphisms)",
+            "IsAutomorphismGroup",
+            "Tester(IsAutomorphismGroup)",
+            "IsAutomorphismGroupOfFreeGroup"
+        ],
+        "name": "IsAutomorphismGroupOfFreeGroup",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(FGA_WhiteheadParams)"
+        ],
+        "name": "Tester(FGA_WhiteheadParams)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FGA_WhiteheadAutomorphisms)"
+        ],
+        "name": "Tester(FGA_WhiteheadAutomorphisms)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FGA_NielsenAutomorphisms)"
+        ],
+        "name": "Tester(FGA_NielsenAutomorphisms)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsListOrCollection",
+            "IsCollection",
+            "IsInvAutomatonCategory",
+            "IsSimpleInvAutomatonRep"
+        ],
+        "name": "IsSimpleInvAutomatonRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsIrreducibleMatrixGroup",
+            "Tester(IsIrreducibleMatrixGroup)"
+        ],
+        "name": "IsIrreducibleMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIrreducibleMatrixGroup)"
+        ],
+        "name": "Tester(IsIrreducibleMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ComputedIsIrreducibleMatrixGroups)"
+        ],
+        "name": "Tester(ComputedIsIrreducibleMatrixGroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAbsolutelyIrreducibleMatrixGroup",
+            "Tester(IsAbsolutelyIrreducibleMatrixGroup)"
+        ],
+        "name": "IsAbsolutelyIrreducibleMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAbsolutelyIrreducibleMatrixGroup)"
+        ],
+        "name": "Tester(IsAbsolutelyIrreducibleMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ComputedIsPrimitiveMatrixGroups)"
+        ],
+        "name": "Tester(ComputedIsPrimitiveMatrixGroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimalBlockDimensionOfMatrixGroup)"
+        ],
+        "name": "Tester(MinimalBlockDimensionOfMatrixGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedMinimalBlockDimensionOfMatrixGroups)"
+        ],
+        "name": "Tester(ComputedMinimalBlockDimensionOfMatrixGroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CharacteristicOfField)"
+        ],
+        "name": "Tester(CharacteristicOfField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RepresentationIsomorphism)"
+        ],
+        "name": "Tester(RepresentationIsomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup",
+            "Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"
+        ],
+        "name": "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"
+        ],
+        "name": "Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ImprimitivitySystems)"
+        ],
+        "name": "Tester(ImprimitivitySystems)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedImprimitivitySystemss)"
+        ],
+        "name": "Tester(ComputedImprimitivitySystemss)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TraceField)"
+        ],
+        "name": "Tester(TraceField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ConjugatingMatTraceField)"
+        ],
+        "name": "Tester(ConjugatingMatTraceField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(FingerprintMatrixGroup)"
+        ],
+        "name": "Tester(FingerprintMatrixGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IdIrreducibleSolvableMatrixGroup)"
+        ],
+        "name": "Tester(IdIrreducibleSolvableMatrixGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IdPrimitiveSolvableGroup)"
+        ],
+        "name": "Tester(IdPrimitiveSolvableGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsMultiplicativeElement",
+            "IsMultiplicativeElementWithOne",
+            "IsMultiplicativeElementWithInverse",
+            "IsAssociativeElement",
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "Tester(RespectsMultiplication)",
+            "RespectsAddition",
+            "Tester(RespectsAddition)",
+            "RespectsZero",
+            "Tester(RespectsZero)",
+            "RespectsAdditiveInverses",
+            "Tester(RespectsAdditiveInverses)",
+            "RespectsScalarMultiplication",
+            "Tester(RespectsScalarMultiplication)",
+            "IsNilpotentLieAutomorphismRep"
+        ],
+        "name": "IsNilpotentLieAutomorphismRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsLieNilpotentOverFp",
+            "Tester(IsLieNilpotentOverFp)"
+        ],
+        "name": "IsLieNilpotentOverFp",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieNilpotentOverFp)"
+        ],
+        "name": "Tester(IsLieNilpotentOverFp)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(AutomorphismGroupOfNilpotentLieAlgebra)"
+        ],
+        "name": "Tester(AutomorphismGroupOfNilpotentLieAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(MinimalGeneratorNumber)"
+        ],
+        "name": "Tester(MinimalGeneratorNumber)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieCover",
+            "Tester(IsLieCover)"
+        ],
+        "name": "IsLieCover",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieCover)"
+        ],
+        "name": "Tester(IsLieCover)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(CoverOf)"
+        ],
+        "name": "Tester(CoverOf)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoverHomomorphism)"
+        ],
+        "name": "Tester(CoverHomomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieCover)"
+        ],
+        "name": "Tester(LieCover)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieNucleus)"
+        ],
+        "name": "Tester(LieNucleus)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieMultiplicator)"
+        ],
+        "name": "Tester(LieMultiplicator)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieAlgebraWithNB",
+            "Tester(IsLieAlgebraWithNB)"
+        ],
+        "name": "IsLieAlgebraWithNB",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieAlgebraWithNB)"
+        ],
+        "name": "Tester(IsLieAlgebraWithNB)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NilpotentBasis)"
+        ],
+        "name": "Tester(NilpotentBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNilpotentBasis",
+            "Tester(IsNilpotentBasis)"
+        ],
+        "name": "IsNilpotentBasis",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNilpotentBasis)"
+        ],
+        "name": "Tester(IsNilpotentBasis)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(LieNBDefinitions)"
+        ],
+        "name": "Tester(LieNBDefinitions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieNBWeights)"
+        ],
+        "name": "Tester(LieNBWeights)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupAlgebra",
+            "Tester(IsGroupAlgebra)"
+        ],
+        "name": "IsGroupAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupAlgebra)"
+        ],
+        "name": "Tester(IsGroupAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFModularGroupAlgebra",
+            "Tester(IsFModularGroupAlgebra)"
+        ],
+        "name": "IsFModularGroupAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFModularGroupAlgebra)"
+        ],
+        "name": "Tester(IsFModularGroupAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra",
+            "Tester(IsPModularGroupAlgebra)"
+        ],
+        "name": "IsPModularGroupAlgebra",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPModularGroupAlgebra)"
+        ],
+        "name": "Tester(IsPModularGroupAlgebra)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingRing)"
+        ],
+        "name": "Tester(UnderlyingRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingField)"
+        ],
+        "name": "Tester(UnderlyingField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Support)"
+        ],
+        "name": "Tester(Support)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CoefficientsBySupport)"
+        ],
+        "name": "Tester(CoefficientsBySupport)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TraceOfMagmaRingElement)"
+        ],
+        "name": "Tester(TraceOfMagmaRingElement)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Augmentation)"
+        ],
+        "name": "Tester(Augmentation)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsSymmetric)"
+        ],
+        "name": "Tester(IsSymmetric)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(IsUnitary)"
+        ],
+        "name": "Tester(IsUnitary)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(WeightedBasis)"
+        ],
+        "name": "Tester(WeightedBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentationIdealPowerSeries)"
+        ],
+        "name": "Tester(AugmentationIdealPowerSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentationIdealNilpotencyIndex)"
+        ],
+        "name": "Tester(AugmentationIdealNilpotencyIndex)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)"
+        ],
+        "name": "Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfUnitsOfMagmaRing",
+            "Tester(IsGroupOfUnitsOfMagmaRing)"
+        ],
+        "name": "IsGroupOfUnitsOfMagmaRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsGroupOfUnitsOfMagmaRing)"
+        ],
+        "name": "Tester(IsGroupOfUnitsOfMagmaRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsUnitGroupOfGroupRing",
+            "Tester(IsUnitGroupOfGroupRing)"
+        ],
+        "name": "IsUnitGroupOfGroupRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsUnitGroupOfGroupRing)"
+        ],
+        "name": "Tester(IsUnitGroupOfGroupRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsListOrCollection",
+            "IsCollection",
+            "CanComputeSize",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "CategoryCollections(IsMultiplicativeElementWithOne)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+            "IsGeneralizedDomain",
+            "IsMagma",
+            "IsMagmaWithOne",
+            "IsMagmaWithInversesIfNonzero",
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(IsAssociative)",
+            "Tester(MultiplicativeNeutralElement)",
+            "IsSimpleSemigroup",
+            "Tester(IsSimpleSemigroup)",
+            "IsRegularSemigroup",
+            "Tester(IsRegularSemigroup)",
+            "IsInverseSemigroup",
+            "Tester(IsInverseSemigroup)",
+            "IsCompletelyRegularSemigroup",
+            "Tester(IsCompletelyRegularSemigroup)",
+            "IsGroupAsSemigroup",
+            "Tester(IsGroupAsSemigroup)",
+            "IsMonoidAsSemigroup",
+            "Tester(IsMonoidAsSemigroup)",
+            "IsOrthodoxSemigroup",
+            "Tester(IsOrthodoxSemigroup)",
+            "CanComputeSizeAnySubgroup",
+            "IsSolvableGroup",
+            "Tester(IsSolvableGroup)",
+            "CanEasilyComputePcgs",
+            "IsNormalizedUnitGroupOfGroupRing",
+            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+        ],
+        "name": "IsNormalizedUnitGroupOfGroupRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+        ],
+        "name": "Tester(IsNormalizedUnitGroupOfGroupRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingGroupRing)"
+        ],
+        "name": "Tester(UnderlyingGroupRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NormalizedUnitGroup)"
+        ],
+        "name": "Tester(NormalizedUnitGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PcNormalizedUnitGroup)"
+        ],
+        "name": "Tester(PcNormalizedUnitGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ComputedAugmentationIdealPowerFactorGroups)"
+        ],
+        "name": "Tester(ComputedAugmentationIdealPowerFactorGroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PcUnits)"
+        ],
+        "name": "Tester(PcUnits)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalBijectionToPcNormalizedUnitGroup)"
+        ],
+        "name": "Tester(NaturalBijectionToPcNormalizedUnitGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalBijectionToNormalizedUnitGroup)"
+        ],
+        "name": "Tester(NaturalBijectionToNormalizedUnitGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GroupBases)"
+        ],
+        "name": "Tester(GroupBases)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BicyclicUnitGroup)"
+        ],
+        "name": "Tester(BicyclicUnitGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(UnitarySubgroup)"
+        ],
+        "name": "Tester(UnitarySubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsExtAElement",
+            "CategoryCollections(IsExtAElement)",
+            "CategoryCollections(IsNearAdditiveElement)",
+            "CategoryCollections(IsNearAdditiveElementWithZero)",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "IsExtLElement",
+            "CategoryCollections(IsExtLElement)",
+            "IsExtRElement",
+            "CategoryCollections(IsExtRElement)",
+            "CategoryCollections(IsMultiplicativeElement)",
+            "IsGeneralizedDomain",
+            "IsExtLSet",
+            "IsAssociativeLOpDProd",
+            "IsAssociativeLOpEProd",
+            "IsDistributiveLOpDSum",
+            "IsDistributiveLOpESum",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByRing",
+            "IsLeftActedOnByDivisionRing",
+            "Tester(IsLeftActedOnByDivisionRing)",
+            "IsMagma",
+            "IsNearAdditiveMagma",
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveGroup",
+            "IsAdditivelyCommutative",
+            "Tester(IsAdditivelyCommutative)",
+            "IsLDistributive",
+            "Tester(IsLDistributive)",
+            "IsRDistributive",
+            "Tester(IsRDistributive)",
+            "IsAnticommutative",
+            "Tester(IsAnticommutative)",
+            "IsJacobianRing",
+            "Tester(IsJacobianRing)",
+            "IsZeroSquaredRing",
+            "Tester(IsZeroSquaredRing)",
+            "IsFreeLeftModule",
+            "IsLieAlgebraByAssociativeAlgebra"
+        ],
+        "name": "IsLieAlgebraByAssociativeAlgebra",
+        "type": "GAP_Category"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingAssociativeAlgebra)"
+        ],
+        "name": "Tester(UnderlyingAssociativeAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieAlgebraOfGroupRing",
+            "Tester(IsLieAlgebraOfGroupRing)"
+        ],
+        "name": "IsLieAlgebraOfGroupRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieAlgebraOfGroupRing)"
+        ],
+        "name": "Tester(IsLieAlgebraOfGroupRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsBasisOfLieAlgebraOfGroupRing",
+            "Tester(IsBasisOfLieAlgebraOfGroupRing)"
+        ],
+        "name": "IsBasisOfLieAlgebraOfGroupRing",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsBasisOfLieAlgebraOfGroupRing)"
+        ],
+        "name": "Tester(IsBasisOfLieAlgebraOfGroupRing)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NaturalBijectionToLieAlgebra)"
+        ],
+        "name": "Tester(NaturalBijectionToLieAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalBijectionToAssociativeAlgebra)"
+        ],
+        "name": "Tester(NaturalBijectionToAssociativeAlgebra)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AugmentationHomomorphism)"
+        ],
+        "name": "Tester(AugmentationHomomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieMetabelian",
+            "Tester(IsLieMetabelian)"
+        ],
+        "name": "IsLieMetabelian",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieMetabelian)"
+        ],
+        "name": "Tester(IsLieMetabelian)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsLieCentreByMetabelian",
+            "Tester(IsLieCentreByMetabelian)"
+        ],
+        "name": "IsLieCentreByMetabelian",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsLieCentreByMetabelian)"
+        ],
+        "name": "Tester(IsLieCentreByMetabelian)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(LieUpperNilpotencyIndex)"
+        ],
+        "name": "Tester(LieUpperNilpotencyIndex)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieLowerNilpotencyIndex)"
+        ],
+        "name": "Tester(LieLowerNilpotencyIndex)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieDerivedLength)"
+        ],
+        "name": "Tester(LieDerivedLength)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(SubgroupsOfIndexTwo)"
+        ],
+        "name": "Tester(SubgroupsOfIndexTwo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DihedralDepth)"
+        ],
+        "name": "Tester(DihedralDepth)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(DimensionBasis)"
+        ],
+        "name": "Tester(DimensionBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieDimensionSubgroups)"
+        ],
+        "name": "Tester(LieDimensionSubgroups)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(LieUpperCodimensionSeries)"
+        ],
+        "name": "Tester(LieUpperCodimensionSeries)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(RootsAsMatrices)"
+        ],
+        "name": "Tester(RootsAsMatrices)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSolvablePolynomial",
+            "Tester(IsSolvablePolynomial)"
+        ],
+        "name": "IsSolvablePolynomial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSolvablePolynomial)"
+        ],
+        "name": "Tester(IsSolvablePolynomial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSeparablePolynomial",
+            "Tester(IsSeparablePolynomial)"
+        ],
+        "name": "IsSeparablePolynomial",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSeparablePolynomial)"
+        ],
+        "name": "Tester(IsSeparablePolynomial)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(IsomorphismMatrixField)"
+        ],
+        "name": "Tester(IsomorphismMatrixField)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(GaloisGroupOnRoots)"
+        ],
+        "name": "Tester(GaloisGroupOnRoots)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CanComputeSize",
+            "CanEasilyTestMembership",
+            "CanComputeSizeAnySubgroup",
+            "IsAffineCrystGroupOnRight",
+            "Tester(IsAffineCrystGroupOnRight)",
+            "IsAffineCrystGroupOnLeftOrRight",
+            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+        ],
+        "name": "IsAffineCrystGroupOnRight",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAffineCrystGroupOnRight)"
+        ],
+        "name": "Tester(IsAffineCrystGroupOnRight)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "CanComputeSize",
+            "CanEasilyTestMembership",
+            "CanComputeSizeAnySubgroup",
+            "IsAffineCrystGroupOnLeft",
+            "Tester(IsAffineCrystGroupOnLeft)",
+            "IsAffineCrystGroupOnLeftOrRight",
+            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+        ],
+        "name": "IsAffineCrystGroupOnLeft",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAffineCrystGroupOnLeft)"
+        ],
+        "name": "Tester(IsAffineCrystGroupOnLeft)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "CanComputeSize",
+            "CanEasilyTestMembership",
+            "CanComputeSizeAnySubgroup",
+            "IsAffineCrystGroupOnLeftOrRight",
+            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+        ],
+        "name": "IsAffineCrystGroupOnLeftOrRight",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+        ],
+        "name": "Tester(IsAffineCrystGroupOnLeftOrRight)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSpaceGroup",
+            "Tester(IsSpaceGroup)"
+        ],
+        "name": "IsSpaceGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSpaceGroup)"
+        ],
+        "name": "Tester(IsSpaceGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsStandardAffineCrystGroup",
+            "Tester(IsStandardAffineCrystGroup)"
+        ],
+        "name": "IsStandardAffineCrystGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsStandardAffineCrystGroup)"
+        ],
+        "name": "Tester(IsStandardAffineCrystGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsSymmorphicSpaceGroup",
+            "Tester(IsSymmorphicSpaceGroup)"
+        ],
+        "name": "IsSymmorphicSpaceGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsSymmorphicSpaceGroup)"
+        ],
+        "name": "Tester(IsSymmorphicSpaceGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsPointGroup",
+            "Tester(IsPointGroup)"
+        ],
+        "name": "IsPointGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPointGroup)"
+        ],
+        "name": "Tester(IsPointGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NormalizerPointGroupInGLnZ)"
+        ],
+        "name": "Tester(NormalizerPointGroupInGLnZ)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CentralizerPointGroupInGLnZ)"
+        ],
+        "name": "Tester(CentralizerPointGroupInGLnZ)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AffineCrystGroupOfPointGroup)"
+        ],
+        "name": "Tester(AffineCrystGroupOfPointGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PointGroup)"
+        ],
+        "name": "Tester(PointGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(PointHomomorphism)"
+        ],
+        "name": "Tester(PointHomomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TranslationBasis)"
+        ],
+        "name": "Tester(TranslationBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(InternalBasis)"
+        ],
+        "name": "Tester(InternalBasis)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TransParts)"
+        ],
+        "name": "Tester(TransParts)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(TranslationNormalizer)"
+        ],
+        "name": "Tester(TranslationNormalizer)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(AffineNormalizer)"
+        ],
+        "name": "Tester(AffineNormalizer)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPointHomomorphism",
+            "Tester(IsPointHomomorphism)"
+        ],
+        "name": "IsPointHomomorphism",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsPointHomomorphism)"
+        ],
+        "name": "Tester(IsPointHomomorphism)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NiceToCryst)"
+        ],
+        "name": "Tester(NiceToCryst)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFromAffineCrystGroupToFpGroup",
+            "Tester(IsFromAffineCrystGroupToFpGroup)"
+        ],
+        "name": "IsFromAffineCrystGroupToFpGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFromAffineCrystGroupToFpGroup)"
+        ],
+        "name": "Tester(IsFromAffineCrystGroupToFpGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsFromAffineCrystGroupToPcpGroup",
+            "Tester(IsFromAffineCrystGroupToPcpGroup)"
+        ],
+        "name": "IsFromAffineCrystGroupToPcpGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsFromAffineCrystGroupToPcpGroup)"
+        ],
+        "name": "Tester(IsFromAffineCrystGroupToPcpGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsWyckoffPosition"
+        ],
+        "name": "IsWyckoffPosition",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "Tester(WyckoffStabilizer)"
+        ],
+        "name": "Tester(WyckoffStabilizer)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(WyckoffOrbit)"
+        ],
+        "name": "Tester(WyckoffOrbit)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(WyckoffPositions)"
+        ],
+        "name": "Tester(WyckoffPositions)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsWyckoffGraph"
+        ],
+        "name": "IsWyckoffGraph",
+        "type": "GAP_Filter"
+    },
+    {
+        "filters": [
+            "Tester(CocVecs)"
+        ],
+        "name": "Tester(CocVecs)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsColorGroup",
+            "Tester(IsColorGroup)"
+        ],
+        "name": "IsColorGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsColorGroup)"
+        ],
+        "name": "Tester(IsColorGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(ColorSubgroup)"
+        ],
+        "name": "Tester(ColorSubgroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ColorCosetList)"
+        ],
+        "name": "Tester(ColorCosetList)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ColorPermGroup)"
+        ],
+        "name": "Tester(ColorPermGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(ColorHomomorphism)"
+        ],
+        "name": "Tester(ColorHomomorphism)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(CrystCatRecord)"
+        ],
+        "name": "Tester(CrystCatRecord)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAlmostCrystallographic",
+            "Tester(IsAlmostCrystallographic)"
+        ],
+        "name": "IsAlmostCrystallographic",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAlmostCrystallographic)"
+        ],
+        "name": "Tester(IsAlmostCrystallographic)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsAlmostBieberbachGroup",
+            "Tester(IsAlmostBieberbachGroup)"
+        ],
+        "name": "IsAlmostBieberbachGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsAlmostBieberbachGroup)"
+        ],
+        "name": "Tester(IsAlmostBieberbachGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(AlmostCrystallographicInfo)"
+        ],
+        "name": "Tester(AlmostCrystallographicInfo)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(NaturalHomomorphismOnHolonomyGroup)"
+        ],
+        "name": "Tester(NaturalHomomorphismOnHolonomyGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(HolonomyGroup)"
+        ],
+        "name": "Tester(HolonomyGroup)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(OrientationModule)"
+        ],
+        "name": "Tester(OrientationModule)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(BettiNumbers)"
+        ],
+        "name": "Tester(BettiNumbers)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsIsomorphismByFinitePolycyclicMatrixGroup",
+            "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"
+        ],
+        "name": "IsIsomorphismByFinitePolycyclicMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"
+        ],
+        "name": "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsIsomorphismByPolycyclicMatrixGroup",
+            "Tester(IsIsomorphismByPolycyclicMatrixGroup)"
+        ],
+        "name": "IsIsomorphismByPolycyclicMatrixGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsIsomorphismByPolycyclicMatrixGroup)"
+        ],
+        "name": "Tester(IsIsomorphismByPolycyclicMatrixGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsTriangularizableMatGroup",
+            "Tester(IsTriangularizableMatGroup)"
+        ],
+        "name": "IsTriangularizableMatGroup",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsTriangularizableMatGroup)"
+        ],
+        "name": "Tester(IsTriangularizableMatGroup)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsZ_pi",
+            "Tester(IsZ_pi)"
+        ],
+        "name": "IsZ_pi",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZ_pi)"
+        ],
+        "name": "Tester(IsZ_pi)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(NoninvertiblePrimes)"
+        ],
+        "name": "Tester(NoninvertiblePrimes)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsResidueClassUnion"
+        ],
+        "name": "IsResidueClassUnion",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsResidueClassUnion",
+            "IsResidueClassUnionOfZ",
+            "IsResidueClassUnionOfZorZ_pi"
+        ],
+        "name": "IsResidueClassUnionOfZ",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsResidueClassUnion",
+            "IsResidueClassUnionOfZxZ"
+        ],
+        "name": "IsResidueClassUnionOfZxZ",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsResidueClassUnion",
+            "IsResidueClassUnionOfZ_pi",
+            "IsResidueClassUnionOfZorZ_pi"
+        ],
+        "name": "IsResidueClassUnionOfZ_pi",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsResidueClassUnion",
+            "IsResidueClassUnionOfGFqx"
+        ],
+        "name": "IsResidueClassUnionOfGFqx",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsResidueClassUnion",
+            "IsResidueClassUnionOfZorZ_pi"
+        ],
+        "name": "IsResidueClassUnionOfZorZ_pi",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsResidueClassUnionResidueListRep"
+        ],
+        "name": "IsResidueClassUnionResidueListRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsResidueClassUnionsIteratorRep"
+        ],
+        "name": "IsResidueClassUnionsIteratorRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsResidueClass",
+            "Tester(IsResidueClass)"
+        ],
+        "name": "IsResidueClass",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsResidueClass)"
+        ],
+        "name": "Tester(IsResidueClass)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(UnderlyingIndeterminate)"
+        ],
+        "name": "Tester(UnderlyingIndeterminate)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsZxZ",
+            "Tester(IsZxZ)"
+        ],
+        "name": "IsZxZ",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsZxZ)"
+        ],
+        "name": "Tester(IsZxZ)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(SizeOfSmallestResidueClassRing)"
+        ],
+        "name": "Tester(SizeOfSmallestResidueClassRing)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "Tester(Density)"
+        ],
+        "name": "Tester(Density)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsUnionOfResidueClassesWithFixedRepresentatives"
+        ],
+        "name": "IsUnionOfResidueClassesWithFixedRepresentatives",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsUnionOfResidueClassesWithFixedRepresentatives",
+            "IsUnionOfResidueClassesOfZWithFixedRepresentatives",
+            "IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"
+        ],
+        "name": "IsUnionOfResidueClassesOfZWithFixedRepresentatives",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsUnionOfResidueClassesWithFixedRepresentatives",
+            "IsUnionOfResidueClassesOfZ_piWithFixedRepresentatives",
+            "IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"
+        ],
+        "name": "IsUnionOfResidueClassesOfZ_piWithFixedRepresentatives",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsUnionOfResidueClassesWithFixedRepresentatives",
+            "IsUnionOfResidueClassesOfGFqxWithFixedRepresentatives"
+        ],
+        "name": "IsUnionOfResidueClassesOfGFqxWithFixedRepresentatives",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsListOrCollection",
+            "IsCollection",
+            "IsDuplicateFree",
+            "Tester(IsDuplicateFree)",
+            "IsGeneralizedDomain",
+            "IsUnionOfResidueClassesWithFixedRepresentatives",
+            "IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"
+        ],
+        "name": "IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives",
+        "type": "GAP_Category"
+    },
+    {
+        "implied": [
+            "IsComponentObjectRep",
+            "IsAttributeStoringRep",
+            "IsUnionOfResidueClassesWithFixedRepsStandardRep"
+        ],
+        "name": "IsUnionOfResidueClassesWithFixedRepsStandardRep",
+        "type": "GAP_Representation"
+    },
+    {
+        "filters": [
+            "IsResidueClassWithFixedRepresentative",
+            "Tester(IsResidueClassWithFixedRepresentative)"
+        ],
+        "name": "IsResidueClassWithFixedRepresentative",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsResidueClassWithFixedRepresentative)"
+        ],
+        "name": "Tester(IsResidueClassWithFixedRepresentative)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "IsOverlappingFree",
+            "Tester(IsOverlappingFree)"
+        ],
+        "name": "IsOverlappingFree",
+        "type": "GAP_Property"
+    },
+    {
+        "implied": [
+            "Tester(IsOverlappingFree)"
+        ],
+        "name": "Tester(IsOverlappingFree)",
+        "type": "GAP_TrueProperty"
+    },
+    {
+        "filters": [
+            "Tester(Rho)"
+        ],
+        "name": "Tester(Rho)",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "Name",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "InfoText",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "String",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsImpossible",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "CollectionsFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "ElementsFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "IsEmpty",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "IsTrivial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "IsNonTrivial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "IsFinite",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "IsWholeFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "Size",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "Representative",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "RepresentativeSmallest",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "PseudoRandomSeed",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "Enumerator",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "EnumeratorSorted",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "UnderlyingCollection",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "AsList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "AsSortedList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "AsSSortedList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "CanEasilyCompareElements",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "CanEasilySortElements",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "RandomizerAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "CheapRandomizerAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "IsSmallList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "Length",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "ConstantTimeAccessList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "IsSortedList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "IsSSortedList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsDenseList"
+        ],
+        "name": "IsNSortedList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "IsDuplicateFree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsDenseList"
+        ],
+        "name": "IsPositionsList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "AsDuplicateFreeList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "SortingPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "NestingDepthA",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "NestingDepthM",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithZero",
+            "IsAdditiveElement"
+        ],
+        "name": "IsZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElementWithOne"
+        ],
+        "name": "IsOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithZero",
+            "IsAdditiveElement"
+        ],
+        "name": "ZeroImmutable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement"
+        ],
+        "name": "AdditiveInverseImmutable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElementWithOne"
+        ],
+        "name": "OneImmutable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "InverseImmutable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "Int",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "Rat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "Characteristic",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElementWithOne"
+        ],
+        "name": "Order",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsExtLElement",
+            "IsExtRElement",
+            "IsHomogeneousList",
+            "IsOddAdditiveNestingDepthObject",
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElementWithInverse)"
+        ],
+        "name": "NormedRowVector",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "IsCommutativeFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "IsSkewFieldFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "IsUFDFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "AdditiveElementsAsMultiplicativeElementsFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAdditiveElement"
+        ],
+        "name": "AdditiveElementAsMultiplicativeElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElement"
+        ],
+        "name": "IsIdempotent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFFE"
+        ],
+        "name": "DegreeFFE",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFFE"
+        ],
+        "name": "IntFFE",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFFE"
+        ],
+        "name": "IntFFESymm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFFE"
+        ],
+        "name": "AsInternalFFE",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralizedDomain",
+            "IsCollection"
+        ],
+        "name": "GeneratorsOfDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralizedDomain",
+            "IsCollection"
+        ],
+        "name": "ParentAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsIntegralCyclotomic",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCyc"
+        ],
+        "name": "Conductor",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRecord"
+        ],
+        "name": "RecNames",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsList"
+        ],
+        "name": "IsRectangularTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPerm"
+        ],
+        "name": "SmallestGeneratorPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPerm"
+        ],
+        "name": "SmallestMovedPoint",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPerm"
+        ],
+        "name": "LargestMovedPoint",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPerm"
+        ],
+        "name": "NrMovedPoints",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPerm"
+        ],
+        "name": "MovedPoints",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPerm"
+        ],
+        "name": "SignPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPerm"
+        ],
+        "name": "CycleStructurePerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Cos",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Sin",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Tan",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Sec",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Csc",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Cot",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Asin",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Acos",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Atan",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Cosh",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Sinh",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Tanh",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Sech",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Csch",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Coth",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Asinh",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Acosh",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Atanh",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Log2",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Log10",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Log1p",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Exp",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Exp2",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Exp10",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Expm1",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "CubeRoot",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Square",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Ceil",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Floor",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Round",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Trunc",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "FrExp",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Argument",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "AbsoluteValue",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Frac",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "SinCos",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Erf",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Zeta",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Gamma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "ComplexI",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "PrecisionFloat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "SignFloat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Sup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Inf",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "Mid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "AbsoluteDiameter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "RelativeDiameter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "IsPInfinity",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "IsNInfinity",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "IsXInfinity",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFloat"
+        ],
+        "name": "IsNaN",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryFamily(IsDirectProductElement)"
+        ],
+        "name": "ComponentsOfDirectProductElementsFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "EmptyRowVector",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtASet"
+        ],
+        "name": "GeneratorsOfExtASet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtASet"
+        ],
+        "name": "AdditivelyActingDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtLSet",
+            "IsLeftActedOnByRing"
+        ],
+        "name": "IsLeftActedOnByDivisionRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtLSet"
+        ],
+        "name": "GeneratorsOfExtLSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtLSet"
+        ],
+        "name": "LeftActingDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtRSet"
+        ],
+        "name": "GeneratorsOfExtRSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtRSet"
+        ],
+        "name": "RightActingDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtUSet"
+        ],
+        "name": "GeneratorsOfExtUSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExtRSet"
+        ],
+        "name": "UpperActingDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryFamily(IsGeneralMapping)"
+        ],
+        "name": "FamilyRange",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryFamily(IsGeneralMapping)"
+        ],
+        "name": "FamilySource",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "FamiliesOfGeneralMappingsAndRanges",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsConstantTimeAccessGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsEndoGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsTotal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsSingleValued",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsInjective",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsSurjective",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "Range",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "Source",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "UnderlyingRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "UnderlyingGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "IdentityMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "InverseGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "ImagesSource",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "PreImagesRange",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "MappingGeneratorsImages",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "RespectsMultiplication",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "RespectsOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "RespectsInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "KernelOfMultiplicativeGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "CoKernelOfMultiplicativeGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "RespectsAddition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "RespectsZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "RespectsAdditiveInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "KernelOfAdditiveGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "CoKernelOfAdditiveGeneralMapping",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "RespectsScalarMultiplication",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsFieldHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "TransformsMultiplicationIntoAddition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "TranformsOneIntoZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "TransformsInversesIntoAdditiveInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "TransformsAdditionIntoMultiplication",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "TransformsZeroIntoOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "TransformsAdditiveInversesIntoInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "Successors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "DegreeOfBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsReflexiveBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsSymmetricBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsTransitiveBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsAntisymmetricBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsPreOrderBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsPartialOrderBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsLatticeOrderBinaryRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsEquivalenceRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "IsHasseDiagram",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEndoGeneralMapping"
+        ],
+        "name": "PartialOrderOfHasseDiagram",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEquivalenceRelation"
+        ],
+        "name": "EquivalenceRelationPartition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEquivalenceRelation"
+        ],
+        "name": "GeneratorsOfEquivalenceRelationPartition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEquivalenceClass"
+        ],
+        "name": "EquivalenceClassRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEquivalenceRelation"
+        ],
+        "name": "EquivalenceClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "AsMagma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "GeneratorsOfMagma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithOne"
+        ],
+        "name": "GeneratorsOfMagmaWithOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses"
+        ],
+        "name": "GeneratorsOfMagmaWithInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "IsGeneratorsOfMagmaWithInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithOne"
+        ],
+        "name": "TrivialSubmagmaWithOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "IsAssociative",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "IsCommutative",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "MultiplicativeNeutralElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "Centre",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "Idempotents",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "CentralizerInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "MagmaGeneratorsOfFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsLeftActedOnBySuperset",
+            "IsMagma",
+            "IsRightActedOnBySuperset"
+        ],
+        "name": "GeneratorsOfMagmaIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElementWithZero"
+        ],
+        "name": "MultiplicativeZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "InjectionZeroMagma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElementWithZero",
+            "IsMagmaWithZeroAdjoinedElementRep"
+        ],
+        "name": "MagmaWithZeroAdjoined",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithZeroAdjoined"
+        ],
+        "name": "UnderlyingInjectionZeroMagma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLeftMagmaCongruence"
+        ],
+        "name": "GeneratingPairsOfLeftMagmaCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLeftMagmaCongruence"
+        ],
+        "name": "PartialClosureOfCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRightMagmaCongruence"
+        ],
+        "name": "GeneratingPairsOfRightMagmaCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaCongruence"
+        ],
+        "name": "GeneratingPairsOfMagmaCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLeftMagmaCongruence"
+        ],
+        "name": "IsLeftSemigroupCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRightMagmaCongruence"
+        ],
+        "name": "IsRightSemigroupCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaCongruence"
+        ],
+        "name": "IsSemigroupCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSemigroupCongruence"
+        ],
+        "name": "IsReesCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "AsSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "IsGeneratorsOfSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "CayleyGraphSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "CayleyGraphDualSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsZeroGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsSimpleSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsZeroSimpleSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "ANonReesCongruenceOfSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsReesCongruenceSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsRegularSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsInverseSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "NilpotencyDegree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsBand",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsBrandtSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsCliffordSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsCommutativeSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsCompletelyRegularSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsCompletelySimpleSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsGroupAsSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsIdempotentGenerated",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsLeftZeroSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsMonogenicSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsMonoidAsSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsNilpotentSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsOrthodoxSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsRectangularBand",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsRightZeroSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsSemiband",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsSemilattice",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsZeroSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsLeftActedOnBySuperset"
+        ],
+        "name": "IsLeftSemigroupIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsRightActedOnBySuperset"
+        ],
+        "name": "IsRightSemigroupIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsLeftActedOnBySuperset",
+            "IsMagma",
+            "IsRightActedOnBySuperset"
+        ],
+        "name": "IsSemigroupIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsLeftActedOnBySuperset",
+            "IsMagma",
+            "IsRightActedOnBySuperset"
+        ],
+        "name": "ReesCongruenceOfSemigroupIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "AsMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NameIsomorphismClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsCyclic",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsElementaryAbelian",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsFinitelyGeneratedGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSubsetLocallyFiniteGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "KnowsHowToDecompose",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsPGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPGroup"
+        ],
+        "name": "PrimePGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPGroup"
+        ],
+        "name": "PClassPGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPGroup"
+        ],
+        "name": "RankPGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsNilpotentGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsPerfectGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSporadicSimpleGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSimpleGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAlmostSimpleGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSupersolvableGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsMonomialGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSolvableGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsPolycyclicGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AbelianInvariants",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsInfiniteAbelianizationGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "AsGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ChiefSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CommutatorFactorGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CompositionSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ConjugacyClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ConjugacyClassesMaximalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MaximalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MaximalSubgroupClassReps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PerfectResiduum",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RepresentativesPerfectSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RepresentativesSimpleSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ConjugacyClassesPerfectSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ConjugacyClassesSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "LatticeSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DerivedLength",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "HirschLength",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DerivedSeriesOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DerivedSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MaximalAbelianQuotient",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CommutatorLength",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DimensionsLoewyFactors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ElementaryAbelianSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ElementaryAbelianSeriesLargeSteps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Exponent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FittingSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PrefrattiniSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FrattiniSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InvariantForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "JenningsSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "LowerCentralSeriesOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NilpotencyClassOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MaximalNormalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalMaximalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MinimalNormalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NrConjugacyClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedOmegas",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedAgemos",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RadicalGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RationalClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma"
+        ],
+        "name": "GeneratorsSmallest",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "LargestElementGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MinimalGeneratingSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SmallGeneratingSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SupersolvableResiduum",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComplementSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SylowSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "HallSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Socle",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "UpperCentralSeriesOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CoreInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IndexInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IndexInWholeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "IsCommutative"
+        ],
+        "name": "IndependentGeneratorsOfAbelianGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsNormalInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedIsPNilpotents",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedIsPSolvables",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalClosureInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "NormalizerInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedPCentralSeriess",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedPRumps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedPCores",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SubnormalSeriesInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedSylowSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedSylowComplements",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedHallSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(GeneratorsOfMagmaWithInverses)"
+        ],
+        "name": "GrowthFunctionOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ElementTestFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RightTransversalInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismTypeInfoFiniteSimpleGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismPcGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismSpecialPcGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismPermGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismFpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElement"
+        ],
+        "name": "PrimePowerComponents",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsListOrCollection"
+        ],
+        "name": "IsGeneratorsOfInverseSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInverseSemigroup"
+        ],
+        "name": "GeneratorsOfInverseMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInverseSemigroup"
+        ],
+        "name": "GeneratorsOfInverseSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "AsInverseSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCollection"
+        ],
+        "name": "AsInverseMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "ReverseNaturalPartialOrder",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "NaturalPartialOrder",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagma"
+        ],
+        "name": "IsAdditivelyCommutative",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagma"
+        ],
+        "name": "GeneratorsOfNearAdditiveMagma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagmaWithZero"
+        ],
+        "name": "GeneratorsOfNearAdditiveMagmaWithZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup"
+        ],
+        "name": "GeneratorsOfNearAdditiveGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagmaWithZero"
+        ],
+        "name": "TrivialSubnearAdditiveMagmaWithZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagma"
+        ],
+        "name": "AdditiveNeutralElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "IsLDistributive",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "IsRDistributive",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfSemiring",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagmaWithOne",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfSemiringWithOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfSemiringWithZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagmaWithZero",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagmaWithOne",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfSemiringWithOneAndZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "AsSemiring",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "AsSemiringWithOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "AsSemiringWithZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "AsSemiringWithOneAndZero",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "CentralIdempotentsOfSemiring",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "AsNearRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+            "CategoryCollections(IsAdditiveElement)",
+            "CategoryCollections(IsMultiplicativeElement)"
+        ],
+        "name": "AsRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne"
+        ],
+        "name": "GeneratorsOfRingWithOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsAnticommutative",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsIntegralRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsJacobianRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsZeroSquaredRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsZeroMultiplicationRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "Units",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "IsGeneralizedCartanMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "BaseMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "BaseOrthogonalSpaceMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "DefaultFieldOfMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "DepthOfUpperTriangularMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "DeterminantMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "DimensionsMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "NullspaceMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "TriangulizedNullspaceMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "ProjectiveOrder",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "RankMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "SemiEchelonMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "SemiEchelonMatTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "TransposedMatImmutable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "IsMonomialMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "JordanDecomposition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "CharacteristicPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+        ],
+        "name": "BaseIntMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+        ],
+        "name": "NullspaceIntMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsCyclotomic)"
+        ],
+        "name": "AbelianInvariantsOfList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "MatrixByBlockMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsTwoSidedIdealInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsLeftIdealInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "IsRightIdealInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfTwoSidedIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfLeftIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "GeneratorsOfRightIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "LeftActingRingOfIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "RightActingRingOfIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "IsFiniteDimensional",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "IsFullRowModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "IsFullMatrixModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "Dimension",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum"
+        ],
+        "name": "GeneratorsOfLeftOperatorAdditiveGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtRSet",
+            "IsDistributiveROpDSum"
+        ],
+        "name": "GeneratorsOfRightOperatorAdditiveGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "IsRowModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "IsMatrixModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "DimensionOfVectors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsCanonicalBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsCanonicalBasisFullRowModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsCanonicalBasisFullMatrixModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsIntegralBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsNormalBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsSemiEchelonized",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "BasisVectors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "EnumeratorByBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "StructureConstantsTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "UnderlyingLeftModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "Basis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "SemiEchelonBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasisByNiceBasis"
+        ],
+        "name": "NiceBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "NiceFreeLeftModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule",
+            "IsHandledByNiceBasis"
+        ],
+        "name": "NiceFreeLeftModuleInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "CanonicalBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGaussianSpace"
+        ],
+        "name": "NormedRowVectors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne"
+        ],
+        "name": "Subspaces",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGaussianSpace"
+        ],
+        "name": "OrthogonalSpaceInFullRowSpace",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "IsVectorSpaceHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "AsLeftModuleGeneralMappingByImages",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule"
+        ],
+        "name": "IsFullHomModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsPseudoCanonicalBasisFullHomModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "IsSimpleAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "GeneratorsOfLeftOperatorRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "GeneratorsOfLeftOperatorRingWithOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "PowerSubalgebraSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "AdjointBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IndicesOfAdjointBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "RadicalOfAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "DirectSumDecomposition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "NullAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "LieAlgebraByDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "LeviMalcevDecomposition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "Grading",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations"
+        ],
+        "name": "CoefficientsAndMagmaElements",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations"
+        ],
+        "name": "ZeroCoefficient",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeMagmaRing"
+        ],
+        "name": "IsGroupRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeMagmaRing"
+        ],
+        "name": "UnderlyingMagma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeMagmaRing"
+        ],
+        "name": "AugmentationIdeal",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "CategoryCollections(IsElementOfFpAlgebra)"
+        ],
+        "name": "IsFullFpAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubalgebraFpAlgebra",
+            "IsFullFpAlgebra"
+        ],
+        "name": "FreeGeneratorsOfFpAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubalgebraFpAlgebra",
+            "IsFullFpAlgebra"
+        ],
+        "name": "RelatorsOfFpAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubalgebraFpAlgebra",
+            "IsFullFpAlgebra"
+        ],
+        "name": "FreeAlgebraOfFpAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsNormalForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "NiceNormalFormByExtRepFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubalgebraFpAlgebra"
+        ],
+        "name": "NiceAlgebraMonomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "IsLieAbelian",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "IsLieNilpotent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "IsRestrictedLieAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieDerivedSubalgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieDerivedSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "IsLieSolvable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieLowerCentralSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieUpperCentralSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieCentre",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "RightDerivations",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "LeftDerivations",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "KillingMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "CartanSubalgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "PthPowerImages",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "NonNilpotentElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieNilRadical",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieSolvableRadical",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "SemiSimpleType",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieCentralizerInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieNormalizerInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "PowerS",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystemFromLieAlgebra"
+        ],
+        "name": "UnderlyingLieAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "RootSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystem"
+        ],
+        "name": "PositiveRoots",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystem"
+        ],
+        "name": "NegativeRoots",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystemFromLieAlgebra"
+        ],
+        "name": "PositiveRootVectors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystemFromLieAlgebra"
+        ],
+        "name": "NegativeRootVectors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystem"
+        ],
+        "name": "SimpleSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystem"
+        ],
+        "name": "CartanMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystem"
+        ],
+        "name": "BilinearFormMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystemFromLieAlgebra"
+        ],
+        "name": "CanonicalGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "ChevalleyBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "UniversalEnvelopingAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "JenningsLieAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PCentralLieAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "CategoryCollections(IsSCAlgebraObj)"
+        ],
+        "name": "IsFullSCAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsCanonicalBasisFullSCAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "IsomorphismFpFLMLOR",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFreeLeftModule",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "IsomorphismMatrixFLMLOR",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsomorphismSCFLMLOR",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "LieFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "UnderlyingFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsMultiplicativeElement"
+        ],
+        "name": "LieObject",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieObject"
+        ],
+        "name": "UnderlyingRingElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne"
+        ],
+        "name": "IsAlgebraModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne"
+        ],
+        "name": "IsLeftAlgebraModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne"
+        ],
+        "name": "IsRightAlgebraModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAlgebraModule"
+        ],
+        "name": "LeftActingAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAlgebraModule"
+        ],
+        "name": "RightActingAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAlgebraModule"
+        ],
+        "name": "GeneratorsOfAlgebraModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "AdjointModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd"
+        ],
+        "name": "FaithfulModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsWeylGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystem"
+        ],
+        "name": "WeylGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsWeylGroup"
+        ],
+        "name": "SparseCartanMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsWeylGroup"
+        ],
+        "name": "LongestWeylWordPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRootSystem"
+        ],
+        "name": "PositiveRootsAsWeights",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LatticeGeneratorsInUEA",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInt"
+        ],
+        "name": "PrimeDivisors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "CategoryCollections(IsSCRingObj)"
+        ],
+        "name": "StandardGeneratorsSubringSCRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "Subrings",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "Ideals",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DirectSumInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "RationalFunctionsFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "CoefficientsFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialFunction"
+        ],
+        "name": "NumeratorOfRationalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRationalFunction"
+        ],
+        "name": "DenominatorOfRationalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialFunction"
+        ],
+        "name": "IsPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialFunction",
+            "IsPolynomial"
+        ],
+        "name": "AsPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRationalFunction"
+        ],
+        "name": "IsUnivariateRationalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialFunction"
+        ],
+        "name": "IsLaurentPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialFunction"
+        ],
+        "name": "IsConstantRationalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialFunction"
+        ],
+        "name": "ExtRepNumeratorRatFun",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRationalFunction"
+        ],
+        "name": "ExtRepDenominatorRatFun",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialFunction",
+            "IsPolynomial"
+        ],
+        "name": "ExtRepPolynomialRatFun",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLaurentPolynomial"
+        ],
+        "name": "CoefficientsOfLaurentPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "IndeterminateNumberOfUnivariateRationalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "IndeterminateOfUnivariateRationalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "CoefficientsOfUnivariatePolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLaurentPolynomial"
+        ],
+        "name": "DegreeOfLaurentPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "CoefficientsOfUnivariateRationalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "Derivative",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial"
+        ],
+        "name": "Discriminant",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing"
+        ],
+        "name": "PrimeField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing"
+        ],
+        "name": "IsPrimeField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "DefiningPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing"
+        ],
+        "name": "DegreeOverPrimeField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing"
+        ],
+        "name": "GeneratorsOfDivisionRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "NormalBase",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing"
+        ],
+        "name": "PrimitiveElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative",
+            "IsFinite"
+        ],
+        "name": "PrimitiveRoot",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "RootOfDefiningPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "Subfields",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "Conjugates",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "Norm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "Trace",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "GaloisGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "ComplexConjugate",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "RealPart",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveElementWithInverse",
+            "IsAdditiveElement",
+            "IsMultiplicativeElementWithInverse"
+        ],
+        "name": "ImaginaryPart",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "FrobeniusAutomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsZmodnZObj"
+        ],
+        "name": "ModulusOfZmodnZObj",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsZmodnZepsObj"
+        ],
+        "name": "Cyclotomic",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne"
+        ],
+        "name": "IsRingOfIntegralCyclotomics",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "GaloisMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "RationalizedMat",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "IsNumberField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "IsAbelianNumberField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInversesIfNonzero",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNonTrivial",
+            "IsAssociative",
+            "IsEuclideanRing",
+            "IsCommutative"
+        ],
+        "name": "IsCyclotomicField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAbelianNumberField"
+        ],
+        "name": "GaloisStabilizer",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued"
+        ],
+        "name": "ExponentOfPowering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialRing"
+        ],
+        "name": "CoefficientsRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomialRing"
+        ],
+        "name": "IndeterminatesOfPolynomialRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial"
+        ],
+        "name": "SplittingField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial"
+        ],
+        "name": "IrrFacsPol",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsRationalFunctionsFamilyElement"
+        ],
+        "name": "MinimizedBombieriNorm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "AlgebraicElementsFamilies",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAlgebraicExtension"
+        ],
+        "name": "DefectApproximation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections((IsWord and IsAssociativeElement))",
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsFreeSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))",
+            "IsMagmaWithOne",
+            "IsAssociative"
+        ],
+        "name": "IsFreeMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsWord",
+            "IsAssociativeElement"
+        ],
+        "name": "NumberSyllables",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRowVectorObj"
+        ],
+        "name": "BaseDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMatrixObj"
+        ],
+        "name": "RowLength",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsBuiltFromAdditiveMagmaWithInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsBuiltFromMagma",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsBuiltFromMagmaWithOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsBuiltFromMagmaWithInverses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsBuiltFromGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsBuiltFromSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsBuiltFromMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "SemigroupOfRewritingSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "MonoidOfRewritingSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "ConfluentRws",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "GeneratorsOfRws",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "NumberGeneratorsOfRws",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "Rules",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "OrderingOfRewritingSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "IsConfluent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem",
+            "IsMutable"
+        ],
+        "name": "IsReduced",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "RelativeOrders",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "DefiningPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMonomialOrdering"
+        ],
+        "name": "MonomialComparisonFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "MonomialExtrepComparisonFun",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMonomialOrdering"
+        ],
+        "name": "OccuringVariableIndices",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "CategoryCollections(IsRationalFunction)",
+            "Tester(LeftActingRingOfIdeal)",
+            "Tester(RightActingRingOfIdeal)"
+        ],
+        "name": "StoredGroebnerBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsModuloPcgs"
+        ],
+        "name": "PcGroupWithPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "GroupOfPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "OneOfPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "PcSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsPcgsElementaryAbelianSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PcgsElementaryAbelianSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IndicesEANormalSteps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "EANormalSeriesByPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsPcgsCentralSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PcgsCentralSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IndicesCentralNormalSteps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "CentralNormalSeriesByPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsPcgsPCentralSeriesPGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PcgsPCentralSeriesPGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IndicesPCentralNormalStepsPGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "PCentralNormalSeriesByPcgsPGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsPcgsChiefSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PcgsChiefSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IndicesChiefNormalSteps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "ChiefNormalSeriesByPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IndicesNormalSteps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "NormalSeriesByPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralPcgs"
+        ],
+        "name": "IsPrimeOrdersPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralPcgs"
+        ],
+        "name": "IsFiniteOrdersPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RefinedPcGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismRefinedPcGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInducedPcgs"
+        ],
+        "name": "LeadCoeffsIGS",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInducedPcgs"
+        ],
+        "name": "ParentPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInducedPcgs"
+        ],
+        "name": "CanonicalPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInducedPcgs"
+        ],
+        "name": "IsCanonicalPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInducedPcgs"
+        ],
+        "name": "IsParentPcgsFamilyPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "ElementaryAbelianSubseries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsFamilyPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsModuloPcgs"
+        ],
+        "name": "DenominatorOfModuloPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsModuloPcgs"
+        ],
+        "name": "NumeratorOfModuloPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsModuloPcgs"
+        ],
+        "name": "IsNumeratorParentPcgsFamilyPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsSpecialPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "SpecialPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "LGHeads",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "LGTails",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "LGWeights",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "LGLayers",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "LGFirst",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "LGLength",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InducedPcgsWrtSpecialPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CanonicalPcgsWrtSpecialPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsInducedPcgsWrtSpecialPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcgs"
+        ],
+        "name": "IsCanonicalPcgsWrtSpecialPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CanonicalPcgsWrtFamilyPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CanonicalPcgsWrtHomePcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FamilyPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "HomePcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InducedPcgsWrtFamilyPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedInducedPcgses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InducedPcgsWrtHomePcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Pcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "GeneralizedPcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "OmegaSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "Tester(HomePcgs)"
+        ],
+        "name": "NormalizerInHomePcgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsHomogeneousList"
+        ],
+        "name": "MultiplicationTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "AllBlocks",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "TransitiveIdentification",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "PrimitiveIdentification",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "ONanScottType",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "SocleTypePrimitiveGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "TwoClosure",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "RespectsInverses"
+        ],
+        "name": "AsGroupGeneralMappingByImages",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "RespectsInverses"
+        ],
+        "name": "MappingOfWhichItIsAsGGMBI",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NaturalHomomorphismByNormalSubgroupNCInParent",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "RespectsInverses"
+        ],
+        "name": "IsConjugatorIsomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "RespectsInverses"
+        ],
+        "name": "IsInnerAutomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsConjugatorIsomorphism"
+        ],
+        "name": "ConjugatorOfConjugatorIsomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "RespectsInverses"
+        ],
+        "name": "ImagesSmallestGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RegularActionHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DirectProductInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SubdirectProductInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SemidirectProductInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "WreathProductInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FreeProductInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "IsNaturalSymmetricGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "IsNaturalAlternatingGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAlternatingGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSymmetricGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "SymmetricParentGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "AlternatingSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "OrbitStabilizingParentGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DirectFactorsOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SemidirectFactorsOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DecompositionTypesOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsDihedralGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DihedralGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsQuaternionGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "QuaternionGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsQuasiDihedralGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "QuasiDihedralGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsPSL",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ParametersOfGroupViewedAsPSL",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ParametersOfGroupViewedAsSL",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ParametersOfGroupViewedAsGL",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AlternatingDegree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SymmetricDegree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PSLDegree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PSLUnderlyingField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SLDegree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SLUnderlyingField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "GLDegree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "GLUnderlyingField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "StructureDescription",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuotientSystem"
+        ],
+        "name": "IsPQuotientSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuotientSystem"
+        ],
+        "name": "IsNilpQuotientSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "ActingDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "HomeEnumerator",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "ActionKernelExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLinearActionHomomorphism"
+        ],
+        "name": "LinearActionBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "FunctionAction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "StabilizerOfExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "CanonicalRepresentativeOfExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "CanonicalRepresentativeDeterminatorOfExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "CanEasilyDetermineCanonicalRepresentativeExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "ActorOfExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "ActionHomomorphismAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "SurjectiveActionHomomorphismAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsActionHomomorphism"
+        ],
+        "name": "UnderlyingExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "ExternalSet",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "Orbits",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "OrbitsDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "OrbitLengths",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "OrbitLengthsDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "ExternalOrbits",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "ExternalOrbitsStabilizers",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "Transitivity",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "BlocksAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "MaximalBlocksAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "RepresentativesMinimalBlocksAttr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "Earns",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "IsTransitive",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "IsPrimitive",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "IsPrimitiveAffine",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "IsSemiRegular",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "IsRegular",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsExternalSet"
+        ],
+        "name": "RankAction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "StabChainMutable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "StabChainImmutable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "StabChainOptions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "BaseOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "MinimalStabChain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRationalClassGroupRep"
+        ],
+        "name": "DecomposedRationalClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "StoredPermliftSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedAscendingChains",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsDoubleCoset"
+        ],
+        "name": "LeftActingGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsDoubleCoset"
+        ],
+        "name": "RightActingGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsDoubleCoset"
+        ],
+        "name": "RepresentativesContainedRightCosets",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NaturalHomomorphismsPool",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SocleComplement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SocleDimensions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ModuleOfExtension",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "OmegaAndLowerPCentralSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SchurCover",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "EpimorphismSchurCover",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AbelianInvariantsMultiplier",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Epicentre",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsCentralFactor",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Zuppos",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLatticeSubgroupsRep"
+        ],
+        "name": "MaximalSubgroupsLattice",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLatticeSubgroupsRep"
+        ],
+        "name": "MinimalSupergroupsLattice",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "TomDataAlmostSimpleRecognition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsFrattiniFree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsStraightLineProgram"
+        ],
+        "name": "LinesOfStraightLineProgram",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsStraightLineProgram"
+        ],
+        "name": "NrInputsOfStraightLineProgram",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "StraightLineProgElmType",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsStraightLineProgram"
+        ],
+        "name": "SlotUsagePattern",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsStraightLineProgram"
+        ],
+        "name": "LargestNrSlots",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "TypeOfObjWithMemory",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryFamily(IsElementOfFpGroup)"
+        ],
+        "name": "FpElmEqualityMethod",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryFamily(IsElementOfFpGroup)"
+        ],
+        "name": "FpElmComparisonMethod",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryFamily(IsElementOfFpGroup)"
+        ],
+        "name": "FpElementNFFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CosetTableInWholeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CosetTableNormalClosureInWholeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup"
+        ],
+        "name": "AsSubgroupOfWholeGroupByQuotient",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup",
+            "IsGroupOfFamily"
+        ],
+        "name": "FreeGeneratorsOfFpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup",
+            "IsGroupOfFamily"
+        ],
+        "name": "RelatorsOfFpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup",
+            "IsGroupOfFamily"
+        ],
+        "name": "FreeGroupOfFpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup",
+            "IsGroupOfFamily"
+        ],
+        "name": "IndicesInvolutaryGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup"
+        ],
+        "name": "StoredExcludedOrders",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "FPFaithHom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AugmentedCosetTableMtcInWholeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AugmentedCosetTableRrsInWholeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AugmentedCosetTableNormalClosureInWholeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPresentation"
+        ],
+        "name": "PrimaryGeneratorWords",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup"
+        ],
+        "name": "TietzeOrigin",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPresentation"
+        ],
+        "name": "TzOptions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupGeneralMappingByImages"
+        ],
+        "name": "IsWordDecompHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "CosetTableFpHom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsSubgroupFpGroup"
+        ],
+        "name": "IsomorphismSimplifiedFpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "EpimorphismFromFreeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "NiceMonomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "RespectsInverses"
+        ],
+        "name": "IsCanonicalNiceMonomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "CanonicalNiceMonomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "NiceObject",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsHandledByNiceMonomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SeedFaithfulAction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralizedDomain",
+            "IsCollection"
+        ],
+        "name": "AutomorphismGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsGroupOfAutomorphisms",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsGroupOfAutomorphismsFiniteGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfAutomorphisms"
+        ],
+        "name": "AutomorphismDomain",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfAutomorphisms"
+        ],
+        "name": "IsAutomorphismGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InnerAutomorphismsAutomorphismGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DefaultFieldOfMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DimensionOfMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FieldOfMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "TransposedMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsGeneralLinearGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsNaturalGL",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSpecialLinearGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsNaturalSL",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSubgroupSL",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InvariantBilinearForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsFullSubgroupGLorSLRespectingBilinearForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InvariantSesquilinearForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsFullSubgroupGLorSLRespectingSesquilinearForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InvariantQuadraticForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsFullSubgroupGLorSLRespectingQuadraticForm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FittingFreeLiftSetup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued"
+        ],
+        "name": "RecogDecompinfoHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DirectFactorsFittingFreeSocle",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ChiefSeriesTF",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsRationalMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsIntegerMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ZClassRepsQClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalizerInGLnZ",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CentralizerInGLnZ",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsBravaisGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "BravaisGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "BravaisSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "BravaisSupergroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalizerInGLnZBravaisGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "InvariantLattice",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PerfectIdentification",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DataAboutSimpleGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ImfRecord",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "OrderingsFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "IsWellFoundedOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "IsTotalOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "FamilyForOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "LessThanFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "LessThanOrEqualFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "IsOrderingOnFamilyOfAssocWords",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrderingOnFamilyOfAssocWords"
+        ],
+        "name": "LetterRepWordsLessFunc",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering",
+            "IsOrderingOnFamilyOfAssocWords"
+        ],
+        "name": "IsTranslationInvariantOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering",
+            "IsOrderingOnFamilyOfAssocWords"
+        ],
+        "name": "OrderingOnGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering",
+            "IsOrderingOnFamilyOfAssocWords"
+        ],
+        "name": "IsShortLexOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering",
+            "IsOrderingOnFamilyOfAssocWords"
+        ],
+        "name": "WeightOfGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering",
+            "IsOrderingOnFamilyOfAssocWords"
+        ],
+        "name": "IsWeightLexOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "IsBasicWreathProductOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering"
+        ],
+        "name": "IsWreathProductOrdering",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdering",
+            "IsWreathProductOrdering"
+        ],
+        "name": "LevelsOfGenerators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "LargestImageOfMovedPoint",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "SmallestImageOfMovedPoint",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "RankOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAssociativeElement"
+        ],
+        "name": "AsPermutation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAssociativeElement"
+        ],
+        "name": "AsTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "PermutationOfImage",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsTransformation)"
+        ],
+        "name": "DegreeOfTransformationCollection",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "FlatKernelOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "ImageSetOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "IndexPeriodOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "KernelOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAssociativeElement"
+        ],
+        "name": "SmallestIdempotentPower",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "ComponentRepsOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "NrComponentsOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "ComponentsOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTransformation"
+        ],
+        "name": "CyclesOfTransformation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAssociativeElement"
+        ],
+        "name": "LeftOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAssociativeElement"
+        ],
+        "name": "RightOne",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "DomainOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "ImageListOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "ImageSetOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "IndexPeriodOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "ComponentRepsOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "NrComponentsOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "ComponentsOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "FixedPointsOfPartialPerm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPartialPerm"
+        ],
+        "name": "NrFixedPoints",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "DegreeOfPartialPermCollection",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "CodegreeOfPartialPermCollection",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "RankOfPartialPermCollection",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "DomainOfPartialPermCollection",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "ImageOfPartialPermCollection",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued",
+            "IsEndoGeneralMapping"
+        ],
+        "name": "TransformationRepresentation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsElementOfFpSemigroup)",
+            "IsWholeFamily"
+        ],
+        "name": "FreeGeneratorsOfFpSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsElementOfFpSemigroup)",
+            "IsWholeFamily"
+        ],
+        "name": "FreeSemigroupOfFpSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsElementOfFpSemigroup)",
+            "IsWholeFamily"
+        ],
+        "name": "RelationsOfFpSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismFpSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithOne",
+            "IsAssociative",
+            "CategoryCollections(IsElementOfFpMonoid)",
+            "IsWholeFamily"
+        ],
+        "name": "FreeGeneratorsOfFpMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithOne",
+            "IsAssociative",
+            "CategoryCollections(IsElementOfFpMonoid)",
+            "IsWholeFamily"
+        ],
+        "name": "FreeMonoidOfFpMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithOne",
+            "IsAssociative",
+            "CategoryCollections(IsElementOfFpMonoid)",
+            "IsWholeFamily"
+        ],
+        "name": "RelationsOfFpMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithOne",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismFpMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "ReducedConfluentRewritingSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "FreeMonoidOfRewritingSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "FamilyForRewritingSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRewritingSystem"
+        ],
+        "name": "FreeSemigroupOfRewritingSystem",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsKnuthBendixRewritingSystem"
+        ],
+        "name": "TzRules",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRightMagmaCongruence"
+        ],
+        "name": "CosetTableOfFpSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "AdjoinedIdentityFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "UnderlyingSemigroupFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "AdjoinedIdentityDefaultType",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "MonoidByAdjoiningIdentity",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMonoidByAdjoiningIdentity"
+        ],
+        "name": "UnderlyingSemigroupOfMonoidByAdjoiningIdentity",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMultiplicativeElement",
+            "IsAssociativeElement"
+        ],
+        "name": "MonoidByAdjoiningIdentityElt",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMonoidByAdjoiningIdentityElt"
+        ],
+        "name": "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensRelation"
+        ],
+        "name": "IsFiniteSemigroupGreensRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensRRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensLRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensJRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensDRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensHRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsElementOfFpSemigroup)",
+            "IsWholeFamily"
+        ],
+        "name": "AssociatedConcreteSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "AssociatedFpSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensRClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensLClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensJClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensDClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "GreensHClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensHClass"
+        ],
+        "name": "RClassOfHClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensHClass"
+        ],
+        "name": "LClassOfHClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensHClass"
+        ],
+        "name": "DClassOfHClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensLClass"
+        ],
+        "name": "DClassOfLClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensRClass"
+        ],
+        "name": "DClassOfRClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensDClass"
+        ],
+        "name": "GroupHClassOfGreensDClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensDClass"
+        ],
+        "name": "IsRegularDClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensHClass"
+        ],
+        "name": "IsGroupHClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensDClass"
+        ],
+        "name": "EggBoxOfDClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensRelation"
+        ],
+        "name": "InternalRepGreensRelation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensClass"
+        ],
+        "name": "CanonicalGreensClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfFpSemigroup"
+        ],
+        "name": "IsFpSemigpReducedElt",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfFpMonoid"
+        ],
+        "name": "IsFpMonoidReducedElt",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsFullTransformationSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsTransformation)"
+        ],
+        "name": "DegreeOfTransformationSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismTransformationSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismTransformationMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "AntiIsomorphismTransformationSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsReesMatrixSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsReesZeroMatrixSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsReesMatrixSemigroupElement)"
+        ],
+        "name": "Matrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsReesMatrixSemigroupElement)"
+        ],
+        "name": "Rows",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsReesMatrixSemigroupElement)"
+        ],
+        "name": "Columns",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsReesMatrixSemigroupElement)"
+        ],
+        "name": "UnderlyingSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGreensDClass"
+        ],
+        "name": "AssociatedReesMatrixSemigroupOfDClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismReesMatrixSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismReesZeroMatrixSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "ReesMatrixSemigroupOfFamily",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsReesMatrixSemigroupElement)"
+        ],
+        "name": "TypeReesMatrixSemigroupElements",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuotientSemigroup"
+        ],
+        "name": "QuotientSemigroupPreimage",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuotientSemigroup"
+        ],
+        "name": "QuotientSemigroupCongruence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsQuotientSemigroup"
+        ],
+        "name": "QuotientSemigroupHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "DegreeOfPartialPermSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "CodegreeOfPartialPermSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "RankOfPartialPermSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative",
+            "CategoryCollections(IsPartialPerm)"
+        ],
+        "name": "IsSymmetricInverseSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismPartialPermSemigroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagma",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismPartialPermMonoid",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "UnderlyingGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "IdentificationOfConjugacyClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CharacterDegrees",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Irr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "LinearCharacters",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBrauerTable"
+        ],
+        "name": "IBr",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "OrdinaryCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsAlmostSimpleCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsMonomialCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsNilpotentCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsPerfectCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsSimpleCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsSolvableCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsSporadicSimpleCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsSupersolvableCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "OrdersClassRepresentatives",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "SizesCentralizers",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "SizesConjugacyClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "AutomorphismsOfTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "UnderlyingCharacteristic",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ClassNames",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "CharacterNames",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ClassParameters",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "CharacterParameters",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "Identifier",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "InverseClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "RealClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCharacterTable"
+        ],
+        "name": "ClassRoots",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfNormalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfMaximalNormalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfMinimalNormalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfCentre",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfDirectProductDecompositions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfDerivedSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfElementaryAbelianSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfFittingSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfSolvableRadical",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfLowerCentralSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfUpperCentralSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfSolvableResiduum",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ClassPositionsOfSupersolvableResiduum",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ComputedPrimeBlockss",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "BlocksInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBrauerTable"
+        ],
+        "name": "DecompositionMatrix",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ComputedIsPSolvableCharacterTables",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCharacterTable"
+        ],
+        "name": "ComputedIndicators",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "ComputedBrauerTables",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "DisplayOptions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "FactorsOfDirectProduct",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "CharacterTableIsoclinic",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "SourceOfIsoclinicTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ClassPermutation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "NormalSubgroupClassesInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "UnderlyingCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "ValuesOfClassFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "GlobalPartitionOfClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "TrivialCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NaturalCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsVirtualCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsIrreducibleCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "CentreOfCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "ConstituentsOfCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "DegreeOfCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "KernelOfCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsHomogeneousList"
+        ],
+        "name": "ClassPositionsOfKernel",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "CentralCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "DeterminantOfCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+            "IsTable",
+            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+            "IsTable"
+        ],
+        "name": "BrauerCharacterValue",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ComputedPowerMaps",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping"
+        ],
+        "name": "FusionConjugacyClassesOp",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ComputedClassFusions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "NamesOfFusionSources",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "BaumClausenInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "IsFinite"
+        ],
+        "name": "IrreducibleRepresentations",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IrrBaumClausen",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IrrConlon",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRationalFunction"
+        ],
+        "name": "MolienSeriesInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Alpha",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Delta",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsBergerCondition",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsPrimitiveCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "TestQuasiPrimitive",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsQuasiPrimitive",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsInducedFromNormalSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsMonomialCharacter",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInt",
+            "IsPosRat"
+        ],
+        "name": "IsMonomialNumber",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "TestMonomialQuick",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "TestMonomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "TestSubnormallyMonomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSubnormallyMonomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "TestRelativelySM",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClassFunction"
+        ],
+        "name": "IsRelativelySM",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsMinimalNonmonomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DixonRecord",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IrrDixonSchneider",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "TableOfMarks",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "PermutationTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "MarksTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "SubsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "NrSubsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "OrdersTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "LengthsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "ClassTypesTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "ClassNamesTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "FusionsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "IdempotentsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "IdempotentsTomInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "MatTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "MoebiusTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "WeightsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "IsAbelianTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "IsCyclicTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "IsNilpotentTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "IsPerfectTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "IsSolvableTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "DerivedSubgroupsTomPossible",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "DerivedSubgroupsTomUnique",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "NormalizersTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "CyclicExtensionsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "ComputedCyclicExtensionsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "MaximalSubgroupsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "GeneratorsSubgroupsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks"
+        ],
+        "name": "StraightLineProgramsTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFile"
+        ],
+        "name": "ProcessID",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IdGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "Gap3CatalogueIdGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FrattinifactorSize",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FrattinifactorId",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsRationalFunction"
+        ],
+        "name": "GaloisType",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPerm)"
+        ],
+        "name": "SimsNo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MinimalBlockDimension",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsPrimitiveMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "IrrFacsAlgExtPol",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsUnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued"
+        ],
+        "name": "IsUnitGroupIsomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField"
+        ],
+        "name": "IsNumberFieldByMatrices",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued"
+        ],
+        "name": "IsMultGroupByFieldElemsIsomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField"
+        ],
+        "name": "IntegerDefiningPolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField"
+        ],
+        "name": "IntegerPrimitiveElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField"
+        ],
+        "name": "EquationOrderBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField"
+        ],
+        "name": "MaximalOrderBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField"
+        ],
+        "name": "UnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FieldOfUnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolycyclicCollector"
+        ],
+        "name": "IsWeightedCollector",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFromTheLeftCollectorRep"
+        ],
+        "name": "IsPolynomialCollector",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFromTheLeftCollectorRep"
+        ],
+        "name": "UseLibraryCollector",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFromTheLeftCollectorRep"
+        ],
+        "name": "IsPolycyclicPresentation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcpElement"
+        ],
+        "name": "TailOfElm",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcpElement"
+        ],
+        "name": "RelativeOrderPcp",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcpElement"
+        ],
+        "name": "RelativeIndex",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPcpElement"
+        ],
+        "name": "FactorOrder",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPcpElement)"
+        ],
+        "name": "Igs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPcpElement)"
+        ],
+        "name": "Ngs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPcpElement)"
+        ],
+        "name": "Cgs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPcpElement)"
+        ],
+        "name": "EfaSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPcpElement)"
+        ],
+        "name": "PcpsOfEfaSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsomorphismPcpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PcpGroupByEfaSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupGeneralMappingByImages"
+        ],
+        "name": "IsHomomorphismIntoMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative",
+            "CategoryCollections(IsPcpElement)"
+        ],
+        "name": "SemiSimpleEfaSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FCCentre",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsNilpotentByFinite",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedMaximalSubgroupClassesByIndexs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedLowIndexSubgroupClassess",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedLowIndexNormalSubgroupss",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SchurExtension",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SchurExtensionEpimorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NonAbelianTensorSquare",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NonAbelianExteriorSquare",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "TorsionSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalTorsionSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FiniteSubgroupClasses",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsTorsionFree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsFreeAbelian",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClass"
+        ],
+        "name": "MemberFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "ComputedIsMembers",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClass"
+        ],
+        "name": "IsGroupClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "GroupClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "ContainsTrivialGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsSubgroupClosed",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsNormalSubgroupClosed",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsQuotientClosed",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsResiduallyClosed",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsNormalProductClosed",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsDirectProductClosed",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsSchunckClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "IsSaturated",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "FittingClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClass"
+        ],
+        "name": "InjectorFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsClass"
+        ],
+        "name": "RadicalFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsPrimitiveSolvableGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "SchunckClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "Boundary",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "ProjectorFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "BoundaryFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "OrdinaryFormation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "SaturatedFormation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "FittingFormation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "SaturatedFittingFormation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "ResidualFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupClass"
+        ],
+        "name": "LocalDefinitionFunction",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedProjectors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedCoveringSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedInjectors",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedRadicals",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedResiduals",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CharacteristicSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalGeneratorsOfNilpotentResidual",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "PrimePowerGensPcSequence",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NilpotentProjector",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SupersolvableProjector",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SolvableSocle",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SocleComponents",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SolvableSocleComponents",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedPSocleComponentss",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedPSocles",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AbelianMinimalNormalSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsStraightLineDecision"
+        ],
+        "name": "LinesOfStraightLineDecision",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsStraightLineDecision"
+        ],
+        "name": "NrInputsOfStraightLineDecision",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsStraightLineProgram"
+        ],
+        "name": "AsBBoxProgram",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBBoxProgram"
+        ],
+        "name": "AsStraightLineProgram",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBBoxProgram"
+        ],
+        "name": "AsStraightLineDecision",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnknown"
+        ],
+        "name": "Maxes",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AtlasRepInfoRecord",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "CASInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ConstructionInfoCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "FusionToTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ProjectivesInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "ExtensionInfoCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "GroupInfoForCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "KnowsSomeGroupInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsNontrivialDirectProduct",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "KnowsDeligneLusztigNames",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IsDuplicateTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IdentifierOfMainTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "IdentifiersOfDuplicateTables",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCharacterTable"
+        ],
+        "name": "DeligneLusztigNames",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsCharacter"
+        ],
+        "name": "DeligneLusztigName",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsOrdinaryTable"
+        ],
+        "name": "FingerprintOfCharacterTable",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearlyCharacterTable"
+        ],
+        "name": "SpinSymIngredients",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks",
+            "IsLibTomRep"
+        ],
+        "name": "NamesLibTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks",
+            "IsLibTomRep"
+        ],
+        "name": "NotifiedFusionsOfLibTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks",
+            "IsLibTomRep"
+        ],
+        "name": "FusionsOfLibTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks",
+            "IsLibTomRep"
+        ],
+        "name": "NotifiedFusionsToLibTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsTableOfMarks",
+            "IsLibTomRep"
+        ],
+        "name": "FusionsToLibTom",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "StandardGeneratorsInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInvAutomatonCategory"
+        ],
+        "name": "FGA_States",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsInvAutomatonCategory"
+        ],
+        "name": "FGA_GeneratorsLetterRep",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FreeGeneratorsOfGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RankOfFreeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FreeGroupAutomaton",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FreeGroupExtendedAutomaton",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NormalizerInWholeGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFromFpGroupGeneralMappingByImages"
+        ],
+        "name": "FGA_Source",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsToFpGroupGeneralMappingByImages"
+        ],
+        "name": "FGA_Image",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "RespectsMultiplication",
+            "RespectsInverses",
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued"
+        ],
+        "name": "FGA_WhiteheadParams",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FGA_WhiteheadAutomorphisms",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FGA_NielsenAutomorphisms",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsIrreducibleMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedIsIrreducibleMatrixGroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAbsolutelyIrreducibleMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedIsPrimitiveMatrixGroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "MinimalBlockDimensionOfMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedMinimalBlockDimensionOfMatrixGroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CharacteristicOfField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "RepresentationIsomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ImprimitivitySystems",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ComputedImprimitivitySystemss",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "TraceField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "ConjugatingMatTraceField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "FingerprintMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IdIrreducibleSolvableMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IdPrimitiveSolvableGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieNilpotent"
+        ],
+        "name": "IsLieNilpotentOverFp",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "AutomorphismGroupOfNilpotentLieAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieNilpotent"
+        ],
+        "name": "MinimalGeneratorNumber",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieNilpotentOverFp"
+        ],
+        "name": "IsLieCover",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieCover"
+        ],
+        "name": "CoverOf",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieCover"
+        ],
+        "name": "CoverHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieCover",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieNilpotentOverFp"
+        ],
+        "name": "LieNucleus",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieNilpotentOverFp"
+        ],
+        "name": "LieMultiplicator",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieNilpotentOverFp"
+        ],
+        "name": "IsLieAlgebraWithNB",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "NilpotentBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsNilpotentBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNilpotentBasis"
+        ],
+        "name": "LieNBDefinitions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNilpotentBasis"
+        ],
+        "name": "LieNBWeights",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupRing"
+        ],
+        "name": "IsGroupAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupAlgebra"
+        ],
+        "name": "IsFModularGroupAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFModularGroupAlgebra"
+        ],
+        "name": "IsPModularGroupAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupRing"
+        ],
+        "name": "UnderlyingRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupAlgebra"
+        ],
+        "name": "UnderlyingField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations",
+            "IsMagmaRingObjDefaultRep"
+        ],
+        "name": "Support",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations",
+            "IsMagmaRingObjDefaultRep"
+        ],
+        "name": "CoefficientsBySupport",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations",
+            "IsMagmaRingObjDefaultRep"
+        ],
+        "name": "TraceOfMagmaRingElement",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations",
+            "IsMagmaRingObjDefaultRep"
+        ],
+        "name": "Augmentation",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations",
+            "IsMagmaRingObjDefaultRep"
+        ],
+        "name": "IsSymmetric",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsElementOfMagmaRingModuloRelations",
+            "IsMagmaRingObjDefaultRep"
+        ],
+        "name": "IsUnitary",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "WeightedBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "AugmentationIdealPowerSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "AugmentationIdealNilpotencyIndex",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "AugmentationIdealOfDerivedSubgroupNilpotencyIndex",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsGroupOfUnitsOfMagmaRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfUnitsOfMagmaRing"
+        ],
+        "name": "IsUnitGroupOfGroupRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfUnitsOfMagmaRing"
+        ],
+        "name": "IsNormalizedUnitGroupOfGroupRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupOfUnitsOfMagmaRing"
+        ],
+        "name": "UnderlyingGroupRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "NormalizedUnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "PcNormalizedUnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "ComputedAugmentationIdealPowerFactorGroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "PcUnits",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "NaturalBijectionToPcNormalizedUnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "NaturalBijectionToNormalizedUnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "GroupBases",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNormalizedUnitGroupOfGroupRing"
+        ],
+        "name": "BicyclicUnitGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNormalizedUnitGroupOfGroupRing"
+        ],
+        "name": "UnitarySubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieAlgebraByAssociativeAlgebra"
+        ],
+        "name": "UnderlyingAssociativeAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieAlgebraByAssociativeAlgebra"
+        ],
+        "name": "IsLieAlgebraOfGroupRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsBasis"
+        ],
+        "name": "IsBasisOfLieAlgebraOfGroupRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsAssociative"
+        ],
+        "name": "NaturalBijectionToLieAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsLieAlgebraByAssociativeAlgebra"
+        ],
+        "name": "NaturalBijectionToAssociativeAlgebra",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsMagmaWithOne",
+            "IsAssociativeLOpDProd",
+            "IsGroupRing"
+        ],
+        "name": "AugmentationHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "IsLieMetabelian",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "IsLieCentreByMetabelian",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "LieUpperNilpotencyIndex",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPModularGroupAlgebra"
+        ],
+        "name": "LieLowerNilpotencyIndex",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsLeftActedOnByRing",
+            "IsDistributiveLOpESum",
+            "IsAssociativeLOpEProd",
+            "IsTrivialLOpEOne",
+            "IsLeftActedOnByDivisionRing",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsExtLSet",
+            "IsDistributiveLOpDSum",
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive",
+            "IsAssociativeLOpDProd",
+            "IsZeroSquaredRing",
+            "IsJacobianRing"
+        ],
+        "name": "LieDerivedLength",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "SubgroupsOfIndexTwo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DihedralDepth",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "DimensionBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "LieDimensionSubgroups",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupRing"
+        ],
+        "name": "LieUpperCodimensionSeries",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "RootsAsMatrices",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "IsSolvablePolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "IsSeparablePolynomial",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNumberField"
+        ],
+        "name": "IsomorphismMatrixField",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPolynomial",
+            "IsUnivariateRationalFunction"
+        ],
+        "name": "GaloisGroupOnRoots",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAffineCrystGroupOnRight",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAffineCrystGroupOnLeft",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAffineCrystGroupOnLeftOrRight",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSpaceGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsStandardAffineCrystGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsSymmorphicSpaceGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsPointGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPointGroup"
+        ],
+        "name": "NormalizerPointGroupInGLnZ",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPointGroup"
+        ],
+        "name": "CentralizerPointGroupInGLnZ",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPointGroup"
+        ],
+        "name": "AffineCrystGroupOfPointGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "PointGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "PointHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "TranslationBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "InternalBasis",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "TransParts",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "TranslationNormalizer",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "AffineNormalizer",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupGeneralMappingByImages"
+        ],
+        "name": "IsPointHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsPointGroup"
+        ],
+        "name": "NiceToCryst",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupGeneralMappingByImages"
+        ],
+        "name": "IsFromAffineCrystGroupToFpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGroupGeneralMappingByImages"
+        ],
+        "name": "IsFromAffineCrystGroupToPcpGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsWyckoffPosition"
+        ],
+        "name": "WyckoffStabilizer",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsWyckoffPosition"
+        ],
+        "name": "WyckoffOrbit",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "WyckoffPositions",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsAffineCrystGroupOnLeftOrRight"
+        ],
+        "name": "CocVecs",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsColorGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsColorGroup"
+        ],
+        "name": "ColorSubgroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsColorGroup"
+        ],
+        "name": "ColorCosetList",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsColorGroup"
+        ],
+        "name": "ColorPermGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsColorGroup"
+        ],
+        "name": "ColorHomomorphism",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "CrystCatRecord",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAlmostCrystallographic",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsAlmostBieberbachGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "AlmostCrystallographicInfo",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "NaturalHomomorphismOnHolonomyGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "HolonomyGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "OrientationModule",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "BettiNumbers",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued"
+        ],
+        "name": "IsIsomorphismByFinitePolycyclicMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsGeneralMapping",
+            "IsTotal",
+            "IsSingleValued"
+        ],
+        "name": "IsIsomorphismByPolycyclicMatrixGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+            "IsMagmaWithInverses",
+            "IsAssociative"
+        ],
+        "name": "IsTriangularizableMatGroup",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsEuclideanRing"
+        ],
+        "name": "IsZ_pi",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "NoninvertiblePrimes",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsResidueClass",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsFamily"
+        ],
+        "name": "UnderlyingIndeterminate",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsZxZ",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsNearAdditiveGroup",
+            "IsNearAdditiveMagma",
+            "IsAdditivelyCommutative",
+            "IsMagma",
+            "IsLDistributive",
+            "IsRDistributive"
+        ],
+        "name": "SizeOfSmallestResidueClassRing",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsResidueClassUnion"
+        ],
+        "name": "Density",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsObject"
+        ],
+        "name": "IsResidueClassWithFixedRepresentative",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnionOfResidueClassesWithFixedRepresentatives"
+        ],
+        "name": "IsOverlappingFree",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            "IsUnionOfResidueClassesWithFixedRepresentatives"
+        ],
+        "name": "Rho",
+        "type": "GAP_Attribute"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ViewObj: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 10046
+                },
+                {
+                    "comment": "ViewObj: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 10036
+                },
+                {
+                    "comment": "ViewObj: for groups with known structure description",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(StructureDescription)"
+                        ]
+                    ],
+                    "rank": 10034
+                },
+                {
+                    "comment": "ViewObj: for a Lie matrix in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieMatrix"
+                        ]
+                    ],
+                    "rank": 10033
+                },
+                {
+                    "comment": "ViewObj: for full ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 10023
+                },
+                {
+                    "comment": "ViewObj: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "ViewObj: for group automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "ViewObj: for zero mapping",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ViewObj: for identity mapping",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ViewObj: for a canonical basis",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)"
+                        ]
+                    ],
+                    "rank": 10009
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ]
+                    ],
+                    "rank": 10001
+                },
+                {
+                    "comment": "ViewObj: for an object with name",
+                    "filters": [
+                        [
+                            "Tester(Name)"
+                        ]
+                    ],
+                    "rank": 10001
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 10000
+                },
+                {
+                    "comment": "ViewObj: for a field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 429
+                },
+                {
+                    "comment": "ViewObj: subgroup by property",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(ElementTestFunction)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "ViewObj: for a two-sided ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 129
+                },
+                {
+                    "comment": "ViewObj: for a right ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "ViewObj: for a left ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "ViewObj: for a restricted mapping",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "ViewObj: for a composition mapping",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "ViewObj: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 109
+                },
+                {
+                    "comment": "ViewObj: objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "ViewObj: straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "ViewObj: for cyclotomic field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ViewObj: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "ViewObj: for natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ViewObj: for natural alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ViewObj: for function field",
+                    "filters": [
+                        [
+                            "IsFunctionField"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "ViewObj: for a polynomial ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "ViewObj: for a matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "ViewObj: for algebraic extension",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)",
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "ViewObj: for full matrix module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "ViewObj: for full row module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "ViewObj: fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ViewObj: for a matrix group with stored generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ViewObj: subgroup of free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ViewObj: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ViewObj: for a Lie algebra with known dimension",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ViewObj: for a matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ViewObj: pc group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ViewObj: for a Lie algebra with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ViewObj: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ViewObj: for an algebra-with-one with known dimension",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "ViewObj: for an algebra-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftOperatorRingWithOne)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "ViewObj: for an algebra-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "ViewObj: for a FLMLOR-with-one with known dimension",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "ViewObj: for an algebra with known dimension",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ViewObj: for a FLMLOR-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorRingWithOne)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ViewObj: for an algebra with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ViewObj: for a FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ViewObj: for an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "ViewObj: for a FLMLOR with known dimension",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "ViewObj: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ViewObj: for a FLMLOR with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ViewObj: for a FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ViewObj: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ViewObj: for Z_(pi) (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ViewObj: for a virtual character",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ViewObj: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ViewObj: for a semigroup Congruence with known generating pairs",
+                    "filters": [
+                        [
+                            "Tester(GeneratingPairsOfMagmaCongruence)",
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ViewObj: for a semigroup congruence",
+                    "filters": [
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ViewObj: for ranges",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRange",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ViewObj: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ViewObj: for null map matrix",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ViewObj: for a ring-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRingWithOne)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ViewObj: for an alg. hom. from f. p. algebra",
+                    "filters": [
+                        [
+                            "IsAlgebraHomomorphismFromFpRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ViewObj: for an operation algebra homomorphism",
+                    "filters": [
+                        [
+                            "IsOperationAlgebraHomomorphismDefaultRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ViewObj: for a ring-with-one",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ViewObj: for a RightSemigroupCongruence with generators",
+                    "filters": [
+                        [
+                            "Tester(GeneratingPairsOfMagmaCongruence)",
+                            "IsRightSemigroupCongruence",
+                            "Tester(IsRightSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ViewObj: for a LeftSemigroupCongruence with known generating pairs",
+                    "filters": [
+                        [
+                            "Tester(GeneratingPairsOfMagmaCongruence)",
+                            "IsLeftSemigroupCongruence",
+                            "Tester(IsLeftSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ViewObj: For a compressed MatFFE",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ViewObj: for an empty row vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ViewObj: for algebra module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewObj: for vector space with known dimension",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewObj: for a ring with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewObj: for a magma congruence with generating pairs",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence",
+                            "Tester(GeneratingPairsOfMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewObj: for a RightMagmaCongruence with generators",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence",
+                            "Tester(GeneratingPairsOfMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewObj: for a LeftMagmaCongruence with known generating pairs",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence",
+                            "Tester(GeneratingPairsOfMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewObj: for an enumerator that perhaps has its own `ViewObj' function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewObj: for vector space with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ViewObj: for a ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ViewObj: for a magma congruence",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ViewObj: for a fp monoid with generators",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ViewObj: for a free monoid containing the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ViewObj: for an algebra g.m.b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ViewObj: for vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ViewObj: pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDefaultRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ViewObj: For a compressed VecFFE",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ViewObj: for free left module with known generators",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ViewObj: for free left module with known dimension",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ViewObj: for a RightSemigrouCongruence",
+                    "filters": [
+                        [
+                            "IsRightSemigroupCongruence",
+                            "Tester(IsRightSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ViewObj: for a LeftSemigroupCongruence",
+                    "filters": [
+                        [
+                            "IsLeftSemigroupCongruence",
+                            "Tester(IsLeftSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ViewObj: for saturated Fitting formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for GreensHRelation",
+                    "filters": [
+                        [
+                            "IsGreensHRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for GreensDRelation",
+                    "filters": [
+                        [
+                            "IsGreensDRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for GreensJRelation",
+                    "filters": [
+                        [
+                            "IsGreensJRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for embedding into wreath product",
+                    "filters": [
+                        [
+                            "IsEmbeddingWreathProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for projection from subdirect product",
+                    "filters": [
+                        [
+                            "IsProjectionSubdirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for projection from a direct product",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for embedding into direct product",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for nat. hom. of pc group",
+                    "filters": [
+                        [
+                            "IsNaturalHomomorphismPcGroupRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for an ring g.m.b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for a left module m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for a left module g.m.b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for a zero group",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsMagmaWithZeroAdjoined"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for an iterator that perhaps has its own `ViewObj' function",
+                    "filters": [
+                        [
+                            "IsIterator",
+                            "IsIteratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ViewObj: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ViewObj: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ViewObj: for action homomorphism",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ViewObj: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ViewObj: for a RightMagmaCongruence",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ViewObj: for a LeftMagmaCongruence",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ViewObj: for a free semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep (32 Bits, up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep (16 Bits, up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep (8 Bits, up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "ViewObj: for product of Fitting formations",
+                    "filters": [
+                        [
+                            "IsFittingProductRep",
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsUnicodeCharacter"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj: for a fp semigroup with generators",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep (32 Bits)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep (16 Bits)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep (8 Bits)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep (up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj: for a free semigroup containing the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewObj: for Fitting formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj: for a saturated formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj: for homomorphisms into matrix groups",
+                    "filters": [
+                        [
+                            "IsHomomorphismIntoMatrixGroup",
+                            "Tester(IsHomomorphismIntoMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj: combinatorial collector rep",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is32BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is16BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is8BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj: for mapping by function with inverse",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionWithInverseRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewObj: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ViewObj: for a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroup",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ViewObj: for a semigroup ideal with known generators",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagmaIdeal)",
+                            "IsSemigroupIdeal",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ViewObj: empty strings",
+                    "filters": [
+                        [
+                            "IsString",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ViewObj: for a Schunck class",
+                    "filters": [
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for a subsemigroup of a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for a subsemigroup of a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for a free magma-with-one containing the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "CategoryCollections(IsWord)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: For large finite field elements",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for an add. magma-with-inverses with generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for a semigroup ideal",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "IsSemigroupIdeal",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewObj: for a Molien series",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "Tester(MolienSeriesInfo)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ViewObj: RightCoset",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ViewObj: for a MagmaIdeal with generators",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagmaIdeal)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ViewObj: for formation product",
+                    "filters": [
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for Fitting product",
+                    "filters": [
+                        [
+                            "IsFittingProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for Fitting class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for an add. magma-with-zero with generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for a MagmaIdeal",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for a direct product element",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewObj: for Fitting set",
+                    "filters": [
+                        [
+                            "IsClassByPropertyRep",
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewObj: for a quotient semigroup with generators",
+                    "filters": [
+                        [
+                            "IsQuotientSemigroup"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewObj: for a free magma containing the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "CategoryCollections(IsWord)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewObj: for a RightMagmaIdeal with generators",
+                    "filters": [
+                        [
+                            "IsRightActedOnBySuperset",
+                            "Tester(GeneratorsOfExtRSet)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewObj: for a LeftMagmaIdeal with generators",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "Tester(GeneratorsOfExtLSet)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewObj: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewObj: for from-the-left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ViewObj: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ViewObj: for an add. magma with generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagma)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ViewObj: for a RightMagmaIdeal",
+                    "filters": [
+                        [
+                            "IsRightActedOnBySuperset",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ViewObj: for a LeftMagmaIdeal",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsPowerCommutatorCollector"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ViewObj: for an additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ViewObj: for an add. magma",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ViewObj: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ViewObj: for external orbit",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ViewObj: for a semi-echelonized basis with basis vectors",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonized",
+                            "Tester(IsSemiEchelonized)",
+                            "Tester(BasisVectors)"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ViewObj: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsWeakPointerObject"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ViewObj: for an element of an f.p. group (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ViewObj: sliced perm",
+                    "filters": [
+                        [
+                            "IsSlicedPermInv"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ViewObj: sliced perm",
+                    "filters": [
+                        [
+                            "IsSlicedPerm"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ViewObj: for external subset",
+                    "filters": [
+                        [
+                            "IsExternalSubset"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ViewObj: for a semi-echelonized basis",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonized",
+                            "Tester(IsSemiEchelonized)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ViewObj: for right transversal",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ViewObj: IsString",
+                    "filters": [
+                        [
+                            "IsString",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ViewObj: for a basis with basis vectors",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "Tester(BasisVectors)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ViewObj: IsString",
+                    "filters": [
+                        [
+                            "IsString",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ViewObj: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ViewObj: for IsGroupClass and IsClassByPropertyRep",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewObj: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewObj: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsDenseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewObj: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewObj: for finite lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewObj: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ViewObj: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ViewObj: External Set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ViewObj: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ViewObj:  for IsGroupClassByListRep",
+                    "filters": [
+                        [
+                            "IsGroupClassByListRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: for IsClassByUnionRep",
+                    "filters": [
+                        [
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: for IsClassByIntersectionRep",
+                    "filters": [
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: for IsClassByComplementRep",
+                    "filters": [
+                        [
+                            "IsClassByComplementRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: for IsClassByPropertyRep",
+                    "filters": [
+                        [
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsBuiltFromSemigroup",
+                            "Tester(IsBuiltFromSemigroup)",
+                            "IsKnuthBendixRewritingSystem"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsBuiltFromMonoid",
+                            "Tester(IsBuiltFromMonoid)",
+                            "IsKnuthBendixRewritingSystem"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewObj: for a worker farm by fork",
+                    "filters": [
+                        [
+                            "IsWorkerFarmByFork"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ViewObj: for a background job by fork",
+                    "filters": [
+                        [
+                            "IsBackgroundJobByFork"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ViewObj: for a monoid rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMonoid",
+                            "Tester(IsBuiltFromMonoid)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ViewObj: for a semigroup rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromSemigroup",
+                            "Tester(IsBuiltFromSemigroup)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ViewObj: for an infinite list of generators",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfGeneratorsRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ViewObj: for an infinite list of names",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfNamesRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ViewObj: for iterators of residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsIterator",
+                            "IsResidueClassUnionsIteratorRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: Wyckoff position",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for a tcp server",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for a real random source",
+                    "filters": [
+                        [
+                            "IsRealRandomSource"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: lattice",
+                    "filters": [
+                        [
+                            "IsLatticeSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for dictionaries",
+                    "filters": [
+                        [
+                            "IsDictionary"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for a mutable basis of a Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianMatrixSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for a mutable basis of a Gaussian row space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianRowSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for mutable basis represented by a nice mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaNiceMutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for mutable basis represented by an immutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisByImmutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ViewObj: for an IO_Result",
+                    "filters": [
+                        [
+                            "IO_Result"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsRewritingSystem"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ViewObj: for vector search tables",
+                    "filters": [
+                        [
+                            "IsVectorSearchTable"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ViewObj: default directory rep",
+                    "filters": [
+                        [
+                            "IsDirectoryRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ViewObj: for an operation",
+                    "filters": [
+                        [
+                            "IsOperation"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ViewObj: for a straight line decision",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: for a black box program",
+                    "filters": [
+                        [
+                            "IsBBoxProgram"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: for IsFile objects",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: for a straight line program",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: for an ordering",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: stabilizer chain records",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: IsChar",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: default method trying ViewString",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: for a function",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewObj: default method using `PrintObj'",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ViewObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ViewString: for a symmetric inverse monoid",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSymmetricInverseSemigroup",
+                            "Tester(IsSymmetricInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 10031
+                },
+                {
+                    "comment": "ViewString: for a group as semigroup",
+                    "filters": [
+                        [
+                            "IsGroupAsSemigroup",
+                            "Tester(IsGroupAsSemigroup)",
+                            "IsSemigroupIdeal",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 10031
+                },
+                {
+                    "comment": "ViewString: for a full transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFullTransformationSemigroup",
+                            "Tester(IsFullTransformationSemigroup)"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "ViewString: for an object with name",
+                    "filters": [
+                        [
+                            "Tester(Name)"
+                        ]
+                    ],
+                    "rank": 10001
+                },
+                {
+                    "comment": "ViewString: for a field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 429
+                },
+                {
+                    "comment": "ViewString: for natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ViewString: for natural alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ViewString: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "ViewString: for a field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "ViewString: for full row modules",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "ViewString: for a group of partial perms",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ViewString: for a group of transformations",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ViewString: for a group with generators and size",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "ViewString: for a group with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ViewString: for a group with known generators (as a semigroup)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ViewString: for Z_(pi) (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ViewString: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ViewString: for a polynomial ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ViewString: for a group as semigroup with known generators (as a semigroup)",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfMagma)",
+                            "IsGroupAsSemigroup",
+                            "Tester(IsGroupAsSemigroup)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ViewString: for an inverse monoid with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseMonoid)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ViewString: for a inverse monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ViewString: for an inverse semigroup with inverse semigroup generators",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewString: for an inverse semigroup with semigroup generators",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfMagma)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ViewString: for univariate polynomial over finite field (ResClasses)",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewString: for a inverse semigroup",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewString: for a monoid with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ViewString: for a monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ViewString: for integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ViewString: for a finite field element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewString: for rationals",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewString: For large finite field elements",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewString: for an internal FFE delegating to String",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewString: for a magma-with-inverses with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ViewString: RightCoset",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ViewString: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ViewString: for a semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewString: for a magma-with-one with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ViewString: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ViewString: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ViewString: for a magma with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ViewString: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ViewString: for residue classes of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZxZ",
+                            "IsResidueClass",
+                            "Tester(IsResidueClass)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ViewString: DoubleCoset",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ViewString: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ViewString: for a Green's class",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewString: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewString: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewString: call ViewString and incorporate hints",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ViewString: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewString: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ViewString: for residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassWithFixedRepresentative",
+                            "Tester(IsResidueClassWithFixedRepresentative)"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ViewString: for residue classes (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClass",
+                            "Tester(IsResidueClass)"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ViewString: IsChar",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ViewString: generic default method",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ViewString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NameFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetNameFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumberArgumentsFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CallFuncList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "=: for two lists, the second being empty",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 10019
+                },
+                {
+                    "comment": "=: for two lists, the first being empty",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 10019
+                },
+                {
+                    "comment": "=: for a list and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 10011
+                },
+                {
+                    "comment": "=: for a residue class union and a list (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 10011
+                },
+                {
+                    "comment": "=: handled by nice monomorphism: attribute CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 734
+                },
+                {
+                    "comment": "=: for 32 bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is32BitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 222
+                },
+                {
+                    "comment": "=: for 16 bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is16BitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 222
+                },
+                {
+                    "comment": "=: for 8 bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is8BitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 222
+                },
+                {
+                    "comment": "=: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 220
+                },
+                {
+                    "comment": "=: two objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 214
+                },
+                {
+                    "comment": "=: perm with straight line program element",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 118
+                },
+                {
+                    "comment": "=: straight line program element with perm",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 118
+                },
+                {
+                    "comment": "=: for two abelian number fields",
+                    "filters": [
+                        [
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "=: for two finite fields in the same family",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 112
+                },
+                {
+                    "comment": "=: objects with memory with x",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "=: x with straight line program element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "=: straight line program element with x",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "=: for two compressed 8 bit matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "=: for subgroups of free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "=: for two division rings",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "=: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "=: for GF2 matrix and GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 90
+                },
+                {
+                    "comment": "=: for certain cyclotomic semirings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "=: subgroups of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "=: pcgs computable groups using family pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(CanonicalPcgsWrtFamilyPcgs)",
+                            "Tester(FamilyPcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(CanonicalPcgsWrtFamilyPcgs)",
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "=: pcgs computable groups using home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(CanonicalPcgsWrtHomePcgs)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(CanonicalPcgsWrtHomePcgs)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "=: for two ordinary block matrices",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "=: for Z_(pi)'s (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "=: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "=: for two class functions",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "=: for two rings with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "=: for two ANF automorphisms",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "=: for two Frobenius automorphisms",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "=: For 2 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "=: pc group homomorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "=: for two field homomorphisms",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ],
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "=: for two free left modules (at least one fin. dim.)",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that is a field homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "=: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "=: for group automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "=: for GreensRelation",
+                    "filters": [
+                        [
+                            "IsGreensRelation"
+                        ],
+                        [
+                            "IsGreensRelation"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "=: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "=: for ANF automorphism and identity mapping",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "=: for identity mapping and ANF automorphism",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "=: for Frobenius automorphism and identity mapping",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "=: for identity mapping and Frobenius automorphism",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "=: for eqivalence relations",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,one,scal. mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsUnicodeCharacter"
+                        ],
+                        [
+                            "IsUnicodeCharacter"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "=: for an inverse semigroups with generators",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ],
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "=: for two underlying relations of general mappings",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "=: homomorphism by images with homomorphism: compare generator images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "=: homomorphism with general mapping: test b=a",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "=: for ring ring general mapping and ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "=: for ring g.m.b.i. and ring general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,scal. mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect mult.,one,add.,add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "=: for two unknowns in default representation",
+                    "filters": [
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ],
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "=: for internal FFE and element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "=: for element in Z/pZ (ModulusRep) and internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "=: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: BFElm=BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: BFElm<AlgElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: AlgElm=BFElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: AlgElm=AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: laurent",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,scal. mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect mult.,add.,add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "=: for a list and a class function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "=: for a class function and a list",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "=: IsTransformationRepOfEndo, IsTransformationRepOfEndo",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "=: RightCosets",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ],
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "=: for two elements in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "=: for cyclotomic and unknown",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "=: for unknown and cyclotomic",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "=: for `-infinity' and cyclotomic",
+                    "filters": [
+                        [
+                            "IsNegInfinity"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "=: for cyclotomic and `-infinity'",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsNegInfinity"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "=: for `infinity' and cyclotomic",
+                    "filters": [
+                        [
+                            "IsInfinity"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "=: for cyclotomic and `infinity'",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "=: for two plist matrices",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "=: univariate = univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect add. and add. inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect mult. and inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "=: for two direct product elements",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "=: for a collection, and an empty row vector in the same family",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "=: for an empty row vector, and a collection in the same family",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "=: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "=: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "=: IsEndoMapping, IsTransformationRepOfEndo",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "=: IsTransformationRepOfEndo, IsEndoMapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ],
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ],
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "=: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "=: for additive group and additive coset",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "=: for additive coset and additive group",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "=: for semigroup with generators and semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "=: classes for perm group",
+                    "filters": [
+                        [
+                            "IsConjugacyClassPermGroupRep"
+                        ],
+                        [
+                            "IsConjugacyClassPermGroupRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: compare source generator images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: rational functions",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: for s. c. ring elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: for two Lie objects in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: for s. c. algebra elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect add. and zero",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect mult. and one",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "=: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "=: FElm=BFElm",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "=: BFElm=FElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "=: FElm=AlgElm",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "=: AlgElm=FElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsRationalClassPermGroupRep"
+                        ],
+                        [
+                            "IsRationalClassPermGroupRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "=: xorbs which know their size",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "IsExternalOrbit"
+                        ],
+                        [
+                            "Tester(Size)",
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "=: for two UEALattice elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "=: for two additive cosets",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ],
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "=: for binary relss over [1..n] with images list",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ],
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ],
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: xorbs with canonicalRepresentativeDeterminator",
+                    "filters": [
+                        [
+                            "IsExternalOrbit",
+                            "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
+                        ],
+                        [
+                            "IsExternalOrbit",
+                            "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: for two plist vectors",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: for s. c. algebra elements",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: for two normalized f.p. algebra elements",
+                    "filters": [
+                        [
+                            "IsElementOfFpAlgebra",
+                            "IsNormalForm",
+                            "Tester(IsNormalForm)"
+                        ],
+                        [
+                            "IsElementOfFpAlgebra",
+                            "IsNormalForm",
+                            "Tester(IsNormalForm)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: for two free magma ring elements",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect add.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings that respect mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "=: xorbs",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ],
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "=: for two weight rep elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "=: for two cochains",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "=: for direct sum elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "=: for sparse rowspace elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "=: for monomial elements",
+                    "filters": [
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ],
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "=: for two algebra module elements in packed representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "=: for two residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "=: for two f.p. algebra elements (try nice monomorphism)",
+                    "filters": [
+                        [
+                            "IsElementOfFpAlgebra"
+                        ],
+                        [
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "=: method for two s.v. gen. mappings",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "=: for two small lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "=: for fp monoid elts produced by the Froidure-Pin algorithm",
+                    "filters": [
+                        [
+                            "IsFpMonoidReducedElt",
+                            "Tester(IsFpMonoidReducedElt)"
+                        ],
+                        [
+                            "IsFpMonoidReducedElt",
+                            "Tester(IsFpMonoidReducedElt)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "=: DoubleCosets",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ],
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "=: for two inf. bits assoc. words",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ],
+                        [
+                            "IsInfBitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "=: for two 32 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "=: for two 16 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "=: for two 8 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for fp semigp elts produced by the Froidure-Pin algorithm",
+                    "filters": [
+                        [
+                            "IsFpSemigpReducedElt",
+                            "Tester(IsFpSemigpReducedElt)"
+                        ],
+                        [
+                            "IsFpSemigpReducedElt",
+                            "Tester(IsFpSemigpReducedElt)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for Green's classes",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ],
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for two f.p. group elements",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ],
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: wreath elements",
+                    "filters": [
+                        [
+                            "IsWreathProductElement"
+                        ],
+                        [
+                            "IsWreathProductElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for two elements of magma by mult. table",
+                    "filters": [
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ],
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for two elements of a magma with zero adjoined",
+                    "filters": [
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ],
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for two general mappings",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for two finite lists (not necessarily small)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "=: for two unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=: for a list of elements and an infinite domain (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=: for an infinite domain and a list of elements (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ],
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=: for two elements of a f.p. monoid",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ],
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=: assoc words in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=: for two equivalence classes",
+                    "filters": [
+                        [
+                            "IsEquivalenceClass"
+                        ],
+                        [
+                            "IsEquivalenceClass"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "=: for elements of a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: for elements of a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: for two Knuth-Bendix rewriting systems",
+                    "filters": [
+                        [
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ],
+                        [
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: for two elements of a f.p. semigroup",
+                    "filters": [
+                        [
+                            "IsElementOfFpSemigroup"
+                        ],
+                        [
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: for two domains",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: for a domain and a list",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: for a list and a domain",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ],
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "=: for two words",
+                    "filters": [
+                        [
+                            "IsWord"
+                        ],
+                        [
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "=",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ],
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "=: for two lists with length - last resort",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Tester(LENGTH)"
+                        ],
+                        [
+                            "IsList",
+                            "Tester(LENGTH)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "=: for classes",
+                    "filters": [
+                        [
+                            "IsClass"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "=: for two IO_Results",
+                    "filters": [
+                        [
+                            "IO_Result"
+                        ],
+                        [
+                            "IO_Result"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "=: for two lists - last resort",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "=: for two info classes",
+                    "filters": [
+                        [
+                            "IsInfoClassListRep"
+                        ],
+                        [
+                            "IsInfoClassListRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "=: for two IsFile objects",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsFile"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "=: for another object and an IO_Result",
+                    "filters": [
+                        [],
+                        [
+                            "IO_Result"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "=: for an IO_Result and another object",
+                    "filters": [
+                        [
+                            "IO_Result"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "=: for two directories",
+                    "filters": [
+                        [
+                            "IsDirectory"
+                        ],
+                        [
+                            "IsDirectory"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "=: for two families: delegate to `IsIdenticalObj'",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "=: record = record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "=:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "=: for two objects in different families",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "=",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "<: for 32 bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is32BitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 222
+                },
+                {
+                    "comment": "<: for 16 bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is16BitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 222
+                },
+                {
+                    "comment": "<: method for 8 bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is8BitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 222
+                },
+                {
+                    "comment": "<: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 220
+                },
+                {
+                    "comment": "<: two objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 214
+                },
+                {
+                    "comment": "<: RightCosets of perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsRightCoset"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "<: for two inf. bits assoc. words",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ],
+                        [
+                            "IsInfBitsAssocWord"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "<: for two abelian number fields",
+                    "filters": [
+                        [
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "<: x with objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "<: objects with memory with x",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "<: x with straight line program element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "<: straight line program element with x",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "<: for two compressed 8 bit matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "<: two AffineCrystGroupOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "<: two AffineCrystGroupOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "<: for GF2 matrix and GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 90
+                },
+                {
+                    "comment": "<: cgs comparison",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "<: groups by smallest generating sets",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "<: for two class functions",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "<: for two ANF automorphisms",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "<: for two Frobenius automorphisms",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "<: For 2 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "<: for two free left modules",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "<: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "<: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "<: for ANF automorphism and identity mapping",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "<: for identity mapping and ANF automorphism",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "<: for a Frobenius automorphism, and an identity mapping",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "<: for an identity mapping, and a Frobenius automorphism",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "<: for two underlying relations of general mappings",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "<: for transformation semigroups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "<: for two elements in Z/pZ (ModulusRep, small)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "<: for two elements in Z/pZ (ModulusRep, large)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsLexOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsLexOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsLexOrderedFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsLexOrderedFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "<: for internal FFE and element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "<: for element in Z/pZ (ModulusRep) and internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "<: for two unknowns in default representation",
+                    "filters": [
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ],
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "<: group homomorphisms: Images of smallest generators",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "<: for two elements in Z/nZ (ModulusRep, nonprime)",
+                    "filters": [
+                        [
+                            "IsZmodnZObjNonprime",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsZmodnZObjNonprime",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "<: BFElm<BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "<: BFElm<AlgElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "<: AlgElm<BFElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "<: AlgElm<AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "<: Univariate Polynomials",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "<: for a module and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "<: for a residue class union and a module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "<: for a list and a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "<: for a class function and a list",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "<: for a ring and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "<: for a residue class union and a ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "<: IsTransformationRepOfEndo, IsTransformationRepOfEndo",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "<: for cyclotomic and unknown",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "<: for unknown and cyclotomic",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "<: for `-infinity' and cyclotomic",
+                    "filters": [
+                        [
+                            "IsNegInfinity"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "<: for cyclotomic and `-infinity'",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsNegInfinity"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "<: for `infinity' and cyclotomic",
+                    "filters": [
+                        [
+                            "IsInfinity"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "<: for cyclotomic and `infinity'",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "<: for two plist matrices",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "<: for two direct product elements",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "<: for two finite field elements in different characteristic",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "<: for a finite field element, and a cyclotomic",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "<: for a cyclotomic, and a finite field element",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "<: for a module and a list of elements (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "<: for a list of elements and a module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "<: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "<: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "<: IsTransformationRepOfEndo, IsEndoMapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "<: IsEndoMapping, IsTransformationRepOfEndo",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "<: for a ring and a list of elements (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "<: for a list of elements and a ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ],
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ],
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "<: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "<: for s. c. ring elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "<: for two Lie objects in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "<: for s. c. algebra elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "<: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "<: FElm<BFElm",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "<: BFElm<FElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "<: FElm<AlgElm",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "<: AlgElm<FElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "<: rational functions",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "<: for two UEALattice elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "<: for binary rels over [1..n] with images list",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "<: for a permutation, and a finite field element",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "<: for a permutation, and a cyclotomic",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "<: for a finite field element, and a permutation",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "<: for a cyclotomic, and a permutation",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "<: for a transformation and finite field element",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: for a finite field element and transformation",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: for a cyclotomic and transformation",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: for a transformation and cyclotomic",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: for two plist vectors",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: for s. c. algebra elements",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: for two normalized f.p. algebra elements",
+                    "filters": [
+                        [
+                            "IsElementOfFpAlgebra",
+                            "IsNormalForm",
+                            "Tester(IsNormalForm)"
+                        ],
+                        [
+                            "IsElementOfFpAlgebra",
+                            "IsNormalForm",
+                            "Tester(IsNormalForm)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: for two free magma ring elements",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "<: xorbs, via AsSSortedList",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ],
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "<: for two weight rep elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "<: for two cochains",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "<: for direct sum elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "<: for sparse rowspace elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "<: for monomial elements",
+                    "filters": [
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ],
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "<: for two algebra module elements in packed representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "<: for two residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "<: for two f.p. algebra elements (try nice monomorphism)",
+                    "filters": [
+                        [
+                            "IsElementOfFpAlgebra"
+                        ],
+                        [
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "<: for two small homogeneous lists",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "<: for two small lists, possibly in different families",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "<: for a list, and a finite field element",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "<: for a list, and a cyclotomic",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "<: for a finite field element, and a list",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "<: for a cyclotomic, and a list",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "<: for fp monoid elts produced by the Froidure-Pin algorithm",
+                    "filters": [
+                        [
+                            "IsFpMonoidReducedElt",
+                            "Tester(IsFpMonoidReducedElt)"
+                        ],
+                        [
+                            "IsFpMonoidReducedElt",
+                            "Tester(IsFpMonoidReducedElt)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for two 32 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for two 16 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for two 8 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a character, and a finite field element",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a character, and a cyclotomic",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a boolean, and a finite field element",
+                    "filters": [
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a boolean, and a cyclotomic",
+                    "filters": [
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a finite field element, and a character",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a finite field element, and a boolean",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a cyclotomic, and a character",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for a cyclotomic, and a boolean",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "<: for fp semigp elts produced by the Froidure-Pin algorithm",
+                    "filters": [
+                        [
+                            "IsFpSemigpReducedElt",
+                            "Tester(IsFpSemigpReducedElt)"
+                        ],
+                        [
+                            "IsFpSemigpReducedElt",
+                            "Tester(IsFpSemigpReducedElt)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "<: for two f.p. group elements",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ],
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "<: wreath elements",
+                    "filters": [
+                        [
+                            "IsWreathProductElement"
+                        ],
+                        [
+                            "IsWreathProductElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "<: for two elements of magma by mult. table",
+                    "filters": [
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ],
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "<: for two elements of magmas with zero adjoined",
+                    "filters": [
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ],
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "<: for two general mappings",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "<: for two finite homogeneous lists (not necessarily small)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "<: for two unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "<: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ],
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "<: for two elements of a f.p. monoid",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ],
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "<: assoc words in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "<: for two equivalence classes",
+                    "filters": [
+                        [
+                            "IsEquivalenceClass"
+                        ],
+                        [
+                            "IsEquivalenceClass"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "<: for elements of a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: for elements of a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: for two elements of a f.p. semigroup",
+                    "filters": [
+                        [
+                            "IsElementOfFpSemigroup"
+                        ],
+                        [
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: assoc words",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: for a domain and a list",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: for a list and a domain",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: for a list, and a permutation",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: for a permutation, and a list",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ],
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "<: for a character, and a permutation",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "<: for a boolean, and a permutation",
+                    "filters": [
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "<: for a permutation, and a character",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "<: for a permutation, and a boolean",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "<: for a residue class union and a list (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "<: for a list and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "<: nonassoc words",
+                    "filters": [
+                        [
+                            "IsWord"
+                        ],
+                        [
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "<",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ],
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "<: for classes",
+                    "filters": [
+                        [
+                            "IsClass"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "<: for two info classes",
+                    "filters": [
+                        [
+                            "IsInfoClassListRep"
+                        ],
+                        [
+                            "IsInfoClassListRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "<: for two finite lists, possibly in different families",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "<: for a list, and a character",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "<: for a list, and a boolean",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "<: for a character, and a list",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "<: for a boolean, and a list",
+                    "filters": [
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "<: for two IsFile objects",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsFile"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "<: for a character, and a boolean",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "<: for a boolean, and a character",
+                    "filters": [
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "<: record < record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "<",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "in: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 10014
+                },
+                {
+                    "comment": "in: for an object, and a collection that contains the whole family",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)"
+                        ]
+                    ],
+                    "rank": 10004
+                },
+                {
+                    "comment": "in: for wrong family relation",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10002
+                },
+                {
+                    "comment": "in: TF method, use tree",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingFreeLiftSetup)"
+                        ]
+                    ],
+                    "rank": 434
+                },
+                {
+                    "comment": "in: for a FFE, and a field of FFEs",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 434
+                },
+                {
+                    "comment": "in: special linear group",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalSL",
+                            "Tester(IsNaturalSL)"
+                        ]
+                    ],
+                    "rank": 427
+                },
+                {
+                    "comment": "in: general linear group",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)"
+                        ]
+                    ],
+                    "rank": 425
+                },
+                {
+                    "comment": "in: for groups of FFE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "CategoryCollections(IsFFE)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 410
+                },
+                {
+                    "comment": "in: respecting sesquilinear form",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFullSubgroupGLorSLRespectingSesquilinearForm",
+                            "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"
+                        ]
+                    ],
+                    "rank": 408
+                },
+                {
+                    "comment": "in: respecting bilinear form",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFullSubgroupGLorSLRespectingBilinearForm",
+                            "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"
+                        ]
+                    ],
+                    "rank": 408
+                },
+                {
+                    "comment": "in: by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 372
+                },
+                {
+                    "comment": "in: subgroup by property",
+                    "filters": [
+                        [],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(ElementTestFunction)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "in: for matrix and SL(n,Z)",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNaturalSL",
+                            "Tester(IsNaturalSL)",
+                            "IsIntegerMatrixGroup",
+                            "Tester(IsIntegerMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "in: for matrix and GL(n,Z)",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)",
+                            "IsIntegerMatrixGroup",
+                            "Tester(IsIntegerMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "in: for cyclotomic and Rationals",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "in: for subgroups of Z/p^aZ, p<>2",
+                    "filters": [
+                        [
+                            "IsZmodnZObjNonprime"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "in: for cyclotomic and cyclotomic field",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "in: for cyclotomic and abelian number field",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "in: for CrystGroup",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "in: perm in natsymmetric group",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "in: alternating",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "in: Alg in Ext",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement"
+                        ],
+                        [
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "in: for a permutation, and a permutation group",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "in: FElm in Ext",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "in: for full row module",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "in: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsGaussianIntegers"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "in: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "in: LAGUNA: for a Lie algebra that comes from an associative algebra and a Lie object",
+                    "filters": [
+                        [
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "in: for integers",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "in",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsIEEE754PseudoField"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "in: for a pcp element and a pcp group",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "in: for s. c. algebra element, and full s. c. algebra",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsFullSCAlgebra",
+                            "Tester(IsFullSCAlgebra)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "in: for automorphism groups of free groups",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsAutomorphismGroupOfFreeGroup"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "in: generic wreath product",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)",
+                            "CategoryCollections(IsWreathProductElement)"
+                        ],
+                        [
+                            "IsWreathProductElement"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "in: generic direct product",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "in: for full matrix module",
+                    "filters": [
+                        [],
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "in: polynomial ideal",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)",
+                            "CategoryCollections(IsRationalFunction)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "in: for ring element, and magma ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "in",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "in: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "in: for nonnegative integers",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsNonnegativeIntegers"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "in: for pc group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FamilyPcgs)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "in: for row vector and Gaussian row space",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "in: for positive integers",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsPositiveIntegers"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "in: subgroup of fp group by quotient rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "in: for pcgs computable groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(InducedPcgsWrtHomePcgs)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "in: SC Rings",
+                    "filters": [
+                        [
+                            "IsSCRingObj"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "in: subgroup of fp group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "in: for pcgs computable groups with induced pcgs",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(ComputedInducedPcgses)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "in: ratfun in fctfield",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsFunctionField"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "in: polynomial in polynomial ring",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsPolynomialRing"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "in: default method, checking for <g> being among the generators",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "in: for an element and an underlying relation of a general mapping",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "in: for object and Z_(pi) (ResClasses)",
+                    "filters": [
+                        [],
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "in: for vector and free left module that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ],
+                        [
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "in: for vector and fin. dim. free left module",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ],
+                        [
+                            "IsFreeLeftModule",
+                            "IsFiniteDimensional",
+                            "Tester(IsFiniteDimensional)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "in: for eq relation with partition",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "Tester(EquivalenceRelationPartition)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "in: for a transformation and a full transformation semigroup",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsFullTransformationSemigroup",
+                            "Tester(IsFullTransformationSemigroup)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "in: perm class rep",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsConjugacyClassPermGroupRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "in: for a right coset with representative",
+                    "filters": [
+                        [],
+                        [
+                            "Tester(Representative)",
+                            "Tester(ActingDomain)",
+                            "Tester(FunctionAction)",
+                            "IsRightCosetDefaultRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "in",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsRationalClassPermGroupRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "in: xset: Test representative equal",
+                    "filters": [
+                        [],
+                        [
+                            "Tester(Representative)",
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "in: for an object, and an empty list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "in: for additive element and additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveElement"
+                        ],
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "in: for binary rels over [1..n] with images list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "in: for a simple inverse automaton",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsSimpleInvAutomatonRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "in: double coset",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "in: by CanonicalRepresentativeDeterminator",
+                    "filters": [
+                        [],
+                        [
+                            "IsExternalOrbit",
+                            "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "in: xorb HasAsSSortedList",
+                    "filters": [
+                        [],
+                        [
+                            "Tester(AsSSortedList)",
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "in: for a res.-cl. and a union of res.-cl. with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "in: xorb HasAsList",
+                    "filters": [
+                        [],
+                        [
+                            "Tester(AsList)",
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "in: very small xorbs: test in AsList",
+                    "filters": [
+                        [],
+                        [
+                            "Tester(Size)",
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "in",
+                    "filters": [
+                        [],
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "in: xorb: HasEnumerator",
+                    "filters": [
+                        [],
+                        [
+                            "Tester(Enumerator)",
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "in: xorb: RepresentativeAction",
+                    "filters": [
+                        [],
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "in: for a magma congruence class",
+                    "filters": [
+                        [],
+                        [
+                            "IsCongruenceClass"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "in: for a ring element and a residue class union (ResClasses)",
+                    "filters": [
+                        [],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "in: for an object, and a small list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "in: membership test of Green's class",
+                    "filters": [
+                        [],
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "in: for an enumerator that perhaps has its own membership test function",
+                    "filters": [
+                        [],
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "in: empty class",
+                    "filters": [
+                        [],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "in: for element and equivalence class",
+                    "filters": [
+                        [],
+                        [
+                            "IsEquivalenceClass"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "in: for a domain, and an element",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "in: for group class",
+                    "filters": [
+                        [],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "in: for class, delegate to IsMember",
+                    "filters": [
+                        [],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "in: for an object, and a list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "in:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "in",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ShallowCopy: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ShallowCopy: for class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ShallowCopy: For a compressed MatFFE",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ShallowCopy: for an empty row vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ShallowCopy: For a compressed VecFFE",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ShallowCopy: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ShallowCopy: combinatorial collector rep",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ShallowCopy: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "IsSortLookupDictionary"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ShallowCopy: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ShallowCopy: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsWeakPointerObject"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "TableHasIntKeyFun",
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "IsPositionDictionary"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "IsListLookupDictionary"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ShallowCopy: for a strictly sorted dense list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "IsSortDictionary"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ShallowCopy: for a strictly sorted list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "IsPositionDictionary"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ShallowCopy",
+                    "filters": [
+                        [
+                            "IsCopyable",
+                            "IsListDictionary"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ShallowCopy: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ShallowCopy: for a presentation in default representation",
+                    "filters": [
+                        [
+                            "IsPresentation",
+                            "IsPresentationDefaultRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ShallowCopy: for iterators of residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsIterator",
+                            "IsResidueClassUnionsIteratorRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ShallowCopy: for a dense list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ShallowCopy: for `IsIteratorByFunctions'",
+                    "filters": [
+                        [
+                            "IsIterator",
+                            "IsIteratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ShallowCopy: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ShallowCopy: generic method for mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "ShallowCopy: for a (not copyable) object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ShallowCopy",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Name: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Name)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Name",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Name): generic test routine",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 10001
+                },
+                {
+                    "comment": "Setter(Name): set name of indeterminate",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Setter(Name): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Name): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Name)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Name)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InfoText: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InfoText)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InfoText",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InfoText): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InfoText): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InfoText)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InfoText)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "String: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(String)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "String",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 10000
+                },
+                {
+                    "comment": "String: for a field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 429
+                },
+                {
+                    "comment": "String: for cyclotomic field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "String: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "String: for natural alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "String: for natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "String: for a polynomial ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "String: for full row modules",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "String: for a group with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "String: for Z_(pi) (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "String: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "String: for a range",
+                    "filters": [
+                        [
+                            "IsRange"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "String: for a inverse monoid with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseMonoid)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "String: for a inverse monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "String: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "String: for a inverse semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "String: for a inverse semigroup",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "String: for monoid with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "String: for element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "String: for an unknown in default representation",
+                    "filters": [
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "String: for monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "String: for an integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "String: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "String: For large finite field elements",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "String: for an internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "String: AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "String: BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "String: laurent polynomial",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "String: for a rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "String: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "String: for -infinity",
+                    "filters": [
+                        [
+                            "IsNegInfinity"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "String: for infinity",
+                    "filters": [
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "String: for a cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "String: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "String: for plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "String: univar",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "String: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "String: for a semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "String: from-the-left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "String: rational function",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "String: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "String: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "String: for s. c. ring element",
+                    "filters": [
+                        [
+                            "IsSCRingObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "String: for s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "String: for magma ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "String: pcword",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "String: for an element of an f.p. group (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "String: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "String: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "String: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "String: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "String: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "String: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "String: for an fp monoid element",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "String: for an f.p. semigroup element",
+                    "filters": [
+                        [
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "String: for an associative word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "String: for a nonassociative word",
+                    "filters": [
+                        [
+                            "IsNonassocWord"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "String: for a string (do nothing)",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "String: for a (finite) list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "String: for a boolean",
+                    "filters": [
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "String: record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "String: for a character",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "String",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "String: for an object, and zero",
+                    "filters": [
+                        [],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "String: for an object, and a negative integer",
+                    "filters": [
+                        [],
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "String: for an object, and a positive integer",
+                    "filters": [
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "String",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(String): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(String): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(String)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(String)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrintObj: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 10036
+                },
+                {
+                    "comment": "PrintObj: for full ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 10023
+                },
+                {
+                    "comment": "PrintObj: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "PrintObj: for group automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "PrintObj: for zero mapping",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "PrintObj: for identity mapping",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "PrintObj: for a Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "PrintObj: for a canonical basis",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)"
+                        ]
+                    ],
+                    "rank": 10009
+                },
+                {
+                    "comment": "PrintObj: for an object with name",
+                    "filters": [
+                        [
+                            "Tester(Name)"
+                        ]
+                    ],
+                    "rank": 10001
+                },
+                {
+                    "comment": "PrintObj: for a field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 429
+                },
+                {
+                    "comment": "PrintObj: subgroup by property",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(ElementTestFunction)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "PrintObj: for a restricted mapping",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "PrintObj: for a composition mapping",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "PrintObj: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 109
+                },
+                {
+                    "comment": "PrintObj: objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "PrintObj: for cyclotomic field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "PrintObj: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "PrintObj: for natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "PrintObj: for natural alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "PrintObj: for a function field",
+                    "filters": [
+                        [
+                            "IsFunctionField"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "PrintObj: for a polynomial ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "PrintObj: for a matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "PrintObj: for algebraic extension",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)",
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "PrintObj: for a field with known generators",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "Tester(GeneratorsOfDivisionRing)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "PrintObj: for a field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "PrintObj: for full matrix module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "PrintObj: for full row module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "PrintObj: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "PrintObj: for a matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "PrintObj: for a semigroup with known generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "PrintObj: for an algebra-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "PrintObj: for an algebra-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "PrintObj: for a semigroup with known generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "PrintObj: for a FLMLOR-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "PrintObj: for an algebra with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "PrintObj: for a FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "PrintObj: for an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "PrintObj: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "PrintObj: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "PrintObj: for a FLMLOR with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "PrintObj: for a FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PrintObj: for a group with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PrintObj: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PrintObj: for Z_(pi) (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PrintObj: for a virtual character",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PrintObj: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PrintObj: for a semigroup Congruence with known generating pairs",
+                    "filters": [
+                        [
+                            "Tester(GeneratingPairsOfMagmaCongruence)",
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PrintObj: for a semigroup congruence",
+                    "filters": [
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "PrintObj: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PrintObj: for an algebra-with-one hom. b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PrintObj: for null map matrix",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PrintObj: for a ring-with-one with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRingWithOne)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "PrintObj: for an alg. hom. from f. p. algebra",
+                    "filters": [
+                        [
+                            "IsAlgebraHomomorphismFromFpRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PrintObj: for an operation algebra homomorphism",
+                    "filters": [
+                        [
+                            "IsOperationAlgebraHomomorphismDefaultRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PrintObj: for an algebra hom. b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PrintObj: for a two-sided ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PrintObj: for a ring-with-one",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PrintObj: for a right semigroup congruence with known generating pairs",
+                    "filters": [
+                        [
+                            "Tester(GeneratingPairsOfMagmaCongruence)",
+                            "IsRightSemigroupCongruence",
+                            "Tester(IsRightSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PrintObj: for a left semigroup congruence with known generating pairs",
+                    "filters": [
+                        [
+                            "Tester(GeneratingPairsOfMagmaCongruence)",
+                            "IsLeftSemigroupCongruence",
+                            "Tester(IsLeftSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PrintObj: For a compressed MatFFE",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PrintObj: for a right ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PrintObj: for a left ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PrintObj: for inner automorphism",
+                    "filters": [
+                        [
+                            "IsInnerAutomorphism",
+                            "Tester(IsInnerAutomorphism)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for an ring hom. b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for algebra module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for an algebra-with-one g.m.b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for a left module hom. b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for a ring with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for a magma Congruence with known generating pairs",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence",
+                            "Tester(GeneratingPairsOfMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for a right magma congruence with known generating pairs",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence",
+                            "Tester(GeneratingPairsOfMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for a left magma congruence with known generating pairs",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence",
+                            "Tester(GeneratingPairsOfMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PrintObj: for ANF automorphism",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "PrintObj: for a Frobenius automorphism",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "PrintObj: method for vector space with left module generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "PrintObj: for a ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "PrintObj: for a magma congruence",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "PrintObj: for an algebra g.m.b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PrintObj: method for vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PrintObj: for a inverse monoid with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseMonoid)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PrintObj: pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDefaultRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PrintObj: For a compressed VecFFE",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PrintObj: for free left module with known generators",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PrintObj: for a right semigroup congruence",
+                    "filters": [
+                        [
+                            "IsRightSemigroupCongruence",
+                            "Tester(IsRightSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PrintObj: for a left semigroup congruence",
+                    "filters": [
+                        [
+                            "IsLeftSemigroupCongruence",
+                            "Tester(IsLeftSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PrintObj: for saturated Fitting formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for embedding into wreath product",
+                    "filters": [
+                        [
+                            "IsEmbeddingImprimitiveWreathProductMatrixGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for projection from a direct product",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductMatrixGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for embedding into direct product",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductMatrixGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for embedding into wreath product",
+                    "filters": [
+                        [
+                            "IsEmbeddingWreathProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for projection from subdirect product",
+                    "filters": [
+                        [
+                            "IsProjectionSubdirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for projection from a direct product",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for embedding into direct product",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: method for a PcGroupHomomorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for nat. hom. of pc group",
+                    "filters": [
+                        [
+                            "IsNaturalHomomorphismPcGroupRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for an ring g.m.b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for a left module m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for a left module g.m.b.i",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for a magma with zero adjoined",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsMagmaWithZeroAdjoined"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PrintObj: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PrintObj: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PrintObj: for action homomorphism",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PrintObj: for a right magma congruence",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PrintObj: for a left magma congruence",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PrintObj: for GHBI",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector rep (32 Bits, up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector rep (16 Bits, up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector rep (8 Bits, up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PrintObj: for an equivalence relation",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PrintObj: for product of Fitting formations",
+                    "filters": [
+                        [
+                            "IsFittingProductRep",
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsUnicodeCharacter"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj: modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector rep (32 Bits)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector rep (16 Bits)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector rep (8 Bits)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector (up to date)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj: for a inverse semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintObj: for Fitting formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj: for a saturated formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj: for a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsReesMatrixSemigroup",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj: combinatorial collector",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is32BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is16BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "Is8BitsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj: for monoid with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj: for mapping by function with inverse",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionWithInverseRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintObj: for a subsemigroup of a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PrintObj: for a subsemigroup of a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PrintObj: zmodnze : for full collection Z/nZ(m)",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZepsObj)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PrintObj: for element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PrintObj: for unknown in default representation",
+                    "filters": [
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PrintObj: for a semigroup ideal with known generators",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagmaIdeal)",
+                            "IsSemigroupIdeal",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PrintObj: for a Schunck class",
+                    "filters": [
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: for group general mapping b.i.",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: for large finite field elements (use String)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: laurent polynomial",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: for an add. magma-with-inverses with generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: for a semigroup ideal",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "IsSemigroupIdeal",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintObj: for a Molien series",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "Tester(MolienSeriesInfo)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PrintObj: RightCoset",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PrintObj: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PrintObj: for a magma ideal with known generators",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagmaIdeal)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PrintObj: for -infinity",
+                    "filters": [
+                        [
+                            "IsNegInfinity"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PrintObj: for infinity",
+                    "filters": [
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PrintObj: for formation product",
+                    "filters": [
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for Fitting product",
+                    "filters": [
+                        [
+                            "IsFittingProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for Fitting class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: univar",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for an add. magma-with-zero with generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for a magma ideal",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for a direct product element",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PrintObj: for Fitting set",
+                    "filters": [
+                        [
+                            "IsClassByPropertyRep",
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj: for a semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj: for a right magma ideal with known generators",
+                    "filters": [
+                        [
+                            "IsRightActedOnBySuperset",
+                            "Tester(GeneratorsOfExtRSet)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj: for a left magma ideal with known generators",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "Tester(GeneratorsOfExtLSet)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintObj: for from-the-left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PrintObj: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PrintObj: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PrintObj: rational function",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PrintObj: for an add. magma with generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagma)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PrintObj: for a right magma ideal",
+                    "filters": [
+                        [
+                            "IsRightActedOnBySuperset",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PrintObj: for a left magma ideal",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsPowerCommutatorCollector"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PrintObj: for UEALattice element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PrintObj: for an additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PrintObj: for an add. magma",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PrintObj: for a binary relation on  n points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for s. c. ring element",
+                    "filters": [
+                        [
+                            "IsSCRingObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for symmetric elements",
+                    "filters": [
+                        [
+                            "IsSymmetricPowerElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for wedge elements",
+                    "filters": [
+                        [
+                            "IsWedgeElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for tensor elements",
+                    "filters": [
+                        [
+                            "IsTensorElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: fp algebra elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for magma ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for a mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintObj: for external orbit",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: pcword",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: for weight rep element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: for direct sum elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: for algebra module element in packed representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: method for a subspaces domain",
+                    "filters": [
+                        [
+                            "IsSubspacesVectorSpace",
+                            "IsSubspacesVectorSpaceDefaultRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: for a semi-echelonized basis with basis vectors",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonized",
+                            "Tester(IsSemiEchelonized)",
+                            "Tester(BasisVectors)"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsWeakPointerObject"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PrintObj: for an element of an f.p. group (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PrintObj: sliced perm",
+                    "filters": [
+                        [
+                            "IsSlicedPermInv"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PrintObj: sliced perm",
+                    "filters": [
+                        [
+                            "IsSlicedPerm"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PrintObj: for external subset",
+                    "filters": [
+                        [
+                            "IsExternalSubset"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PrintObj: for a semi-echelonized basis",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonized",
+                            "Tester(IsSemiEchelonized)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PrintObj: for right transversal",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "PrintObj: for a cochain",
+                    "filters": [
+                        [
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "PrintObj: for a sparse rowspace element",
+                    "filters": [
+                        [
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "PrintObj: for a basis with basis vectors",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "Tester(BasisVectors)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "PrintObj: for IsGroupClass and IsClassByPropertyRep",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for a Green's class",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: wreath elements",
+                    "filters": [
+                        [
+                            "IsWreathProductElement"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for element of magma by mult. table",
+                    "filters": [
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsDenseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for an element of a magma with zero adjoined",
+                    "filters": [
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for an enumerator that perhaps has its own `PrintObj' function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintObj: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsSimpleInvAutomatonRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj: for an fp monoid element",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj: External Set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj: assoc word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj: for an eq. class",
+                    "filters": [
+                        [
+                            "IsEquivalenceClass"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintObj:  for IsGroupClassByListRep",
+                    "filters": [
+                        [
+                            "IsGroupClassByListRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for IsClassByUnionRep",
+                    "filters": [
+                        [
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for IsClassByIntersectionRep",
+                    "filters": [
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for IsClassByComplementRep",
+                    "filters": [
+                        [
+                            "IsClassByComplementRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for IsClassByPropertyRep",
+                    "filters": [
+                        [
+                            "IsClassByPropertyRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for an f.p. semigroup element",
+                    "filters": [
+                        [
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for a presentation in default representation",
+                    "filters": [
+                        [
+                            "IsPresentation",
+                            "IsPresentationDefaultRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for an associative word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for a nonassociative word",
+                    "filters": [
+                        [
+                            "IsNonassocWord"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintObj: for an infinite list of generators",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfGeneratorsRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "PrintObj: for an infinite list of names",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfNamesRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "PrintObj: for an enumerator",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsAttributeStoringRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "PrintObj: Wyckoff position",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj: lattice",
+                    "filters": [
+                        [
+                            "IsLatticeSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj: for mutable basis with underlying mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaUnderlyingMutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj: for a mutable basis of a Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianMatrixSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj: for a mutable basis of a Gaussian row space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianRowSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj: for mutable basis represented by a nice mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaNiceMutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj: for mutable basis represented by an immutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisByImmutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj: for an iterator that perhaps has its own `PrintObj' function",
+                    "filters": [
+                        [
+                            "IsIterator",
+                            "IsIteratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsRewritingSystem"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsRandomSource"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: output text none",
+                    "filters": [
+                        [
+                            "IsOutputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: output text file",
+                    "filters": [
+                        [
+                            "IsOutputTextFileRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: output text string",
+                    "filters": [
+                        [
+                            "IsOutputTextStringRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: input text file",
+                    "filters": [
+                        [
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: default directory rep",
+                    "filters": [
+                        [
+                            "IsDirectoryRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: for an info class",
+                    "filters": [
+                        [
+                            "IsInfoClassListRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: for an operation",
+                    "filters": [
+                        [
+                            "IsOperation"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PrintObj: for a straight line decision",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: for a black box program",
+                    "filters": [
+                        [
+                            "IsBBoxProgram"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: for pcp",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: IsObjToBePrinted",
+                    "filters": [
+                        [
+                            "IsObjToBePrinted"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: for a straight line program",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: for a root system",
+                    "filters": [
+                        [
+                            "IsRootSystem"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: closed stream",
+                    "filters": [
+                        [
+                            "IsClosedStream"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: for an iterator",
+                    "filters": [
+                        [
+                            "IsIterator"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: for 'to be defined' objects",
+                    "filters": [
+                        [
+                            "IsToBeDefinedObj"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PRINT_OBJ: for a type",
+                    "filters": [
+                        [
+                            "IsType"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PRINT_OBJ: for a family",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "PrintObj: default method delegating to PrintString",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrintObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrintString: for a group with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PrintString: for a inverse monoid with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseMonoid)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PrintString: for a inverse semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PrintString: for monoid with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintString: for a magma-with-inverses with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintString: RightCoset",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PrintString: for a semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintString: for a magma-with-one with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PrintString: for a magma with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PrintString: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PrintString: for right transversal",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PrintString: for a Green's class",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintString: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintString: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PrintString: default method delegating to String",
+                    "filters": [
+                        []
+                    ],
+                    "rank": -1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PrintString: for an object, and zero",
+                    "filters": [
+                        [],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PrintString: for an object, and a negative integer",
+                    "filters": [
+                        [],
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrintString: for an object, and a positive integer",
+                    "filters": [
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrintString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Display: for partitions of Z^2 into residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 10002
+                },
+                {
+                    "comment": "Display: for matrix of FFEs (for larger fields)",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "Display: for matrix of FFEs",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Display: for matrix over Integers mod n",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "Display: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Display: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Display: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Display: for a nearly character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Display: For large finite field elements",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Display: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Display: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Display: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Display: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Display: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Display: for vector search tables in default representation",
+                    "filters": [
+                        [
+                            "IsVectorSearchTableDefaultRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Display: for a (finite) list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Display: for a straight line decision",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "Display: for a black box program",
+                    "filters": [
+                        [
+                            "IsBBoxProgram"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "Display: for a straight line program",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "Display: for a table of marks (add empty options record)",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "Display: generic: use DisplayString or otherwise PrintObj",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Display: for a class function, and a record",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Display: for a nearly character table, and a list",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Display: for a nearly character table, and a record",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "Display: for a straight line decision, and a record",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Display: for a straight line program, and a record",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Display: for a table of marks and an options record",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Display",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DisplayString: for a partial perm semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "DisplayString: for a transformation semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "DisplayString: For large finite field elements",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "DisplayString: for an internal FFE via String",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "DisplayString: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "DisplayString: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "DisplayString: IsList",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "DisplayString: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "DisplayString: IsChar",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "DisplayString: generic: return default string",
+                    "filters": [
+                        []
+                    ],
+                    "rank": -1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DisplayString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsInternallyConsistent: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsInternallyConsistent: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsInternallyConsistent: for a straight line decision",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "IsInternallyConsistent: for a straight line program",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "IsInternallyConsistent: for a table of marks, decomposition test",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "IsInternallyConsistent: default method 'ReturnTrue'",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInternallyConsistent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsImpossible: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsImpossible)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "IsImpossible",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsLieMatrix"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsImpossible",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsImpossible): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsImpossible): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsImpossible)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsImpossible)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExtRepOfObj: for a straight line program word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 109
+                },
+                {
+                    "comment": "ExtRepOfObj: using 32Bits_ExtRepOfObj",
+                    "filters": [
+                        [
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "ExtRepOfObj: using 16Bits_ExtRepOfObj",
+                    "filters": [
+                        [
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "ExtRepOfObj: using 8Bits_ExtRepOfObj",
+                    "filters": [
+                        [
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "ExtRepOfObj: for an internal cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyc",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ExtRepOfObj: for element in Z/nZ (ModulusRep, nonprime)",
+                    "filters": [
+                        [
+                            "IsZmodnZObjNonprime",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ExtRepOfObj: ExtElm",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement",
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ExtRepOfObj: baseFieldElm",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement",
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ExtRepOfObj: for s. c. ring element in dense coeff. vector rep.",
+                    "filters": [
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ExtRepOfObj: for s. c. algebra element in dense coeff. vector rep.",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ExtRepOfObj: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ExtRepOfObj: for f.p. algebra element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ExtRepOfObj: for magma ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ExtRepOfObj: for weight rep element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ExtRepOfObj: for an UEALattice element",
+                    "filters": [
+                        [
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ExtRepOfObj: for a cochain",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ExtRepOfObj: for a direct sum element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ExtRepOfObj: for a sparse rowspace element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ExtRepOfObj: for a monomial element",
+                    "filters": [
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ExtRepOfObj: for algebra module element in packed element rep",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ExtRepOfObj: for an element of an f.p. group (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ExtRepOfObj: for a inf. bits assoc. word",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExtRepOfObj: for a 32 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExtRepOfObj: for a 16 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExtRepOfObj: for an 8 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExtRepOfObj: for a nonassoc. word",
+                    "filters": [
+                        [
+                            "IsNonassocWord",
+                            "IsBracketRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ExtRepOfObj: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ExtRepOfObj",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ExtRepOfObj: assoc word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtRepOfObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ObjByExtRep: for floats",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsFloat)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ObjByExtRep: for family of elements in Z/nZ (nonprime), and integer",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsZmodnZObjNonprime)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ObjByExtRep: for a family of nonassociative words, and an integer",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsNonassocWord)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ObjByExtRep: baseFieldElm",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsAlgebraicElement)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ObjByExtRep: for s. c. alg. elms. family with coefficients family",
+                    "filters": [
+                        [
+                            "IsFamilyOverFullCoefficientsFamily",
+                            "CategoryFamily(IsSCAlgebraObj)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ObjByExtRep: for a InfBits-family of associative words, and a homogeneous list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "IsInfBitsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ObjByExtRep: for a 32Bits-family of associative words, and a homogeneous list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "Is32BitsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ObjByExtRep: for a 16Bits-family of associative words, and a homogeneous list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "Is16BitsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ObjByExtRep: for a 8Bits-family of associative words, and a homogeneous list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "Is8BitsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ObjByExtRep: for s. c. ring elements family",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsSCRingObj)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ObjByExtRep: for s. c. algebra elements family",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsSCAlgebraObj)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ObjByExtRep: letter rep family",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "IsLetterWordsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ObjByExtRep: for a family of associative words, and a homogeneous list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "IsSyllableWordsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ObjByExtRep: ExtElm",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsAlgebraicElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ObjByExtRep: for family of f.p. algebra elements with normal form",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpAlgebra)",
+                            "Tester(NiceNormalFormByExtRepFunction)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ObjByExtRep: for family of UEALattice elements, and list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsUEALatticeElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ObjByExtRep: for magma ring elements family, and list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfMagmaRingModuloRelations)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ObjByExtRep: using 32Bits_AssocWord",
+                    "filters": [
+                        [
+                            "IsElementsFamilyBy32BitsSingleCollector"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ObjByExtRep: using 16Bits_AssocWord",
+                    "filters": [
+                        [
+                            "IsElementsFamilyBy16BitsSingleCollector"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ObjByExtRep: using 8Bits_AssocWord",
+                    "filters": [
+                        [
+                            "IsElementsFamilyBy8BitsSingleCollector"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ObjByExtRep: for a family of nonassociative words, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsNonassocWord)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ObjByExtRep: for a family of weight rep elements and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsWeightRepElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ObjByExtRep: for a family of direct sum elements and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsDirectSumElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ObjByExtRep: for a sparse rowspace element family and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsSparseRowSpaceElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ObjByExtRep: for a family of monomial elements and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsMonomialElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ObjByExtRep: reconstruct a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ObjByExtRep: for algebra module elements family, object",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsAlgebraModuleElement)"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ObjByExtRep: for a 32 bits assoc. words family, two integers, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "Is32BitsFamily"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ObjByExtRep: for a 16 bits assoc. words family, two integers, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "Is16BitsFamily"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ObjByExtRep: for an 8 bits assoc. words family, two integers, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "Is8BitsFamily"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ObjByExtRep: letter rep family,integers (ignored)",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "IsLetterWordsFamily"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ObjByExtRep: for an inf. bits assoc. words family, two integers, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "IsInfBitsFamily"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "ObjByExtRep: for a fam. of assoc. words, a cyclotomic, an int., and a homog. list",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))",
+                            "IsSyllableWordsFamily"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ObjByExtRep",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KnownAttributesOfObject: for an object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnownAttributesOfObject",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KnownPropertiesOfObject: for an object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnownPropertiesOfObject",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KnownTruePropertiesOfObject: for an object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnownTruePropertiesOfObject",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CategoriesOfObject: for an object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CategoriesOfObject",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RepresentationsOfObject: for an object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentationsOfObject",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PostMakeImmutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PostMakeImmutable",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PostMakeImmutable",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PostMakeImmutable: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PostMakeImmutable: unless otherwise directed, do nothing",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PostMakeImmutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MemoryUsage: for a plist",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsPlistRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "MemoryUsage: for a rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MemoryUsage: for a type",
+                    "filters": [
+                        [
+                            "IsType"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "MemoryUsage: for a family",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "MemoryUsage: for a function",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "MemoryUsage: for a component object",
+                    "filters": [
+                        [
+                            "IsComponentObjectRep"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "MemoryUsage: for a positional object",
+                    "filters": [
+                        [
+                            "IsPositionalObjectRep"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "MemoryUsage: for a record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "MemoryUsage: fallback method for objs without subobjs",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MemoryUsage",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            []
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FlushCaches",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CollectionsFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CollectionsFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "CollectionsFamily: for a family",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 91
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CollectionsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CollectionsFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CollectionsFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CollectionsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CollectionsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ElementsFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ElementsFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ElementsFamily): method to inherit `Characteristic' to collections families",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsFamily"
+                        ],
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Setter(ElementsFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ElementsFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ElementsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ElementsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UseSubsetRelation: default method that checks maintenances and then returns `true'",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UseSubsetRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UseIsomorphismRelation: default method that checks maintenances and then returns `true'",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UseIsomorphismRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "UseFactorRelation",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "UseFactorRelation: default method that checks maintenances and then returns `true'",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UseFactorRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Iterator: for a trivial collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsTrivial",
+                            "Tester(IsTrivial)"
+                        ]
+                    ],
+                    "rank": 10006
+                },
+                {
+                    "comment": "Iterator",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 432
+                },
+                {
+                    "comment": "Iterator: for a trivial permutation group",
+                    "filters": [
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "Iterator: for `Rationals'",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "Iterator: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Iterator: for a free group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Iterator: for `Integers'",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "Iterator: for `PositiveIntegers'",
+                    "filters": [
+                        [
+                            "IsPositiveIntegers"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Iterator: for free left module (delegate to 'IteratorByBasis')",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Iterator: more helpful error for integers",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Iterator: for a free monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Iterator: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Iterator: for subspaces collection of a (finite) full row module",
+                    "filters": [
+                        [
+                            "IsSubspacesVectorSpace",
+                            "IsSubspacesFullRowSpaceDefaultRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Iterator: for a subspaces domain",
+                    "filters": [
+                        [
+                            "IsSubspacesVectorSpace",
+                            "IsSubspacesVectorSpaceDefaultRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Iterator: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Iterator: for a collection that is a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Iterator: for a mutable iterator",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsIterator"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Iterator: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Iterator: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Iterator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IteratorSorted: for a collection that is a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IteratorSorted: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IteratorSorted: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IteratorSorted",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIterator"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsDoneIterator: primitive groups iterator",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsIterator",
+                            "IsPrimGrpIterRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsDoneIterator: for iterators of residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsIterator",
+                            "IsResidueClassUnionsIteratorRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "IsDoneIterator: for `IsIteratorByFunctions'",
+                    "filters": [
+                        [
+                            "IsIterator",
+                            "IsIteratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsDoneIterator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsIterator"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NextIterator: for iterators of residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsIterator",
+                            "IsResidueClassUnionsIteratorRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "NextIterator: primitive groups iterator",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsIterator",
+                            "IsPrimGrpIterRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "NextIterator: for `IsIteratorByFunctions'",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsIterator",
+                            "IsIteratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "NextIterator: for an immutable iterator (print a reasonable error message)",
+                    "filters": [
+                        [
+                            "IsIterator"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NextIterator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsEmpty: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsEmpty",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "Tester(ContainsTrivialGroup)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsEmpty",
+                    "filters": [
+                        [
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsEmpty",
+                    "filters": [
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsEmpty",
+                    "filters": [
+                        [
+                            "IsClassByComplementRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsEmpty",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(Size)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsEmpty: for generic class",
+                    "filters": [
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IsEmpty: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IsEmpty: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsEmpty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsEmpty): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsEmpty): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsEmpty)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsEmpty)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTrivial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTrivial)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsTrivial: for a division ring",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsTrivial: for a FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "IsTrivial: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsTrivial: for a FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsTrivial: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(Size)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsTrivial",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(IsNonTrivial)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "IsTrivial: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTrivial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTrivial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTrivial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTrivial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTrivial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNonTrivial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNonTrivial)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsNonTrivial",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(IsTrivial)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "IsNonTrivial: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNonTrivial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNonTrivial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNonTrivial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNonTrivial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNonTrivial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ],
+            [
+                [
+                    "IsFloat"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFinite: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsFinite: via Minkowski kernel (short but not too efficient)",
+                    "filters": [
+                        [
+                            "IsIntegerMatrixGroup",
+                            "Tester(IsIntegerMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsFinite: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsFinite: cyclotomic matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsFinite: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsFinite: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsFinite: for a magma ring modulo the span of ``zero''",
+                    "filters": [
+                        [
+                            "IsMagmaRingModuloSpanOfZero"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsFinite: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsFinite",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(IsFiniteDimensional)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsFinite: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsFinite: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsFinite: for an underlying relation of a general mapping",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "IsFinite: for a semigroup of assoc. words",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsFinite: for a Rees 0-matrix subsemigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsFinite: for a Rees matrix subsemigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsFinite",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsFinite: for a magma of nonassoc. words",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsNonassocWord)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsFinite: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsFinite: for an additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsFinite: for a conjugacy class",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsFinite: method for an ext. orbit by stabilizer",
+                    "filters": [
+                        [
+                            "IsExternalOrbitByStabilizerRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsFinite",
+                    "filters": [
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsFinite",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(Size)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsFinite: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFinite",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFinite): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFinite): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFinite)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFinite)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsWholeFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsWholeFamily)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsWholeFamily: for a finitely generated free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsWholeFamily: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsWholeFamily: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsWholeFamily: for s. c. algebra elements collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSCAlgebraObj)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsWholeFamily: for a free monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsWholeFamily: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsWholeFamily: for a subsemigroup of a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsWholeFamily: for a subsemigroup of a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsWholeFamily: for a free magma",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsNonassocWord)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsWholeFamily: default for a collection, print an error message",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsWholeFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsWholeFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsWholeFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsWholeFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsWholeFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Size: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Size)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "Size: natural SL",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalSL",
+                            "Tester(IsNaturalSL)"
+                        ]
+                    ],
+                    "rank": 397
+                },
+                {
+                    "comment": "Size: general linear group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "Size: for groups of FFE",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "Size: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "Size",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "Size",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "Size: for a permutation group that knows to be a direct product",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Size: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Size: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Size",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Size: cyclotomic matrix group not known to be finite",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Size: for a matrix group that knows to be a wreath product",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Size: for a matrix group that knows to be a direct product",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Size: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Size: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Size: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "Size: infinite abelianization",
+                    "filters": [
+                        [
+                            "Tester(AbelianInvariants)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Size: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Size: subgroups of finitely presented groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Size: for a group with known ordinary character table",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(OrdinaryCharacterTable)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Size: subdirect product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SubdirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Size: group direct product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Size: for sc rings and their subrings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Size: characteristic zero ring is infinite",
+                    "filters": [
+                        [
+                            "Tester(Characteristic)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Size: for a free monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Size: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Size: for a character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Size: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Size: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Size: for an underlying relation of a general mapping",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Size",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Size: zmodnze : for full ring Z/nZ(m)",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZepsObj)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Size: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Size: for a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroup",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Size: for a free magma",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsNonassocWord)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Size: for an additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Size: for a magma with a zero adjoined",
+                    "filters": [
+                        [
+                            "IsMagmaWithZeroAdjoined"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Size: method for a rational class",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Size: for a conjugacy class",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Size: method for an ext. orbit by stabilizer",
+                    "filters": [
+                        [
+                            "IsExternalOrbitByStabilizerRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Size: method for a subspaces domain",
+                    "filters": [
+                        [
+                            "IsSubspacesVectorSpace",
+                            "IsSubspacesVectorSpaceDefaultRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Size: for a trivial domain",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Size: double coset",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Size: for Green's classes",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Size: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Size: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsDenseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Size: for a list that is a collection",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Size",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(AsList)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Size",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Size: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Size: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Size",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Size): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Size): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Size)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Size)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Representative: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Representative)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "Representative: for additive-magma-with-zero with known zero",
+                    "filters": [
+                        [
+                            "Tester(ZeroImmutable)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 10018
+                },
+                {
+                    "comment": "Representative: for magma-with-one with known one",
+                    "filters": [
+                        [
+                            "Tester(OneImmutable)",
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 10016
+                },
+                {
+                    "comment": "Representative: for additive coset in default repres.",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset",
+                            "IsAdditiveCosetDefaultRep"
+                        ]
+                    ],
+                    "rank": 10014
+                },
+                {
+                    "comment": "Representative",
+                    "filters": [
+                        [
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Representative: for a division ring with known generators",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "Tester(GeneratorsOfDivisionRing)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "Representative: for full matrix module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Representative: for full row module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Representative: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Representative: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Representative: for left operator ring-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftOperatorRingWithOne)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Representative: for left operator ring with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Representative: for a ring-with-one with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRingWithOne)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Representative: for a ring with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Representative: for a subsemigroup of Rees 0-matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Representative: for a subsemigroup of Rees matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Representative: for right operator additive group with known generators",
+                    "filters": [
+                        [
+                            "IsExtRSet",
+                            "IsDistributiveROpDSum",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfRightOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Representative: for left operator additive group with known generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsDistributiveLOpDSum",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Representative: for additive-magma-with-inverses with known generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Representative: for magma-with-inverses with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Representative: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Representative: for a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroup",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Representative: for additive-magma-with-zero with stored parent",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Representative: for additive-magma-with-zero with known generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Representative: for magma-with-one with stored parent",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Representative: for magma-with-one with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Representative: for additive magma with known generators",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagma)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Representative: for magma with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Representative: External Set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Representative: for a domain with known domain generators",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "Tester(GeneratorsOfDomain)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Representative: for a domain with known elements list",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(AsList)",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Representative: for a collection that is a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Representative: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Representative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Representative): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Representative): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Representative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Representative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RepresentativeSmallest: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RepresentativeSmallest)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "RepresentativeSmallest: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "RepresentativeSmallest: for a strictly sorted list",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "RepresentativeSmallest",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(AsSSortedList)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "RepresentativeSmallest",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(EnumeratorSorted)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "RepresentativeSmallest: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "RepresentativeSmallest: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativeSmallest",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RepresentativeSmallest): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RepresentativeSmallest): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RepresentativeSmallest)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RepresentativeSmallest)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ],
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsRandomSource"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsRandomSource"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 432
+                },
+                {
+                    "comment": "Random: for natural SL",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalSL",
+                            "Tester(IsNaturalSL)"
+                        ]
+                    ],
+                    "rank": 397
+                },
+                {
+                    "comment": "Random: for natural GL",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "Random: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "Random: for an internal list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 119
+                },
+                {
+                    "comment": "Random: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "Random: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsDenseHashRep"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "Random: alternating group: floyd's algorithm",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "Random: symmetric group: floyd's algorithm",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "Random: for Rationals",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "Random: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "Random: for a finite prime field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Random: for a finite field with known primitive root",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "Tester(PrimitiveRoot)"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "Random: Alg",
+                    "filters": [
+                        [
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "Random: for full ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "Random: for full matrix module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Random: for full row module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Random: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Random: fp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Random: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Random: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Random: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Random: for `Integers'",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "Random: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Random: LAGUNA: for full ot normalized unit group of group ring",
+                    "filters": [
+                        [
+                            "IsGroupOfUnitsOfMagmaRing",
+                            "Tester(IsGroupOfUnitsOfMagmaRing)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Random: for a free monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Random: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Random: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Random: zmodnze : for full collection Z/nZ(m)",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZepsObj)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Random: RightCoset",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Random: for a free magma",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsNonassocWord)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Random: for an additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Random: for external orbit: via acting domain",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Random: for a dense small list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Random: double coset",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPadicExtensionNumber)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPurePadicNumber)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Random: for an infinite list of generators",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfGeneratorsRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Random: for a (finite) collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Random: for a dense (small) list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Random:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Random: for two integers",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Random: for a real random source and a list",
+                    "filters": [
+                        [
+                            "IsRealRandomSource"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "IsMersenneTwister"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "IsGAPRandomSource"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "IsGlobalRandomSource"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "IsRandomSource"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Random: for a real random source and two integers",
+                    "filters": [
+                        [
+                            "IsRealRandomSource"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "IsMersenneTwister"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "Random",
+                    "filters": [
+                        [
+                            "IsRandomSource"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Random",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PseudoRandom: for an internal list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 111
+                },
+                {
+                    "comment": "PseudoRandom: subgroups fp group: force generators",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "PseudoRandom: product replacement",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PseudoRandom: polynomial ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PseudoRandom: RightCoset",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "PseudoRandom: double coset",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "PseudoRandom: for a list or collection (delegate to `Random')",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PseudoRandom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PseudoRandomSeed: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PseudoRandomSeed)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PseudoRandomSeed",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PseudoRandomSeed): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PseudoRandomSeed): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PseudoRandomSeed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PseudoRandomSeed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Enumerator: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Enumerator)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "Enumerator: for full ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 10023
+                },
+                {
+                    "comment": "Enumerator: for a collection with known `AsSSortedList' value",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(AsSSortedList)"
+                        ]
+                    ],
+                    "rank": 10003
+                },
+                {
+                    "comment": "Enumerator: for a collection with known `AsList' value",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(AsList)"
+                        ]
+                    ],
+                    "rank": 10003
+                },
+                {
+                    "comment": "Enumerator",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 432
+                },
+                {
+                    "comment": "Enumerator: use nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 377
+                },
+                {
+                    "comment": "Enumerator: for `Rationals'",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "Enumerator: for trivial magma-with-one",
+                    "filters": [
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "Enumerator: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Enumerator: for a finite prime field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Enumerator: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Enumerator: for enumerator of a free group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Enumerator: fp gp.",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Enumerator: finite pc computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Enumerator: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "Enumerator: generic method for a group",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Enumerator: generic method for a ring-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRingWithOne)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Enumerator: generic method for a two-sided ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Enumerator: generic method for a right ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Enumerator: generic method for a left ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Enumerator: generic method for a two-sided ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Enumerator: generic method for a right ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Enumerator: generic method for a left ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Enumerator: generic method for a ring with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Enumerator: for a free monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Enumerator: for free left module (delegate to 'EnumeratorByBasis')",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Enumerator: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)",
+                            "Tester(UnderlyingSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Enumerator: for a full transformation semigroup",
+                    "filters": [
+                        [
+                            "IsFullTransformationSemigroup",
+                            "Tester(IsFullTransformationSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Enumerator: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Enumerator: for an underlying relation of a general mapping",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Enumerator: for trivial add. magma-with-zero",
+                    "filters": [
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Enumerator: zmodnze : for full collection Z/nZ(m)",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZepsObj)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Enumerator: for a semigroup ideal",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfMagmaIdeal)",
+                            "IsSemigroupIdeal",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Enumerator: generic method for a magma ideal",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Enumerator: for a right coset",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Enumerator: for a left semigroup ideal",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfExtLSet)",
+                            "IsLeftSemigroupIdeal",
+                            "Tester(IsLeftSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Enumerator: for a right semigroup ideal",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfExtRSet)",
+                            "IsRightSemigroupIdeal",
+                            "Tester(IsRightSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Enumerator: for a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroup",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Enumerator: for a free magma",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "CategoryCollections(IsWord)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Enumerator: generic method for an add. magma",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Enumerator: for a generic semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Enumerator",
+                    "filters": [
+                        [
+                            "IsConjugacyClassPermGroupRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Enumerator: generic method for a magma",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Enumerator",
+                    "filters": [
+                        [
+                            "IsRationalClassPermGroupRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Enumerator: for an additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Enumerator",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Enumerator: xorb by stabilizer",
+                    "filters": [
+                        [
+                            "IsExternalOrbitByStabilizerRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Enumerator: <xorb by pcgs>",
+                    "filters": [
+                        [
+                            "IsExternalOrbit",
+                            "IsExternalSetByPcgs"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Enumerator: for external orbit: compute orbit",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Enumerator: for external subset with home enumerator",
+                    "filters": [
+                        [
+                            "IsExternalSubset",
+                            "Tester(HomeEnumerator)"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Enumerator: method for a subspaces domain",
+                    "filters": [
+                        [
+                            "IsSubspacesVectorSpace",
+                            "IsSubspacesVectorSpaceDefaultRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Enumerator: for a magma congruence class",
+                    "filters": [
+                        [
+                            "IsCongruenceClass"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Enumerator: for degenerated residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsResidueClassUnionOfZxZ"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Enumerator: for a double coset",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Enumerator",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(EnumeratorSorted)",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Enumerator: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Enumerator: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsDenseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Enumerator: external set -> HomeEnumerator",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Enumerator: for list dictionaries",
+                    "filters": [
+                        [
+                            "IsListDictionary"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Enumerator: for equivalence classes",
+                    "filters": [
+                        [
+                            "IsEquivalenceClass"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Enumerator: for a domain with stored domain generators",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "Tester(GeneratorsOfDomain)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Enumerator: for a collection that is a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Enumerator",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(AsList)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Enumerator: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Enumerator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Enumerator): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Enumerator): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Enumerator)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Enumerator)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EnumeratorSorted: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EnumeratorSorted)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "EnumeratorSorted: for a collection with known `AsSSortedList' value",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(AsSSortedList)"
+                        ]
+                    ],
+                    "rank": 10003
+                },
+                {
+                    "comment": "EnumeratorSorted: for a finite prime field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "EnumeratorSorted: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "EnumeratorSorted: for a plist",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsPlistRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "EnumeratorSorted: for a domain",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "EnumeratorSorted",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(AsSSortedList)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "EnumeratorSorted: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EnumeratorSorted",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EnumeratorSorted): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EnumeratorSorted): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EnumeratorSorted)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EnumeratorSorted)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingCollection: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingCollection)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingCollection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingCollection): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingCollection): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ],
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ListOp: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ListOp: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ListOp: for a collection that is a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ListOp: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ListOp: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ListOp",
+                    "filters": [
+                        [
+                            "IsIterator"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ListOp: for a plist matrix and a function",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ListOp: for a plist vector and a function",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ListOp: for degenerated residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsResidueClassUnionOfZxZ"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ListOp: for a dense list, and a function",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ListOp: for a list, and a function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ListOp: for a list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ListOp",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ],
+                        []
+                    ],
+                    "rank": 1
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ListOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SortedList: for a list or collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SortedList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SSortedList: for a plist",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsPlistRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "SSortedList: for a collection that is a small list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "SSortedList: for a collection that is a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "SSortedList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "SSortedList: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SSortedList: for a list, and a function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "SSortedList: for a collection, and a function",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SSortedList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsList)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AsList",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 432
+                },
+                {
+                    "comment": "AsList: permgp: AsSSortedList",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "AsList: for a finite prime field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "AsList: for full ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "AsList: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "AsList: pc group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "AsList: pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDefaultRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "AsList: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AsList: for classes of subgroups",
+                    "filters": [
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AsList",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AsList: xorb by stabilizer",
+                    "filters": [
+                        [
+                            "IsExternalOrbitByStabilizerRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AsList: for Pc transversals",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalPcGroupRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AsList: external orbit",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AsList: double coset",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AsList",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(AsSSortedList)",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AsList: for an enumerator that perhaps has its own `AsList' function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AsList: for a domain with stored domain generators",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "Tester(GeneratorsOfDomain)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "AsList: for collections that are constant time access lists",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsConstantTimeAccessList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "AsList: for a constant time access list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsConstantTimeAccessList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "AsList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "AsList: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "AsList",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsList): for an underlying relation and a list of direct product elements",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ],
+                        [
+                            "CategoryCollections(IsDirectProductElement)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "Setter(AsList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSortedList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSortedList)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AsSortedList: for a list or collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSortedList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSortedList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSortedList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSortedList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSortedList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSSortedList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSSortedList)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AsSSortedList: via stabchain",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "AsSSortedList: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "AsSSortedList: for full ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "AsSSortedList: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "AsSSortedList: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AsSSortedList: for a plist",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsPlistRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "AsSSortedList: for a left magma ideal",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "Tester(GeneratorsOfExtLSet)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AsSSortedList: for a right magma ideal",
+                    "filters": [
+                        [
+                            "IsRightActedOnBySuperset",
+                            "Tester(GeneratorsOfExtRSet)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AsSSortedList: external orbit",
+                    "filters": [
+                        [
+                            "IsExternalOrbit"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AsSSortedList: for a Green's class",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AsSSortedList: for a collection that is a constant time access list",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsConstantTimeAccessList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "AsSSortedList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "AsSSortedList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "AsSSortedList: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSSortedList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSSortedList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSSortedList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSSortedList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSSortedList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSSortedListNonstored: if `AsSSortedList' is known",
+                    "filters": [
+                        [
+                            "IsListOrCollection",
+                            "Tester(AsSSortedList)"
+                        ]
+                    ],
+                    "rank": 10002
+                },
+                {
+                    "comment": "AsSSortedListNonstored: if `AsList' is known:sort",
+                    "filters": [
+                        [
+                            "IsListOrCollection",
+                            "Tester(AsList)"
+                        ]
+                    ],
+                    "rank": 2502
+                },
+                {
+                    "comment": "AsSSortedListNonstored: via stabchain",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "AsSSortedListNonstored: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "AsSSortedListNonstored: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSSortedListNonstored",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SumOp: for a dense list",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "SumOp: for a list/collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SumOp: for a list, and initial value",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "SumOp: for a dense list, and a function",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "SumOp: for a list/collection, and init. value",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "SumOp: for a list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SumOp: for a list, a function, and initial value",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "SumOp: for a list/collection, and a function, and an initial value",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SumOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ProductOp: for a dense list",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ProductOp: for a list/collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ProductOp: for a list, and initial value",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ProductOp: for a dense list and a function",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ProductOp: for a list/collection, and initial value",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ProductOp: for a list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ProductOp: for a list, a function, and initial value",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ProductOp: for a list/collection, a function, and an initial value",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProductOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FilteredOp: for an empty list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10004
+                },
+                {
+                    "comment": "FilteredOp: for degenerated residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsResidueClassUnionOfZxZ"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "FilteredOp: for a dense list, and a function",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "FilteredOp: for a list, and a function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "FilteredOp: for a list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FilteredOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NumberOp: for a dense list",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "NumberOp: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "NumberOp: for a list/collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NumberOp: for a dense list, and a function",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "NumberOp: for a list, and a function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "NumberOp: for a list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumberOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ForAllOp: for an empty list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10004
+                },
+                {
+                    "comment": "ForAllOp: for degenerated residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsResidueClassUnionOfZxZ"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ForAllOp: for a dense list, and a function",
+                    "filters": [
+                        [
+                            "IsDenseList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ForAllOp: for a list, and a function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ForAllOp: for a list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ForAllOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ForAnyOp: for an empty list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10004
+                },
+                {
+                    "comment": "ForAnyOp: for degenerated residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsResidueClassUnionOfZxZ"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ForAnyOp: for a dense list, and a function",
+                    "filters": [
+                        [
+                            "IsDenseList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ForAnyOp: for a list, and a function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ForAnyOp: for a list/collection, and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ForAnyOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsSubset: permgrp of natsymmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 10120
+                },
+                {
+                    "comment": "IsSubset: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 10092
+                },
+                {
+                    "comment": "IsSubset: test whether domain is parent of the other",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "Tester(ParentAttr)"
+                        ]
+                    ],
+                    "rank": 10011
+                },
+                {
+                    "comment": "IsSubset: for two collections with known sizes, check sizes",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(Size)"
+                        ],
+                        [
+                            "IsCollection",
+                            "Tester(Size)"
+                        ]
+                    ],
+                    "rank": 10008
+                },
+                {
+                    "comment": "IsSubset: for two collections, the first containing the whole family",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10008
+                },
+                {
+                    "comment": "IsSubset: for two collections, check for identity",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10005
+                },
+                {
+                    "comment": "IsSubset: handled by nice monomorphism: attribute CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "IsSubset: field, 8bit-vector",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 475
+                },
+                {
+                    "comment": "IsSubset: field, 8bit-vector",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 472
+                },
+                {
+                    "comment": "IsSubset: polynomial rings",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 129
+                },
+                {
+                    "comment": "IsSubset: for two finite fields in the same family",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 112
+                },
+                {
+                    "comment": "IsSubset: for Integers and Rationals (ResClasses)",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 109
+                },
+                {
+                    "comment": "IsSubset: for Z_pi and Rationals (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 102
+                },
+                {
+                    "comment": "IsSubset: for Rationals and Z_(pi) (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 102
+                },
+                {
+                    "comment": "IsSubset",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "IsSubset",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "IsSubset: for subgroups of free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "IsSubset: for two division rings",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "IsSubset: for certain cyclotomic semirings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "IsSubset: 2-sided ideal in ring, naive",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "IsSubset: for two FLMLORs-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "IsSubset: for Z_(pi) and Integers (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "IsSubset: subgroups of fp group by quot. rep",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "IsSubset: subgroups of fp group: test generators",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "IsSubset: subgp fp group: via quotient rep",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IsSubset: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FamilyPcgs)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "IsSubset: for two FLMLORs",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "IsSubset: for Z_(pi)'s (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "IsSubset: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "IsSubset: for two rings-with-one",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRingWithOne)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "IsSubset: for two rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "IsSubset: for two free left modules",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsSubset: for two magmas with inverses",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ],
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsSubset: for two additive magmas with inverses",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "IsSubset: for two additive magmas with zero",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "IsSubset: for two magmas with one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne"
+                        ],
+                        [
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "IsSubset: for two additive magmas",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsSubset: for two magmas",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsSubset: for two collections that are internal lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsInternalRep",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsSubset: for two internal lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsSubset: for collection and empty list",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsSubset: for empty list and collection",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsSubset: for two residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsSubset: for two unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsSubset: for a residue class union and the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsSubset: for the base ring and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsSubset: for residue class union and element list (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IsSubset: for two collections with known `AsSSortedList'",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "Tester(AsSSortedList)"
+                        ],
+                        [
+                            "IsCollection",
+                            "Tester(AsSSortedList)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "IsSubset: for two collections (loop over the elements of the second)",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsSubset: for two collections in different families",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubset",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Intersection2: domain and whole family",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)"
+                        ]
+                    ],
+                    "rank": 10009
+                },
+                {
+                    "comment": "Intersection2: whole family and domain",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10009
+                },
+                {
+                    "comment": "Intersection2: for two times the same ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 10002
+                },
+                {
+                    "comment": "Intersection2: for two fields of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 838
+                },
+                {
+                    "comment": "Intersection2: handled by nice monomorphism:group CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "Intersection2: for two cyclotomic fields of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "Intersection2: for abelian number field and cyclotomic field",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 132
+                },
+                {
+                    "comment": "Intersection2: for cyclotomic field and abelian number field",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 132
+                },
+                {
+                    "comment": "Intersection2: for two abelian number fields",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 130
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 124
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 124
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 124
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 124
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 120
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 120
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 120
+                },
+                {
+                    "comment": "Intersection2",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 120
+                },
+                {
+                    "comment": "Intersection2: perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "Intersection2: two AffineCrystGroupsOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "Intersection2: two AffineCrystGroupsOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "Intersection2: for Z_(pi) and Rationals (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 102
+                },
+                {
+                    "comment": "Intersection2: for Rationals and Z_(pi) (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 102
+                },
+                {
+                    "comment": "Intersection2: for subgroups of free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "Intersection2: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "Intersection2: for certain cyclotomic semirings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "Intersection2: generic method for two FLMLORs-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "Intersection2: subgroups of fp group by quotient",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "Intersection2: subgroups of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "Intersection2: for two spaces in a common s.c. algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "CategoryCollections(IsSCAlgebraObj)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "CategoryCollections(IsSCAlgebraObj)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "Intersection2: groups with pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "Intersection2: generic method for two FLMLORs",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "Intersection2: for Z_(pi)'s (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "Intersection2: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "Intersection2: for two Gaussian row spaces",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "Intersection2: method for two vector spaces",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "Intersection2: for Fitting sets",
+                    "filters": [
+                        [
+                            "IsFittingSetRep"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Intersection2: for Fitting class and Fitting set",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Intersection2: for Fitting set and Fitting class",
+                    "filters": [
+                        [
+                            "IsFittingSetRep"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Intersection2: for two additive cosets",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ],
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Intersection2: for the empty set and a set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Intersection2: for a set and the empty set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Intersection2: for two residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Intersection2: for two unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Intersection2: for the base ring and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Intersection2: for a residue class union and the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Intersection2: for a residue class union and a finite set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Intersection2: for two group classes by list",
+                    "filters": [
+                        [
+                            "IsGroupClassByListRep"
+                        ],
+                        [
+                            "IsGroupClassByListRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Intersection2: of two class intersections",
+                    "filters": [
+                        [
+                            "IsClassByIntersectionRep"
+                        ],
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Intersection2: for two collections in the same family, both lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Intersection2: for grp class and group class by list",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ],
+                        [
+                            "IsGroupClassByListRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Intersection2: for group class by list and group class",
+                    "filters": [
+                        [
+                            "IsGroupClassByListRep"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Intersection2: of class and small list",
+                    "filters": [
+                        [
+                            "IsClass"
+                        ],
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Intersection2: for a finite set and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Intersection2: of class and small list/coll",
+                    "filters": [
+                        [
+                            "IsClass"
+                        ],
+                        [
+                            "IsListOrCollection",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(Size)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Intersection2: of small list and class/list/coll",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Intersection2: of small list/coll and class",
+                    "filters": [
+                        [
+                            "IsListOrCollection",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(Size)"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Intersection2: for two collections in the same family, the first being a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Intersection2: for two collections in the same family, the second being a list",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Intersection2: of class intersection and class/list/coll",
+                    "filters": [
+                        [
+                            "IsClassByIntersectionRep"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Intersection2: of class/list/coll and class intersection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Intersection2: of two classes",
+                    "filters": [
+                        [
+                            "IsClass"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Intersection2: for two collections in the same family",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Intersection2: for two collections in different families",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Intersection2: for two lists (not necessarily in the same family)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Intersection2: of list/collection and class",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Intersection2: of list/collection and list/collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Intersection2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Union2: for two times the same row module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "Union2: for two times the same ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "Union2: for two residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Union2: for two unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Union2: for the base ring and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Union2: for a residue class union and the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Union2: for a residue class union and a finite set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Union2: for two class unions",
+                    "filters": [
+                        [
+                            "IsClassByUnionRep"
+                        ],
+                        [
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Union2: for two collections that are lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Union2: for a finite set and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Union2: for the base ring and a finite set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Union2: for a finite set and the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Union2: for two collections, the first being a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Union2: for two collections, the second being a list",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Union2: for class union and class/list/collection",
+                    "filters": [
+                        [
+                            "IsClassByUnionRep"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Union2: for class/list/collection and class union",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Union2: for two collections",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Union2: for two lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Union2: for two classes/lists/collections",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Union2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Difference: for a domain and the empty set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "Difference: for two times the same ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10010
+                },
+                {
+                    "comment": "Difference: for a residue class union and a finite set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 111
+                },
+                {
+                    "comment": "Difference: for Z^2 and a finite set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "Difference: for a ring and a finite set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Difference: for collection, and empty list",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Difference: for two residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ],
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Difference: for empty list, and collection",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Difference: for two unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Difference: for a residue class union and the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Difference: for the base ring and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Difference: for two collections that are lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Difference: for group class by list and group class",
+                    "filters": [
+                        [
+                            "IsGroupClassByListRep"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Difference: for a finite set and a residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Difference: for two collections, the second being a list",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Difference: for two collections, the first being a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Difference: for two collections",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Difference: for two lists (assume one can produce a sorted result)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Difference: for two classes/lists/collections",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Difference",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanEasilyCompareElements: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanEasilyCompareElements)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "CanEasilyCompareElements: empty homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "CanEasilyCompareElements: for direct product element",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "CanEasilyCompareElements: homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "CanEasilyCompareElements: family: default false",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "CanEasilyCompareElements: generic: inherit `true' from family",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanEasilyCompareElements",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanEasilyCompareElements): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanEasilyCompareElements): family setter",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        []
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "Setter(CanEasilyCompareElements): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanEasilyCompareElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanEasilyCompareElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanEasilySortElements: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanEasilySortElements)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "CanEasilySortElements: empty homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "CanEasilySortElements: homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "CanEasilySortElements: family: default false",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "CanEasilySortElements: generic: inherit `true' from family",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanEasilySortElements",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanEasilySortElements): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanEasilySortElements): family setter",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        []
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "Setter(CanEasilySortElements): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanEasilySortElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanEasilySortElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CanComputeIsSubset",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "CanComputeIsSubset",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "CanComputeIsSubset: whole fp family group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "CanComputeIsSubset: if membership test works",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CanEasilyTestMembership"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "CanComputeIsSubset: default for domains: no unless identical",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "CanComputeIsSubset: default: no, unless identical",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanComputeIsSubset",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Randomizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CheapRandomizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RandomizerAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RandomizerAttr)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RandomizerAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RandomizerAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RandomizerAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RandomizerAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RandomizerAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CheapRandomizerAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CheapRandomizerAttr)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CheapRandomizerAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CheapRandomizerAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CheapRandomizerAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CheapRandomizerAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CheapRandomizerAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSmallList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsSmallList",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsBasis",
+                            "Tester(UnderlyingLeftModule)"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsSmallList",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsBasis",
+                            "Tester(BasisVectors)"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsSmallList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IsSmallList: for a non-list",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSmallList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSmallList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSmallList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSmallList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSmallList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ],
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Length: system getter",
+                    "filters": [
+                        [
+                            "Tester(LENGTH)",
+                            "IsAttributeStoringRep"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "Length: for a matrix with memory",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "Length: for a straight line program word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 109
+                },
+                {
+                    "comment": "Length: for a word with memory",
+                    "filters": [
+                        [
+                            "IsWord",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 108
+                },
+                {
+                    "comment": "Length: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Length: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Length: for Lie matrix in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieMatrix"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Length: for class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Length: for null map matrix",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Length: For a compressed MatFFE",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Length: for an empty row vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Length: pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDefaultRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Length: For a compressed VecFFE",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Length: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "Length: modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Length: for a direct product element in default representation",
+                    "filters": [
+                        [
+                            "IsDefaultDirectProductElementRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Length: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Length: LAGUNA: for an element of a magma ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Length: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Length: for a right transversal in cosets representation",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalViaCosetsRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Length: for a right transversal in cosets representation",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalViaCosetsRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Length: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsWeakPointerObject"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Length: for degenerated residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsResidueClassUnionOfZxZ"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Length: for an element of an f.p. group (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Length: for right transversal",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Length: for a 32 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Length: for a 16 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Length: for an 8 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Length",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Length: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Length: for an enumerator that perhaps has its own `Length' function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Length: assoc word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Length: for an assoc. word in syllable rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Length: enum-by-niceomorphism",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByNiceomorphismRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Length: enum-by-pcgs",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByPcgsRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Length: for a nonassoc. word",
+                    "filters": [
+                        [
+                            "IsNonassocWord"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Length: for an infinite list of generators",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfGeneratorsRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Length: for an infinite list of names",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfNamesRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Length",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Length",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LENGTH): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LENGTH): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LENGTH)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LENGTH)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsBound[]: for Lie matrix in default representation, and integer",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "IsBound[]: for class function and positive integer",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsBound[]: for an empty row vector, and a positive integer",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "IsBound[]: pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "IsBound[]",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "IsBound[]: for a plist matrix, and a position",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsBound[]: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsWeakPointerObject"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsBound[]: for an enumerator that perhaps has its own `IsBound' function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IsBound[]: for a dense list and positive integer",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBound[]",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsReesMatrixSemigroupElement"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsReesZeroMatrixSemigroupElement"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "[]: for a matrix with memory",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 153
+                },
+                {
+                    "comment": "[]: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "[]: for an ordinary block matrix and a positive integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "[]: for Lie matrix in default representation, and positive integer",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "[]: for class function and positive integer",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "[]: For a compressed MatFFE",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "[]: pcgs, pos int",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDefaultRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "[]: For a compressed VecFFE",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "[]: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "[]: modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "[]: for a direct product element in default repres., and a pos. integer",
+                    "filters": [
+                        [
+                            "IsDefaultDirectProductElementRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "[]: for a plist matrix and a positive integer",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "[]: for classes of subgroups",
+                    "filters": [
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "[]: for a plist vector and a positive integer",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "[]: right transversal fp group",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalFpGroupRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "[]: for Pc transversals",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalPcGroupRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "[]: for right transversal of perm. group, and pos. integer",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalPermGroupRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "[]: factored transversal",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFactoredTransversalRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "[]: rt via coset",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalViaCosetsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "[]: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsWeakPointerObject"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "[]: for degenerated residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsResidueClassUnionOfZxZ"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "[]",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "[]: for a basis and a positive integer",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "[]: for enumerator by functions",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "[]: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "[]: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "[]: enum-by-niceo",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByNiceomorphismRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "[]: enum-by-pcgs",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByPcgsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "[]: for an infinite list of generators",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfGeneratorsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "[]: for an infinite list of names",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfNamesRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "[]",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "[]",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsFlatMatrix"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "{}: For an 8 bit vector and a range",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsRange",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "{}: For an 8 bit vector and a plain list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsDenseList",
+                            "IsPlistRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "{}: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "{}: pcgs, range",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "{}: for a small list and a small dense list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsDenseList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "{}: for a plist matrix and a list",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "{}: for a plist vector and a list",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "{}",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "{}: for a list and a dense list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "{}",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "{}",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Elm0List: For an 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Elm0List: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Elm0List: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "Elm0List",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Elm0List",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Unbind[]: For a compressed MatFFE",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Unbind[]: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Unbind[]: For a compressed VecFFE",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Unbind[]: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Unbind[]: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "Unbind[]: for a plist matrix, and a position",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Unbind[]: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsWeakPointerObject"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Unbind[]",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Unbind[]",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [],
+                []
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsFlatMatrix"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "[]:=",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsUnicodeCharacter"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "[]:=: For a compressed MatFE",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "[]:=: for a checking plist matrix, a positive integer, and a plist vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "[]:=: for a plist matrix, a positive integer, and a plist vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "[]:=: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "[]:=: For a compressed VecFFE",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "[]:=: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "[]:=: for plain list and external objects",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsPlistRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "[]:=: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "[]:=: for a checking plist vector, a positive integer, and an obj",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "[]:=: method for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsWeakPointerObject"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "[]:=: for a plist vector, a positive integer, and an obj",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "[]:=: error message for immutable list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": -79
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "[]:=",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsRowListMatrix"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "{}:=: for a checking plist matrix, a list, and a plist matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "{}:=: for a plist matrix, a list, and a plist matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "{}:=: for a small mutable list, a small dense list, and a small list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsDenseList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "{}:=: for a mutable list, a dense list, and a list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "{}:=",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConstantTimeAccessList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConstantTimeAccessList)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "ConstantTimeAccessList: for a constant time access list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsConstantTimeAccessList"
+                        ]
+                    ],
+                    "rank": 10003
+                },
+                {
+                    "comment": "ConstantTimeAccessList: for a strictly sorted dense list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ConstantTimeAccessList: for a strictly sorted list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ConstantTimeAccessList: for a dense list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ConstantTimeAccessList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConstantTimeAccessList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConstantTimeAccessList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConstantTimeAccessList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConstantTimeAccessList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConstantTimeAccessList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsPlist: for a plist",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsPlistRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "AsPlist: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsPlist",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSortedList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSortedList)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsSortedList: for a finite list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsSortedList: for a list (not nec. finite)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IsSortedList: for non-lists",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSortedList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSortedList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSortedList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSortedList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSortedList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSSortedList: system getter",
+                    "filters": [
+                        [
+                            "Tester(IS_SSORT_LIST)",
+                            "IsAttributeStoringRep"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsSSortedList: for a small homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsSSortedList: for a homogeneous list (not nec. finite)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsSSortedList: for non-lists",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSSortedList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IS_SSORT_LIST): method for an internal list and a Boolean",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Setter(IS_SSORT_LIST): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IS_SSORT_LIST): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IS_SSORT_LIST)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IS_SSORT_LIST)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNSortedList: system getter",
+                    "filters": [
+                        [
+                            "Tester(IS_NSORT_LIST)",
+                            "IsAttributeStoringRep"
+                        ]
+                    ],
+                    "rank": 20006
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNSortedList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IS_NSORT_LIST): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IS_NSORT_LIST): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IS_NSORT_LIST)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IS_NSORT_LIST)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsDuplicateFree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsDuplicateFree)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsDuplicateFree: for a finite list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsDuplicateFree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsDuplicateFree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsDuplicateFree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsDuplicateFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsDuplicateFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPositionsList: system getter",
+                    "filters": [
+                        [
+                            "Tester(IS_POSS_LIST)",
+                            "IsAttributeStoringRep"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "IsPositionsList: for a small homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsPositionsList: for a homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsPositionsList: for non-lists",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPositionsList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IS_POSS_LIST): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IS_POSS_LIST): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IS_POSS_LIST)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IS_POSS_LIST)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Position",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsUnicodeCharacter"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Position: for a plist matrix, and a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Position: for class function, cyclotomic, and nonnegative integer",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "Position: for Lie matrix in default representation, row vector, and integer",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieMatrix"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "Position",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsUnicodeCharacter"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Position: for a plist matrix, and a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Position: pcgs, object, int",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDefaultRep"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Position: modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "Position: for enumerator by functions",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ],
+                        [],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "Position: right transversal fp gp.",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalFpGroupRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Position: for a small sorted list, an object, and an integer",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Position: right transversal: Use PositionCanonical",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Position: enum-by-niceo",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByNiceomorphismRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Position: enum-by-pcgs",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Position: for a small list, an object, and an integer",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Position: for a sorted list, an object, and an integer",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Position",
+                    "filters": [
+                        [
+                            "IsPcp"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Position: for an infinite list of generators, an object, and zero",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfGeneratorsRep"
+                        ],
+                        [],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Position: for an infinite list of names, an object, and zero",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInfiniteListOfNamesRep"
+                        ],
+                        [],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Position: for a basis, an object, and a nonnegative integer",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Position: for duplicate free list, object, and positive integer",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Position: for a homog. list, an object not in the elements family, and an int.",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Position: for a (small) list, an object, and an integer",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Position",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionsOp",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionsOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionCanonical: for 8bit matrices lists, fall back on `Position'",
+                    "filters": [
+                        [
+                            "IsList",
+                            "Is8BitMatrixRep"
+                        ],
+                        []
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PositionCanonical: for internally represented lists, fall back on `Position'",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2MatrixRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PositionCanonical: internal small sorted lists, use `POSITION_SORTED_LIST'",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)",
+                            "IsInternalRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PositionCanonical: for internally represented lists, fall back on `Position'",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        []
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PositionCanonical: for right transversal of perm. group, and permutation",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PositionCanonical: right transversal fp gp.",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalFpGroupRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PositionCanonical: RT",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalPcGroupRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PositionCanonical: factored transversal",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFactoredTransversalRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PositionCanonical: rt via coset",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsRightTransversalViaCosetsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PositionCanonical: enum-by-niceo",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByNiceomorphismRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PositionCanonical: enum-by-pcgs",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEnumeratorByPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PositionCanonical: for enumerator by functions",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsDenseList",
+                            "IsDuplicateFree",
+                            "Tester(IsDuplicateFree)",
+                            "IsEnumeratorByFunctionsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionCanonical",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PositionNthOccurrence: for boolean list, boolean, integer",
+                    "filters": [
+                        [
+                            "IsBlist"
+                        ],
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PositionNthOccurrence: for list, object, integer",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionNthOccurrence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionSortedOp: for a plist matrix, and a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "PositionSortedOp: for small list, and object",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PositionSortedOp",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PositionSortedOp: for a plist matrix, and a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PositionSortedOp: for small list, object, and function",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PositionSortedOp: for list, object, and function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionSortedOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionProperty: for dense list and function",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "PositionProperty: for list and function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PositionProperty: for dense list, function, and integer",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PositionProperty: for list, function, and integer",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionsProperty: for dense list and function",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionsProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PositionBound: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionBound",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionSublist",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PositionSublist: for two args in IsStringRep",
+                    "filters": [
+                        [
+                            "IsStringRep"
+                        ],
+                        [
+                            "IsStringRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "PositionSublist: list, sub",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PositionSublist",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "PositionSublist: list,empty,pos",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PositionSublist: empty list,sub,pos",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PositionSublist: for two args in IsStringRep and offset",
+                    "filters": [
+                        [
+                            "IsStringRep"
+                        ],
+                        [
+                            "IsStringRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PositionSublist: list,sub,pos",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionSublist",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsMatchingSublist: list, sub",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsMatchingSublist: list,empty,pos",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsMatchingSublist: empty list,sub,pos",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsMatchingSublist: list,sub,pos",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMatchingSublist",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Add: for a checking plist matrix and a plist vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Add: for a plist matrix and a plist vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Add: for mutable list and list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Add: three arguments fast version sorted",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)",
+                            "IsPlistRep"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Add: for a checking plist matrix, a plist vector, and a pos",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Add: for a plist matrix, a plist vector, and a pos. int",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Add: three arguments fast version",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsPlistRep"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Add: three arguments general version",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Add",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Remove: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Remove: one argument",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Remove: two arguments, fast",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsPlistRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Remove: for a plist matrix, and a position",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Remove: two arguments, general",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Remove",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ],
+                [
+                    "IsRowListMatrix"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Append: for 8bitm vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsList",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "Append: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Append: for a checking plist matrix, and a plist matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Append: for mutable list in plist representation, and small list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsPlistRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Append: for two plist matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Append",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Append: for mutable list and list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Append",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Compacted: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Compacted",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Collected: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Collected",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DuplicateFreeList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DuplicateFreeList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsDuplicateFreeList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsDuplicateFreeList)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "AsDuplicateFreeList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsDuplicateFreeList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsDuplicateFreeList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsDuplicateFreeList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsDuplicateFreeList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsDuplicateFreeList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DifferenceLists: homogeneous lists",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DifferenceLists",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Flat: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Flat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReversedOp: for a range",
+                    "filters": [
+                        [
+                            "IsRange"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ReversedOp: for an assoc. word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReversedOp: for an assoc. word in syllable rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReversedOp: for a dense list",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReversedOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Shuffle",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Shuffle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sort: for a mutable set",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsSortedList",
+                            "Tester(IsSortedList)"
+                        ]
+                    ],
+                    "rank": 10006
+                },
+                {
+                    "comment": "Sort: for a mutable small list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Sort: for a mutable list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Sort: for an immutable list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Sort: for a mutable small list and a function",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Sort: for a mutable list and a function",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Sort: for an immutable list and a function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sort",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SortBy: for a mutable list and a function",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SortBy",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sortex: for a mutable sorted list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsSortedList",
+                            "Tester(IsSortedList)"
+                        ]
+                    ],
+                    "rank": 10007
+                },
+                {
+                    "comment": "Sortex: for a mutable list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Sortex: for an immutable list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Sortex: for a mutable list and a function",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sortex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SortingPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SortingPerm)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "SortingPerm: for a dense and sorted list",
+                    "filters": [
+                        [
+                            "IsDenseList",
+                            "IsSortedList",
+                            "Tester(IsSortedList)"
+                        ]
+                    ],
+                    "rank": 10005
+                },
+                {
+                    "comment": "SortingPerm",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SortingPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SortingPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SortingPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SortingPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SortingPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsDenseList"
+                ],
+                [
+                    "IsMutable",
+                    "IsDenseList"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsDenseList"
+                ],
+                [
+                    "IsMutable",
+                    "IsDenseList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SortParallel: for a mutable set and a dense mutable list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsSortedList",
+                            "Tester(IsSortedList)"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 10012
+                },
+                {
+                    "comment": "SortParallel: for two dense and mutable lists",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "SortParallel: for two immutable lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SortParallel: for two dense and mutable lists, and function",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "SortParallel: for two immutable lists and function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SortParallel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximumList: for a range",
+                    "filters": [
+                        [
+                            "IsRange"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "MaximumList: for a sorted list",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "MaximumList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MaximumList: for a range and a seed",
+                    "filters": [
+                        [
+                            "IsRange"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "MaximumList: for a sorted list and a seed",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "MaximumList: for a list and a seed",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximumList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimumList: for a range",
+                    "filters": [
+                        [
+                            "IsRange"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "MinimumList: for a sorted list",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "MinimumList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MinimumList: for a range and a seed",
+                    "filters": [
+                        [
+                            "IsRange"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "MinimumList: for a sorted list and a seed",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "MinimumList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimumList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Permuted: for a class function, and a permutation",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "Permuted: for a list and a permutation",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Permuted",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FirstOp: for a list or collection and a function",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FirstOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Iterated: for a list and a function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Iterated",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Iterated",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSmallList",
+                    "Tester(IsSmallList)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PlainListCopyOp: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PlainListCopyOp: for a GF2 matrix",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PlainListCopyOp: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PlainListCopyOp: for a GF2 vector",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PlainListCopyOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionNot: for 8-bit vector and 0*Z(p)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "PositionNot: for GF(2) vector and 0*Z(2)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "PositionNot: default value of third argument ",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PositionNot: for 8-bit vector and 0*Z(p) and starting ix",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "PositionNot: for GF(2) vector and 0*Z(2) and offset",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "PositionNot: default method ",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionNot",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PositionNonZero: for 8-bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PositionNonZero: for GF(2) vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PositionNonZero: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PositionNonZero: General method for a row vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PositionNonZero: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PositionNonZero: default method",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PositionNonZero: for 8-bit vector and starting point",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "PositionNonZero: for GF(2) vector and offset",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "PositionNonZero: for a plist matrix, and a position",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PositionNonZero: default method with start",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionNonZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NestingDepthA: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NestingDepthA)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "IsGeneralizedRowVector",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "IsGeneralizedRowVector",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "IsGeneralizedRowVector",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "IsGeneralizedRowVector",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "NestingDepthA",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NestingDepthA",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NestingDepthA): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NestingDepthA): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NestingDepthA)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NestingDepthA)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NestingDepthM: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NestingDepthM)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "NestingDepthM",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NestingDepthM",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NestingDepthM): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NestingDepthM): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NestingDepthM)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NestingDepthM)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsZero: for null map matrix",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsZero: method for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsZero",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsZero: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsZero",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsZero",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsZero: for a row vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsZero: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsZero: for general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsZero: for an additive-element-with-zero",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ],
+            [
+                [
+                    "IsReesMatrixSemigroupElement"
+                ]
+            ],
+            [
+                [
+                    "IsReesZeroMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsOne)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsOne: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "IsOne: object with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that is a field homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect add.,add.inv.,mult.,one,scal. mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect add.,add.inv.,mult.,scal. mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect mult.,one,add.,add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsOne: using `MappingGeneratorsImages'",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "Tester(MappingGeneratorsImages)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsOne",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect add.,add.inv.,scal. mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect mult.,add.,add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsOne: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect add. and add. inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect mult. and inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect add. and zero",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect mult. and one",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect add.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping that respect mult.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsOne: method for s.v. gen. mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsOne: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsOne: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsOne: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsOne: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsOne: for a multiplicative-element-with-one",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ]
+            ],
+            [
+                [
+                    "IsFamily"
+                ]
+            ],
+            [
+                [
+                    "IsCollection",
+                    "CategoryCollections(IsNearAdditiveElementWithZero)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ZeroImmutable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ZeroImmutable)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "ZeroImmutable: for additive magma with zero (look at family)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 10014
+                },
+                {
+                    "comment": "ZeroImmutable: for GF2 Matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ZeroImmutable: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithZero",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "IsAdditiveElement",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ZeroImmutable",
+                    "filters": [
+                        [
+                            "IsInternalRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "IsRectangularTable",
+                            "Tester(IsRectangularTable)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ZeroImmutable: for a matrix space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ZeroImmutable: for a row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ZeroImmutable: for a right ideal",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ZeroImmutable: for a left ideal",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ZeroImmutable",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ZeroImmutable: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroImmutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroImmutable: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroImmutable: for an add. magma-with-zero with parent (ask the parent)",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroImmutable: for additive magma with zero",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ZeroImmutable: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ZeroImmutable: for additive magma",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ZeroImmutable: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroImmutable: for a zero element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero",
+                            "IsAdditiveElement",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ZeroImmutable",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPadicExtensionNumber)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ZeroImmutable",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPurePadicNumber)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ZeroImmutable: for a family of FFEs",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsFFE)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ZeroImmutable: for an additive-element-with-zero (look at the family)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ZeroImmutable: for any object (call `ZERO')",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroImmutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsCollection",
+                    "CategoryCollections(IsNearAdditiveElementWithZero)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "IsGeneralizedDomain"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ZeroImmutable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ZeroImmutable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ZeroImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ZeroImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ]
+            ],
+            [
+                [
+                    "IsReesMatrixSemigroupElement"
+                ]
+            ],
+            [
+                [
+                    "IsReesZeroMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ZeroMutable: for Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "ZeroMutable: for GF2 Matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ZeroMutable: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithZero",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "IsAdditiveElement",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ZeroMutable: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ZeroMutable: for empty row vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ZeroMutable: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ZeroMutable: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ZeroMutable: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ZeroMutable",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ZeroMutable",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ZeroMutable: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroMutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroMutable: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroMutable: for a direct product element",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroMutable: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ZeroMutable: for a p-adic number",
+                    "filters": [
+                        [
+                            "IsPadicNumber"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ZeroMutable: defer to family",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ZeroMutable: for UEALattice element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ZeroMutable: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroMutable: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroMutable: for s. c. ring element",
+                    "filters": [
+                        [
+                            "IsSCRingObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroMutable: for a 0-cochain",
+                    "filters": [
+                        [
+                            "IsCochain",
+                            "IsZeroCochainRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroMutable: for s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroMutable: for an f.p. algebra element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroMutable: for magma ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroMutable: for weight rep element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ZeroMutable: for a cochain",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ZeroMutable: for direct sum elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ZeroMutable: for sparse rowspace elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ZeroMutable: for monomial elements",
+                    "filters": [
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ZeroMutable: for an algebra module element in packed representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ZeroMutable: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ZeroMutable: for a (non-copyable) zero element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero",
+                            "IsAdditiveElement",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ZeroMutable: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ZeroMutable: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ZeroMutable: for an additive-element-with-zero (look at the family)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroMutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithZero",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ZeroSameMutability: for GF2 Matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ZeroSameMutability: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithZero",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "IsAdditiveElement",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ZeroSameMutability: for null map matrix",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ZeroSameMutability: for GF2 vector, mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ZeroSameMutability: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ZeroSameMutability: for GF2 vector, immutable",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ZeroSameMutability",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ZeroSameMutability: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ZeroSameMutability: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ZeroSameMutability: for an (immutable) object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroSameMutability",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtAElement"
+                ],
+                [
+                    "IsExtAElement"
+                ]
+            ],
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "+: for a scalar and the base module (ResClasses)",
+                    "filters": [
+                        [],
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 10027
+                },
+                {
+                    "comment": "+: for a ring element and the base ring (ResClasses)",
+                    "filters": [
+                        [],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 10026
+                },
+                {
+                    "comment": "+: for the base ring and a ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        []
+                    ],
+                    "rank": 10005
+                },
+                {
+                    "comment": "+: for GF2 matrix and GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 90
+                },
+                {
+                    "comment": "+: For two 8 bit matrices in same characteristic",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "+: for two empty matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "+: for two characters",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ],
+                        [
+                            "IsClassFunction",
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "+: for two ordinary block matrices",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "+: for two virtual characters",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ],
+                        [
+                            "IsClassFunction",
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "+: for two null map matrices",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ],
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "+: for two Gaussian row spaces",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "+: method for two two-sided ideals",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "+: for two empty row vectors in the same family",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "+: for linear m.b.i. and linear m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "+: for linear m.b.m. and linear m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "+: method for two right ideals",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "+: method for two left ideals",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "+: for two rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "+: For two 8 bit vectors in same characteristic",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "+: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "+: For an 8 bit vector of char 2 and a GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "+: For a GF2 vector and an 8 bit vector of char 2",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "+: for two left modules",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "+: for a grv, and an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsGeneralizedRowVector"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "+: for an ordinary block matrix, and a grv",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsGeneralizedRowVector"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "+: for ring ring general mapping and ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "+: for ring g.m.b.i. and ring general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "+: for mapping and linear m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "+: for linear m.b.m. and mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "+: for mapping and linear m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "+: for linear m.b.i. and mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "+: for internal FFE and element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "+: for element in Z/pZ (ModulusRep) and internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: for integer and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: for element in Z/nZ (ModulusRep) and integer",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: BFElm+BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: BFElm+AlgElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: AlgElm+BFElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: AlgElm+AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: laurent + laurent",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "+: for rational and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "+: for element in Z/nZ (ModulusRep) and rational",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "+: for two checking plist matrices",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for a rational and a FFE",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for a FFE and a rational",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for two elements in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for two unknowns",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for cyclotomic and unknown",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for unknown and cyclotomic",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for general mapping and algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for an algebra g.m.b.i. and general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for `-infinity' and `-infinity'",
+                    "filters": [
+                        [
+                            "IsNegInfinity"
+                        ],
+                        [
+                            "IsNegInfinity"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for cyclotomic and `-infinity'",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsNegInfinity"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for `-infinity' and cyclotomic",
+                    "filters": [
+                        [
+                            "IsNegInfinity"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for `infinity' and `infinity'",
+                    "filters": [
+                        [
+                            "IsInfinity"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for cyclotomic and `infinity'",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for `infinity' and cyclotomic",
+                    "filters": [
+                        [
+                            "IsInfinity"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "+: for object, and class function",
+                    "filters": [
+                        [],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "+: for class function, and object",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "+: for two plist matrices",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "+: univariate + univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "+: for general mapping and linear g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "+: for linear g.m.b.i. and general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "+: for two direct product elements",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "+: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "+: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ],
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ],
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "+: zmodnze : for cyclotomic and element in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "+: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep) and cyclotomic",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "+: polynomial + polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "+: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "+: rat-fun + rat-fun",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "+: for s. c. ring elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "+: for two Lie objects in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "+: for s. c. algebra elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "+: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: FElm+BFElm",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: BFElm+FElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: FElm+AlgElm",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: AlgElm+FElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: laurent + coeff(embed)",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: coeff(embed) + laurent",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: laurent + coeff",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: coeff + laurent",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: for a default list, and a direct product element",
+                    "filters": [
+                        [
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: for a direct product element, and a default list",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "+: for two checking plist vectors",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "+: for two UEALattice elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "+: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "+: for zero mapping and general mapping",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "+: for general mapping and zero mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "+: for two info selectors",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)",
+                            "CategoryCollections(IsInfoClass)"
+                        ],
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)",
+                            "CategoryCollections(IsInfoClass)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "+: univariate + coeff",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "+: coeff + univariate",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "+: for two plist vectors",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "+: coeff + polynomial ",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "+: polynomial + coeff",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "+: for two 0-cochains",
+                    "filters": [
+                        [
+                            "IsCochain",
+                            "IsZeroCochainRep"
+                        ],
+                        [
+                            "IsCochain",
+                            "IsZeroCochainRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "+: for s. c. algebra elements",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "+: fp algebra elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "+: for two magma ring elements",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "+: for ring element, and Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "+: for Lie object in default representation, and ring element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "+: coeff + ratfun ",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: ratfun + coeff",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: for weight rep elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: for two cochains",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: for direct sum elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: for sparse rowspace elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: for monomial elements",
+                    "filters": [
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ],
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: for two algebra module elements in packed representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "+: for additive element and additive group",
+                    "filters": [
+                        [
+                            "IsAdditiveElement"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "+: for additive group and additive element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "+: for a vector and an algebra module element in packed representation",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "+: for an algebra module element in packed representation and a vector",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [],
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "+",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        []
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "+: univariate + rat",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "+: rat + univariate",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "+: for additive element and additive coset",
+                    "filters": [
+                        [
+                            "IsAdditiveElement"
+                        ],
+                        [
+                            "IsAdditiveCoset"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "+: for additive coset and additive element",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "+: for a non-list, and a direct product element",
+                    "filters": [
+                        [],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "+: for a direct product element, and a non-list",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        []
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "+: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "+: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "+: for magma ring element and magma element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "+: for magma element and magma ring element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "+: for info selector and info class",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)",
+                            "CategoryCollections(IsInfoClass)"
+                        ],
+                        [
+                            "IsInfoClass"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "+: for info class and info selector",
+                    "filters": [
+                        [
+                            "IsInfoClass"
+                        ],
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)",
+                            "CategoryCollections(IsInfoClass)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "+: rat + ratfun ",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "+: ratfun + rat",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "+: for ring element and residue class union (ResClasses)",
+                    "filters": [
+                        [],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "+: for residue class union and ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        []
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "+: for two info classes",
+                    "filters": [
+                        [
+                            "IsInfoClass"
+                        ],
+                        [
+                            "IsInfoClass"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "+",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdditiveInverseImmutable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdditiveInverseImmutable)"
+                        ]
+                    ],
+                    "rank": 20008
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithZero",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "IsAdditiveElement",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: for a zero element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AdditiveInverseImmutable: for any object (call `AINV')",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditiveInverseImmutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdditiveInverseImmutable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdditiveInverseImmutable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdditiveInverseImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdditiveInverseImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdditiveInverseMutable: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "AdditiveInverseMutable: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithZero",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "IsAdditiveElement",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a virtual character",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a null map matrix",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for empty row vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for base module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "AdditiveInverseMutable: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for linear m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for linear g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AdditiveInverseMutable",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AdditiveInverseMutable: BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AdditiveInverseMutable: AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AdditiveInverseMutable: laurent polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AdditiveInverseMutable",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for an unknown",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for `-infinity'",
+                    "filters": [
+                        [
+                            "IsNegInfinity"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for `infinity'",
+                    "filters": [
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "AdditiveInverseMutable: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a direct product element",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "AdditiveInverseMutable",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AdditiveInverseMutable",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AdditiveInverseMutable: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AdditiveInverseMutable: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "AdditiveInverseMutable: rational function",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for UEALattice element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for s. c. ring element",
+                    "filters": [
+                        [
+                            "IsSCRingObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a 0-cochain",
+                    "filters": [
+                        [
+                            "IsCochain",
+                            "IsZeroCochainRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseMutable: fp algebra element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for magma ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a weight rep element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a cochain",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a direct sum element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a sparse rowspace element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a monomial element",
+                    "filters": [
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for an algebra module element in packed representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for a (non-copyable) zero element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "AdditiveInverseMutable: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditiveInverseMutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdditiveInverseSameMutability: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithZero",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "IsAdditiveElement",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: for a null map matrix",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: for GF2 vector, mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: For an 8 bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: for GF2 vector, immutable",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AdditiveInverseSameMutability: for an (immutable) object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditiveInverseSameMutability",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtAElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "-: for GF2 matrix and GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 90
+                },
+                {
+                    "comment": "-: For two 8 bit matrices in same characteristic",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "-: For two 8bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "-: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "-: For an 8 bit vector of char 2 and a GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "-: For a GF2 vector and an 8 bit vector of char 2",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "-: for internal FFE and element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "-: for element in Z/pZ (ModulusRep) and internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "-: for two unknowns in default representation",
+                    "filters": [
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ],
+                        [
+                            "IsUnknown",
+                            "IsUnknownDefaultRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "-: for integer and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "-: for element in Z/nZ (ModulusRep) and integer",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "-: laurent - laurent",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "-: for rational and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "-: for element in Z/nZ (ModulusRep) and rational",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "-: for two checking plist matrices",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "-: for two elements in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "-: for cyclotomic and unknown",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "-: for unknown and cyclotomic",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "-: for two plist matrices",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "-: univariate - univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "-: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "-: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ],
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "-: for s. c. ring elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "-: for two Lie objects in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "-: for s. c. algebra elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "-: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "-: for two checking plist vectors",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "-: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "-: for two plist vectors",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "-: for s. c. algebra elements",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "-: fp algebra elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "-: for ring element, and Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "-: for Lie object in default representation, and ring element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsGeneralizedRowVector"
+                        ],
+                        [
+                            "IsGeneralizedRowVector"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "-: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "-: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "-: for magma ring element and magma element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "-: for magma ring element and magma element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [],
+                        [
+                            "IsGeneralizedRowVector"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "-",
+                    "filters": [
+                        [
+                            "IsGeneralizedRowVector"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "-: for external add. element, and additive-element-with-zero",
+                    "filters": [
+                        [
+                            "IsExtAElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "-: for ring element and residue class union (ResClasses)",
+                    "filters": [
+                        [],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "-: for residue class union and ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        []
+                    ],
+                    "rank": 1
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "-",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRElement"
+                ],
+                [
+                    "IsExtLElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "*: additive element with zero * zero integer",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero"
+                        ],
+                        [
+                            "IsInt",
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 10024
+                },
+                {
+                    "comment": "*: zero integer * additive element with zero",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsZeroCyc"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithZero"
+                        ]
+                    ],
+                    "rank": 10024
+                },
+                {
+                    "comment": "*: objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 214
+                },
+                {
+                    "comment": "*: straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 214
+                },
+                {
+                    "comment": "*: for a row vector and a matrix with memory",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 151
+                },
+                {
+                    "comment": "*: for a matrix with memory and a scalar",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 144
+                },
+                {
+                    "comment": "*: for a scalar and a matrix with memory",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 144
+                },
+                {
+                    "comment": "*: x with straight line program element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "*: straight line program element with x",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "*: More efficient non-recursive kernel method for vector*matrix of cyclotomics",
+                    "filters": [
+                        [
+                            "IsPlistRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsPlistRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))",
+                            "IsListDefault",
+                            "IsRectangularTable",
+                            "Tester(IsRectangularTable)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "*: More efficient non-recursive method for matrix*matrix of cyclotomics",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))",
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsPlistRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))",
+                            "IsListDefault",
+                            "IsRectangularTable",
+                            "Tester(IsRectangularTable)"
+                        ]
+                    ],
+                    "rank": 95
+                },
+                {
+                    "comment": "*: for GF2 matrix and GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 90
+                },
+                {
+                    "comment": "*: 8 bit matrix * 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "*: for two empty matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "*: for GF2 vector and GF2 matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "*: 8 bit matrix * 8 bit vector",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "*: 8 bit vector * 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "*: For an 8 bit vector and a compatible matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "*: for two ordinary block matrices",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "*: For a GF2 vector and a compatible matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "*: for two characters",
+                    "filters": [
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ],
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "*: for GF2 matrix and GF2 vector",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "*: for two virtual characters",
+                    "filters": [
+                        [
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ],
+                        [
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "*: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsListDefault",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "*: For 2 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "*: for two class functions",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "*: for ffe and ordinary block matrix of integers",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "*: for ordinary block matrix of integers and ffe",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "*: for two null map matrices",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ],
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "*: for matrix and null map matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "*: for GF2 matrix and GF2 element",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "*: for GF2 element and GF2 matrix",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsListDefault",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "*: scalar * 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "*: scalar * 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "*: for empty list, and empty matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "*: for empty matrix, and empty list",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "*: for two empty row vectors in the same family",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "*: for GF2 vector and FFE",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "*: for FFE and GF2 vector",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "*: for character, and positive integer",
+                    "filters": [
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "*: for positive integer, and character",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "*: for ring and right ideal (construct a two-sided ideal)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "*: for left ideal and ring (construct a two-sided ideal)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "*: for integer and ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "*: for ordinary block matrix and integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "*: for virtual character, and integer",
+                    "filters": [
+                        [
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "*: for integer, and virtual character",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "*: for ring element, and empty matrix",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "*: for empty matrix, and ring element",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "*: for empty list and null map matrix",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "*: for empty list and matrix (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "*: for class function, and cyclotomic",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "*: for cyclotomic, and class function",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "*: For an 8 bit vector of char 2 and a GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "*: For a GF2 vector and an 8 bit vector of char 2",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "*: for vector and ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "*: for ordinary block matrix and vector",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "*: for empty row vector, and integer",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "*: for integer, and empty row vector",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "*: for a scalar and Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "*: for FFE and GF2 vector",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "*: for FFE and GF2 vector",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsList",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElement)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPadicNumber)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPadicNumber)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "*: for a mgrv, and an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "*: for an ordinary block matrix, and a mgrv",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "*: For an FFE and an 8 bit vector ",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "*: For an 8 bit vector and an FFE",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "*: for ring element and ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "*: for ordinary block matrix and ring element",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "*: for list in `IsListDefault', and class function",
+                    "filters": [
+                        [
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "*: for class function, and list in `IsListDefault'",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "*: for a null map matrix and a scalar",
+                    "filters": [
+                        [
+                            "IsNullMapMatrix"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "*: for a scalar and a null map matrix",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "*: for two nearly character tables (call `CharacterTableDirectProduct')",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "*: group times element",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "*: for vector and null map matrix",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ],
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "*: for residue class union of Z^2 and matrix (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZxZ"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "*: for a ring element and the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "*: for internal FFE and element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "*: for element in Z/pZ (ModulusRep) and internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "*: for the base module and a scalar / matrix (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "*: internal ffe * (large) integer",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "*: for the base ring and a ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: for integer and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: for element in Z/nZ (ModulusRep) and integer",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: BFElm*BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: BFElm*AlgElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: AlgElm*BFElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: AlgElm*AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ],
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: laurent * laurent",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: for ring and ring element (construct a left ideal)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: for ring element and ring (construct a right ideal)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "*: for rational and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "*: for element in Z/nZ (ModulusRep) and rational",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "*: for list and null map matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsNullMapMatrix"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "*: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: RightCosets",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ],
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: for a rational and a FFE",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: for a FFE and a rational",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: for two elements in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: for two unknowns",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: for cyclotomic and unknown",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: for unknown and cyclotomic",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "*: for s. c. ring element in dense vector rep. and integer",
+                    "filters": [
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "*: for integer and s. c. ring element in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "*: for s. c. algebra element in dense vector rep. and integer",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "*: for integer and s. c. algebra element in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "*: for empty row vector, and multiplicative element",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "*: for multiplicative element, and empty row vector",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsEmptyRowVectorRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "*: for two plist matrices",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsPadicNumber"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsPadicNumber"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "*: univariate * univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "*: for two direct product elements",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "*: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "*: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "*: zmodnze : for element x in Z/nZ and y in Z/nZ(m)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "*: zmodnze : for element x in Z/nZ(m) and y in Z/nZ",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "*: for s. c. algebra element and integer",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "*: for integer and s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ],
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ],
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ],
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ],
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*: zmodnze : for element x in Z/nZ(m) (ZmodnZepsRep) and cyclotomic y",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*: zmodnze : for cyclotomic x and element y in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*: polynomial * polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*: for scalar and algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*: for rational, and magma ring element",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*: for magma ring element, and rational",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "*: for a plist vector and a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: univariate * coeff",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: coeff * univariate",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: rat-fun * rat-fun",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: for s. c. ring elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCRingObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: for two Lie objects in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: for s. c. algebra elements in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: for scalar and linear m.b.m.",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: for scalar and linear g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "*: for an integer and a residue class union of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsResidueClassUnionOfZxZ"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: laurent * coeff",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: coeff * laurent",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: for row vector and Lie object",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: for Lie object and row vector",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: for a default list, and a direct product element",
+                    "filters": [
+                        [
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: for a direct product element, and a default list",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "*: for two UEALattice elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "*: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "*: FElm*Alg",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsAlgebraicElement"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "*: Alg*FElm",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "*: rat-fun * coeff",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "*: coeff * rat-fun",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "*: additive element with inverse * negative integer",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "*: negative integer * additive element with inverse",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "*: for UEALattice element and scalar",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "*: for scalar and UEALattice element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "*: for cochain and scalar",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "*: for scalar and cochain",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "*: for s. c. algebra elements",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "*: fp algebra elements",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "*: for two magma ring elements",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "*: RightCoset with element",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for a scalar and a checking plist vector",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for a scalar and a plist vector",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for a checking plist vector and a scalar",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for a plist vector and a scalar",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for 0-cochain and scalar",
+                    "filters": [
+                        [
+                            "IsCochain",
+                            "IsZeroCochainRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for scalar and 0-cochain",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsCochain",
+                            "IsZeroCochainRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for ring element, and Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for Lie object in default representation, and ring element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for s. c. algebra element in dense vector rep. and ring element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: for ring element and s. c. algebra element in dense vector rep.",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: additive element * positive integer",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: positive integer * additive element",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsNearAdditiveElement"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "*: generic method for n bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for cochain and scalar",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for scalar and cochain",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsCochain"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for a scalar and an algebra module element in packed representation",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for an algebra module element in packed representation and a scalar",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for two magma congruence classes",
+                    "filters": [
+                        [
+                            "IsCongruenceClass"
+                        ],
+                        [
+                            "IsCongruenceClass"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for permutation and binary relation on points",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for binary relation on points and permutation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "*: for s. c. algebra element and ring element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: for ring element and s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: fp algebra el*ring el",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: ring el *fp algebra el",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: for ring element, and magma ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: for magma ring element, and ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: for binary relation on points and transformation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: for transformation and binary relation on points",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: for zero and total general mapping",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "*: for weight rep element and a scalar",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: for weight rep element and a scalar",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: for a direct sum element and a scalar",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: for a direct sum element and a scalar",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsDirectSumElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: for a scalar and a sparse rowspace element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: for a sparse rowspace element and a scalar",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsSparseRowSpaceElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: for a scalar and a monomial element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: for a monomial element and a scalar",
+                    "filters": [
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "*: List*Alg",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsAlgebraicElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "*: Alg*List",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [],
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        []
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "*: for two 32 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "*: for two 16 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "*: for two 8 bits assoc. words",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "*: univariate * rat",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "*: rat * univariate",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "*: for a non-list, and a direct product element",
+                    "filters": [
+                        [],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "*: for a direct product element, and a non-list",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        []
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "*: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for ring element and residue class union (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for residue class union and ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for a transformation and a general mapping",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for a general mapping and a transformation",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for two f.p. group elements",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ],
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: wreath elements",
+                    "filters": [
+                        [
+                            "IsWreathProductElement"
+                        ],
+                        [
+                            "IsWreathProductElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for two elements of magma by mult. table",
+                    "filters": [
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ],
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: assoc words in B letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsBLetterAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsBLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: assoc words in W letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsWLetterAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsWLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for magma ring element and magma element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for magma element and magma ring element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for two elements of a magma with zero adjoined",
+                    "filters": [
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ],
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for two general mappings",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "*: for list and binary relation on points",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "*: for binary relation on points and list",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "*",
+                    "filters": [
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ],
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "*: for two elements of a fp monoid",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ],
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "*: rws-element * rws-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "*: for two assoc. words in syllable rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "*: for elements of a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "*: for elements of a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ],
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "*: for two elements of a f.p. semigroup",
+                    "filters": [
+                        [
+                            "IsElementOfFpSemigroup"
+                        ],
+                        [
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "*: for two assoc. words: force syllable rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "*: for two nonassoc. words",
+                    "filters": [
+                        [
+                            "IsNonassocWord"
+                        ],
+                        [
+                            "IsNonassocWord"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "*: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ],
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "*",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ],
+            [
+                [
+                    "IsFamily"
+                ]
+            ],
+            [
+                [
+                    "IsCollection",
+                    "CategoryCollections(IsMultiplicativeElementWithOne)",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OneImmutable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OneImmutable)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "OneImmutable: for a magma-with-one that has a parent",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 10015
+                },
+                {
+                    "comment": "OneImmutable: partial method for a group (beats to ask family)",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "OneImmutable: partial method for a magma-with-one (ask family)",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "OneImmutable: objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "OneImmutable: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "OneImmutable: for GF2 Matrix",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsOrdinaryMatrix",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "OneImmutable: for matrix group, call `IdentityMat'",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "OneImmutable: for a partial perm monoid with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "OneImmutable: for SC Rings -- try generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "OneImmutable: for finite SC Rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "OneImmutable: for a partial perm semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "OneImmutable",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "OneImmutable: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneImmutable: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneImmutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneImmutable: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneImmutable: for a magma-with-one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "OneImmutable: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "OneImmutable: for binary relation on points and a set of integers",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "OneImmutable: One(<congruence class>)",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsCongruenceClass"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneImmutable: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneImmutable: for a multiplicative element with one collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsMultiplicativeElementWithOne)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "OneImmutable: for an f.p. group element",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "OneImmutable: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneImmutable",
+                    "filters": [
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneImmutable: for an fp monoid element",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneImmutable: for an identity element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsOne",
+                            "Tester(IsOne)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneImmutable",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPadicExtensionNumber)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "OneImmutable",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPurePadicNumber)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "OneImmutable: for a family of FFEs",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsFFE)"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "OneImmutable: for family of s. c. algebra elements",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsSCAlgebraObj)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "OneImmutable: for a multiplicative-element-with-one (look at the family)",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "OneImmutable: for a family of free monoid elements",
+                    "filters": [
+                        [
+                            "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "OneImmutable: for a family of fp monoid elements",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "OneImmutable: for a family of f.p. group elements",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "OneImmutable: for any object (call `OneOp' and make immutable)",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OneImmutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsCollection",
+                    "CategoryCollections(IsMultiplicativeElementWithOne)",
+                    "IsGeneralizedDomain"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OneImmutable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OneImmutable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OneImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OneImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OneMutable: objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "OneMutable: straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "OneMutable: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "OneMutable: for GF2 Matrix",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsOrdinaryMatrix",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "OneMutable: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "OneMutable: for class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "OneMutable: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "OneMutable: for a quaternion",
+                    "filters": [
+                        [
+                            "IsQuaternion",
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "OneMutable",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "OneMutable: Right cosets",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "OneMutable: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneMutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneMutable: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneMutable: for a direct product element",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneMutable: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "OneMutable: for a transformation coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "OneMutable: for a p-adic number",
+                    "filters": [
+                        [
+                            "IsPadicNumber"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "OneMutable: defer to family",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "OneMutable: for UEALattice element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "OneMutable: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneMutable: for s. c. ring element",
+                    "filters": [
+                        [
+                            "IsSCRingObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneMutable: for Lie object",
+                    "filters": [
+                        [
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneMutable: for s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneMutable: for an f.p. algebra element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneMutable: for magma ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "OneMutable",
+                    "filters": [
+                        [
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "OneMutable: for an inf. bits assoc. word-with-one",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsInfBitsAssocWord"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "OneMutable: for a 32 bits assoc. word-with-one",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "OneMutable: for a 16 bits assoc. word-with-one",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "OneMutable: for an 8 bits assoc. word-with-one",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "OneMutable: assoc word in B letter rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsBLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "OneMutable: assoc word in W letter rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsWLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "OneMutable: for an element of a magma with zero adjoined",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "OneMutable: for an f.p. group element",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "OneMutable: wreath elements",
+                    "filters": [
+                        [
+                            "IsWreathProductElement"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "OneMutable: for an element in a magma by mult. table",
+                    "filters": [
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "OneMutable: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "OneMutable: for an fp monoid element",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneMutable: rws-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneMutable: for a nonassoc. word-with-one",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsWord",
+                            "IsNonassocWord"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneMutable: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneMutable: for a (non-copyable) identity element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsOne",
+                            "Tester(IsOne)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "OneMutable: for finite SC Rings family",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "OneMutable: for a multiplicative-element-with-one (look at the family)",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OneMutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OneSameMutability: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "OneSameMutability: for GF2 Matrix",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsOrdinaryMatrix",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "OneSameMutability: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "OneSameMutability",
+                    "filters": [
+                        [
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "OneSameMutability: for an (immutable) object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OneSameMutability",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseImmutable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InverseImmutable)"
+                        ]
+                    ],
+                    "rank": 20008
+                },
+                {
+                    "comment": "InverseImmutable: straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "InverseImmutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "InverseImmutable: for an identity element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOne",
+                            "Tester(IsOne)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseImmutable: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "InverseImmutable: for any object (call `InverseOp' and make immutable)",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseImmutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InverseImmutable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InverseImmutable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InverseImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InverseImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseMutable: objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "InverseMutable: straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "InverseMutable: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "InverseMutable: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "InverseMutable: for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "InverseMutable: for an ordinary matrix over a ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "InverseMutable: for default list whose rows are vectors of FFEs",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "InverseMutable: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "InverseMutable: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "InverseMutable: for default list over a ring without zero divisors",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(IsZDFRE))",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "InverseMutable: for a quaternion",
+                    "filters": [
+                        [
+                            "IsQuaternion",
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "InverseMutable",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "InverseMutable: BFElm",
+                    "filters": [
+                        [
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "InverseMutable: AlgElm",
+                    "filters": [
+                        [
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "InverseMutable: try to express as laurent polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "InverseMutable: Right cosets",
+                    "filters": [
+                        [
+                            "IsRightCoset"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "InverseMutable: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "InverseMutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "InverseMutable: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "InverseMutable: rational function",
+                    "filters": [
+                        [
+                            "IsRationalFunctionsFamilyElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "InverseMutable: for a direct product element",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "InverseMutable",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "InverseMutable",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "InverseMutable: LAGUNA: for an element of modular group algebra",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "InverseMutable: zmodnze : for element in Z/nZ(m) (ZModnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "InverseMutable: for binary relation on points and a set of integers",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "InverseMutable: for s. c. ring element",
+                    "filters": [
+                        [
+                            "IsSCRingObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "InverseMutable: for Lie object",
+                    "filters": [
+                        [
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "InverseMutable: for s. c. algebra element",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "InverseMutable: for magma ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "InverseMutable: generic method for n bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "InverseMutable: assoc word in B letter rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsBLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "InverseMutable: assoc word in W letter rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsWLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "InverseMutable: for an assoc. word with inverse in syllable rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "InverseMutable: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseMutable: for an element of an f.p. group",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseMutable: wreath elements",
+                    "filters": [
+                        [
+                            "IsWreathProductElement"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseMutable: for an element in a magma by mult. table",
+                    "filters": [
+                        [
+                            "IsMagmaByMultiplicationTableObj"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseMutable: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseMutable: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseMutable: for a (non-copyable) identity element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOne",
+                            "Tester(IsOne)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseMutable: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "InverseMutable: rws-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseMutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseSameMutability: 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCommutativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "InverseSameMutability: for GF2 matrix",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "InverseSameMutability: for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "InverseSameMutability: for an ordinary matrix over a ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "InverseSameMutability: for default list whose rows are vectors of FFEs",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "InverseSameMutability: for default list over a ring without zero divisors",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(IsZDFRE))",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "InverseSameMutability: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "InverseSameMutability: for a (non-copyable) identity element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsOne",
+                            "Tester(IsOne)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "InverseSameMutability: for an (immutable) object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseSameMutability",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRElement"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "/: x with straight line perm",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 129
+                },
+                {
+                    "comment": "/: integer and permutation with memory",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "/: generic method for two FLMLORs",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "/: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "/: generic method for two rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "/: for two algebra modules",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "/: for FLMLOR and empty list",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "/: generic method for two vector spaces",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "/: for char. table, and positions list (call `CharacterTableFactorGroup')",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "/: for a free group and an empty list of relators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "/: for free groups and relators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "/: for a semigroup and a congruence",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "/: upol/upol",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "/: for internal FFE and element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "/: for element in Z/pZ (ModulusRep) and internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsLogOrderedFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "/: for FLMLOR and collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "/: for integer and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "/: for element in Z/nZ (ModulusRep) and integer",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "/: for rational and element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "/: for element in Z/nZ (ModulusRep) and rational",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "/: for two elements in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "/: for unknown and cyclotomic",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "/",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "/: univariate / univariate",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsRationalFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "/: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "/: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "/: for an algebra module and collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "/: for magma ring element, and integer",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "/",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ],
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "/: method for vector space and collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "/: for the empty set and a ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "/: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "/: for s. c. algebra element in dense vector rep. and scalar",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj",
+                            "IsDenseCoeffVectorRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "/: for a checking plist vector and a scalar",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "/: for a plist vector and a scalar",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "/: for s. c. algebra element and scalar",
+                    "filters": [
+                        [
+                            "IsSCAlgebraObj"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "/: generic method for n bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "/: for residue class union and unit (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "/: for magma ring element, and ring element",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "/: for multiplicative grvs which might not be IsExtRElement",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ],
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "/: for empty list",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "/: for a semigroup and an empty list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "/: for semigroup and list of pairs",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "/: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "/: for residue class union and ring element (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "/: rws-element, rws-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "/: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "/: for element, and inj. & surj. general mapping",
+                    "filters": [
+                        [],
+                        [
+                            "IsGeneralMapping",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "/: sliced perm",
+                    "filters": [
+                        [],
+                        [
+                            "IsSlicedPerm"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "/: for ext. r elm., and multiplicative-element-with-inverse",
+                    "filters": [
+                        [
+                            "IsExtRElement"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "/",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                [
+                    "IsExtLElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftQuotient: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "LeftQuotient: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "LeftQuotient: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "LeftQuotient: generic method for n bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "LeftQuotient",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ],
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "LeftQuotient: rws-element, rws-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "LeftQuotient",
+                    "filters": [
+                        [],
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "LeftQuotient",
+                    "filters": [
+                        [
+                            "IsMultiplicativeGeneralizedRowVector"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "LeftQuotient: for multiplicative-element-with-inverse, and ext. l elm.",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsExtLElement"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftQuotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "^: for zero mapping and positive integer",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 10036
+                },
+                {
+                    "comment": "^: for identity mapping and integer",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 10035
+                },
+                {
+                    "comment": "^: for a pcp element and an integer",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 10034
+                },
+                {
+                    "comment": "^: integer and permutation with memory",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "^: int with straight line perm",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "^: objects with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 125
+                },
+                {
+                    "comment": "^: power straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 125
+                },
+                {
+                    "comment": "^",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "^",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "^: conjugacy class of a subgroup of a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "^: for class function and group",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "^: for two class functions (conjugation, trivial action)",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "^: for empty matrix, and integer",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "^",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "^: for ring and list of integers (delegate to `FullMatrixModule')",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "^: for block matrix and integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "^: for class function and nearly character table",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "^: for group homomorphism and group (induction)",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "^: for class function and positive integer (pointwise powering)",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "^: using `PROD' for ring element list and ring element table",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "CategoryCollections(IsMultiplicativeElement)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "^: for matrices, use char. poly. for large exponents",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "^: for ANF automorphism and integer",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "^: for a Frobenius automorphism, and an integer",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "^: for ring and integer (delegate to `FullRowModule')",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "^: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "^: for class function and Galois automorphism",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "^: generic method for groups and element",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "^: for unknown and zero",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "^",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "^: for class function and group element",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "^: conjugacy class of an element of a group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "^: for unknown and positive integer",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "^: for element in Z/nZ (ModulusRep), and integer",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "^: orbit of a point under the action of a group",
+                    "filters": [
+                        [],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "^: for binary relation on points and Zero",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "^: for direct product element, and integer",
+                    "filters": [
+                        [
+                            "IsDirectProductElement"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "^: for a 32 bits assoc. word, and zero (in small integer rep)",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "IsZeroCyc",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "^: for a 16 bits assoc. word, and zero (in small integer rep)",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "IsZeroCyc",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "^: for an 8 bits assoc. word, and zero (in small integer rep)",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "IsZeroCyc",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "^: for Lie object in default representation, and positive integer",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "^: for a 32 bits assoc. word, and a small negative integer",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "^: for a 16 bits assoc. word, and a small negative integer",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "^: for an 8 bits assoc. word, and a small negative integer",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "^: for binary relation on points and a positive int",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "^: generic method for n bits pc word rep and small int",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "^: for float and rational",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "^: for rational and float",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "^: for a 32 bits assoc. word, and a small positive integer",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "^: for a 16 bits assoc. word, and a small positive integer",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "^: for an 8 bits assoc. word, and a small positive integer",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "^: sliced perm",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsSlicedPerm"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "^: assoc word in B letter rep and negative integer",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsBLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "^: assoc word in B letter rep and positive integer",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsBLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "^: assoc word in W letter rep and negative integer",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsWLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "^: assoc word in W letter rep and positive integer",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsWLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "^: for an assoc. word with inverse in syllable rep, and an integer",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "^: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "^: for an assoc. word in syllable rep, and a positive integer",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "^: for mult. element-with-one, and zero",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "^: rws-element ^ int",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "^: for mult. element-with-inverse, and negative integer",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "^: for mult. element, and positive integer",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "^: generic method for n bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "^: catch wrong root taking",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "^: for an algebra element and an element of an algebra module",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsRightAlgebraModuleElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "^: for an algebra element and an element of an algebra module",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLeftAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "^: for a Lie algebra element and a weight rep element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "^: sliced perm",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsSlicedPerm"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "^: for two general mappings",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "^: for binary relation on points and a set of integers",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "^: for two pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "^: rws-element ^ rws-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "^: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "^: for two mult.-elm.-with-inverse",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "^: sliced perm",
+                    "filters": [
+                        [],
+                        [
+                            "IsSlicedPermInv"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "^: for element in the source, and general mapping",
+                    "filters": [
+                        [],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "^",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Comm: for arguments enclosed in list brackets (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Comm: generic method for n bits pc word rep",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Comm: for two pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Comm: rws-element, rws-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Comm: for two mult.-elm.-with-inverse",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Comm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LieBracket: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieBracket",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "mod: for `Integers', and integer",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "mod: zmodnze : for RingOfIntegralCyclotomics and a positive integer",
+                    "filters": [
+                        [
+                            "Tester(IsRingOfIntegralCyclotomics)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "mod: two induced pcgs",
+                    "filters": [
+                        [
+                            "IsInducedPcgs"
+                        ],
+                        [
+                            "IsInducedPcgs"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "mod: parent pcgs mod induced pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsInducedPcgs"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "mod: for a vector and a lattice (ResClasses)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "mod: two induced pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "mod: two parent pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "mod: for ord. char. table, and pos. integer (call `BrauerTable')",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "mod: two modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "mod: laurent",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "mod: reduction of univariate rational polynomial at a prime",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "mod: AlgElm",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "mod",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "mod: reduction of general rational polynomial at a prime",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "mod",
+                    "filters": [
+                        [],
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "mod",
+                    "filters": [
+                        [
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "IsListDefault"
+                        ],
+                        []
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "mod:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "mod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Int: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Int)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "Int",
+                    "filters": [
+                        [
+                            "IsUnicodeCharacter"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Int: for an integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Int: for a rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Int: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Int: for a cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Int: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Int: for an FFE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Int: for strings",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Int",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Int): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Int): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Int)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Int)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Rat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Rat)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "Rat: for float intervals",
+                    "filters": [
+                        [
+                            "IsFloatInterval"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Rat: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Rat: for strings",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Rat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Rat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Rat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Rat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Rat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sqrt: for a rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Sqrt: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sqrt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Root: for two integers",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Root",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Log: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Log: for two integers",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Log",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Characteristic: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Characteristic)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "Characteristic: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Characteristic: for sc rings and their subrings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Characteristic: for local formation",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "Tester(LocalDefinitionFunction)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Characteristic: for internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Characteristic: for formation product",
+                    "filters": [
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Characteristic: for Schunck class w/boundary",
+                    "filters": [
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "Tester(BoundaryFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Characteristic: for Fitting product",
+                    "filters": [
+                        [
+                            "IsFittingProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Characteristic: alg elm",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Characteristic: delegate to family (magma)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Characteristic: for union of group classes",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Characteristic: for intersection of group classes",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Characteristic: for an elements family of a magma ring quotient",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloSpanOfZeroFamily"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Characteristic: for generic grp class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Characteristic: for an elements family of an fp subalgebra",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Characteristic: delegate to family (element)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Characteristic: for family delegate to elements family",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "Tester(ElementsFamily)"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Characteristic: ask the family",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "Characteristic: return fail",
+                    "filters": [
+                        []
+                    ],
+                    "rank": -10000
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Characteristic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Characteristic): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Characteristic): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Characteristic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Characteristic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Order: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Order)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "Order: straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 117
+                },
+                {
+                    "comment": "Order: object with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "Order: ordinary matrix of finite field elements",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Order: for a matrix of cyclotomics, with Minkowski kernel",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Order: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Order: generic method for ordinary matrices",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Order: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Order: for automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Order: for an internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Order: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Order: for a cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Order",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Order: for a general FFE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Order: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Order: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Order: fp group element",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Order: method for a pc-element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Order: free group element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Order",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Order: for a mult. element-with-one",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Order",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Order): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Order): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Order)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Order)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "IsAdditiveElement",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "CategoryCollections(IsMultiplicativeElementWithInverse)",
+                    "IsOddAdditiveNestingDepthObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormedRowVector: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormedRowVector)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "NormedRowVector: for GF(2) vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "NormedRowVector: for a row vector of scalars",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsMultiplicativeElementWithInverse)",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormedRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "IsAdditiveElement",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "CategoryCollections(IsMultiplicativeElementWithInverse)",
+                    "IsOddAdditiveNestingDepthObject"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormedRowVector): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormedRowVector): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormedRowVector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "IsAdditiveElement",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "CategoryCollections(IsMultiplicativeElementWithInverse)",
+                    "IsOddAdditiveNestingDepthObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormedRowVector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCommutativeFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCommutativeFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCommutativeFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCommutativeFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCommutativeFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCommutativeFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCommutativeFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSkewFieldFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSkewFieldFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSkewFieldFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSkewFieldFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSkewFieldFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSkewFieldFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSkewFieldFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUFDFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsUFDFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUFDFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsUFDFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsUFDFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsUFDFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsUFDFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdditiveElementsAsMultiplicativeElementsFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdditiveElementsAsMultiplicativeElementsFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AdditiveElementsAsMultiplicativeElementsFamily: for families of additive elements",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditiveElementsAsMultiplicativeElementsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdditiveElementsAsMultiplicativeElementsFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdditiveElementsAsMultiplicativeElementsFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdditiveElementsAsMultiplicativeElementsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdditiveElementsAsMultiplicativeElementsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdditiveElementAsMultiplicativeElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdditiveElementAsMultiplicativeElement)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "AdditiveElementAsMultiplicativeElement: for additive elements with inverse",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "AdditiveElementAsMultiplicativeElement: for additive elements with zero",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithZero",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "AdditiveElementAsMultiplicativeElement: for additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditiveElementAsMultiplicativeElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAdditiveElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdditiveElementAsMultiplicativeElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdditiveElementAsMultiplicativeElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdditiveElementAsMultiplicativeElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdditiveElementAsMultiplicativeElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingElement: using 16Bits_ExtRepOfObj",
+                    "filters": [
+                        [
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "UnderlyingElement: using 16Bits_ExtRepOfObj",
+                    "filters": [
+                        [
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "UnderlyingElement: using 8Bits_ExtRepOfObj",
+                    "filters": [
+                        [
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "UnderlyingElement: for an element of an f.p. group (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "UnderlyingElement: for an element of an fp monoid (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "UnderlyingElement",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "UnderlyingElement: for an element of an f.p. semigroup (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "UnderlyingElement: for an element of a free group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "UnderlyingElement: wrapped additive elements",
+                    "filters": [
+                        [
+                            "IsAdditiveElementAsMultiplicativeElementRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIdempotent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIdempotent)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "IsIdempotent: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsIdempotent: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsIdempotent: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsIdempotent: multiplicative element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIdempotent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIdempotent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIdempotent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIdempotent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIdempotent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LargeGaloisField",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "LargeGaloisField",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "LargeGaloisField",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LargeGaloisField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeFFE: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeFFE)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "DegreeFFE: for 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "DegreeFFE: for a matrix of FFEs",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "DegreeFFE: for GF(2) vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "DegreeFFE: for a row vector of FFEs",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "DegreeFFE: for element in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "DegreeFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "DegreeFFE: for internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeFFE): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeFFE): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeFFE)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeFFE)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ],
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LogFFE: for two elements in Z/pZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "LogFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "LogFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "LogFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "LogFFE: for two internal FFEs",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "LogFFE: for two FFEs (in a prime field)",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LogFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IntFFE: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IntFFE)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "IntFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IntFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IntFFE: for internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IntFFE): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IntFFE): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IntFFE)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IntFFE)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IntFFESymm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IntFFESymm)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "IntFFESymm: vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IntFFESymm: Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IntFFESymm: FFE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntFFESymm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IntFFESymm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IntFFESymm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IntFFESymm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IntFFESymm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject",
+                    "CategoryCollections(IsFFE)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IntVecFFE: for a row vector of FFEs",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntVecFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsInternalFFE: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsInternalFFE)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "AsInternalFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AsInternalFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AsInternalFFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "AsInternalFFE",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsInternalFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsInternalFFE): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsInternalFFE): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsInternalFFE)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsInternalFFE)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RootFFE: for modulus rep, using RootMod",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "RootFFE: use LogFFE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RootFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfDomain)"
+                        ]
+                    ],
+                    "rank": 20008
+                },
+                {
+                    "comment": "GeneratorsOfDomain",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(AsList)",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "GeneratorsOfDomain: for a domain (delegate to `AsList')",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfDomain): for an underlying relation and a list of direct product elements",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ],
+                        [
+                            "CategoryCollections(IsDirectProductElement)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "Setter(GeneratorsOfDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DomainByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DomainByGenerators: for family and empty list",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "DomainByGenerators: for family and list & collection",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DomainByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ParentAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ParentAttr)"
+                        ]
+                    ],
+                    "rank": 20008
+                },
+                {
+                    "comment": "ParentAttr: for a subsemigroup of a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ParentAttr: for a subsemigroup of a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParentAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ParentAttr): method that calls 'UseSubsetRelation'",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "Setter(ParentAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ParentAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ParentAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ParentAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIntegralCyclotomic: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIntegralCyclotomic)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "IsIntegralCyclotomic: for an internally represented cyclotomic",
+                    "filters": [
+                        [
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIntegralCyclotomic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIntegralCyclotomic): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIntegralCyclotomic): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIntegralCyclotomic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIntegralCyclotomic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCyc"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Conductor: system getter",
+                    "filters": [
+                        [
+                            "Tester(CONDUCTOR)",
+                            "IsAttributeStoringRep"
+                        ]
+                    ],
+                    "rank": 20019
+                },
+                {
+                    "comment": "Conductor: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "Conductor: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Conductor",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCyc"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CONDUCTOR): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CONDUCTOR): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CONDUCTOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCyc"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CONDUCTOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCyc"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GaloisCyc: for a class function, and an integer",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "GaloisCyc: for a list of cyclotomics, and an integer",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "GaloisCyc: for a list of lists of cyclotomics, and an integer",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GaloisCyc",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsEqualSet: for two internally represented lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsEqualSet: for two lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsEqualSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsSubsetSet: for two internally represented lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsSubsetSet: for two lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubsetSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AddSet: for mutable internally represented list, and object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "AddSet: for mutable list, and object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RemoveSet: for mutable internally represented list, and object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "RemoveSet: for mutable list, and object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RemoveSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UniteSet: for two internally represented lists, the first being mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "UniteSet: for two lists, the first being mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UniteSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IntersectSet: for two ranges",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsRange",
+                            "IsRangeRep"
+                        ],
+                        [
+                            "IsRange",
+                            "IsRangeRep"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "IntersectSet: for two internally represented lists, the first being mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "IntersectSet: for two lists, the first being mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntersectSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SubtractSet: for two internally represented lists, the first being mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "SubtractSet: for two lists, the first being mutable",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubtractSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": ".: generators of a free group containing the whole family",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": ".: generators of a s.c. algebra containing the whole family",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfLeftOperatorRing)",
+                            "CategoryCollections(IsSCAlgebraObj)",
+                            "IsFullSCAlgebra",
+                            "Tester(IsFullSCAlgebra)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": ".: generators of a magma ring-with-one containing the whole family",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftOperatorRingWithOne)",
+                            "IsMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": ".: generators of a magma ring containing the whole family",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfLeftOperatorRing)",
+                            "IsMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": ".: group generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": ".: generators of a whole SC ring",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": ".: polynomial ring indeterminates",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": ".: for an inverse monoid with generators and pos int",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseMonoid)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": ".: for an inverse semigroup with generators and pos int",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": ".: for class names of a nearly character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": ".: for a monoid with generators and pos int",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": ".: generators of a free magma-with-one containing the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "CategoryCollections(IsWord)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": ".: generators of a free magma containing the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "CategoryCollections(IsWord)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": ".: for a semigroup with generators and pos int",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": ".: for a presentation in default representation",
+                    "filters": [
+                        [
+                            "IsPresentation",
+                            "IsPresentationDefaultRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": ".: for a root system and a record component",
+                    "filters": [
+                        [
+                            "IsRootSystem"
+                        ],
+                        []
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": ".: catch error",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": ".",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsBound.: for a presentation in default representation",
+                    "filters": [
+                        [
+                            "IsPresentation",
+                            "IsPresentationDefaultRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsBound.: catch error",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBound.",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": ".:=: for a mutable presentation in default representation",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPresentation",
+                            "IsPresentationDefaultRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": ".:=: catch error",
+                    "filters": [
+                        [],
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": ".:=",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Unbind.: for a mutable presentation in default representation",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPresentation",
+                            "IsPresentationDefaultRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Unbind.: catch error",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Unbind.",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RecNames: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RecNames)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "RecNames: for a record in internal representation",
+                    "filters": [
+                        [
+                            "IsRecord",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RecNames",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RecNames): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RecNames): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RecNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RecNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE",
+                    "IsInternalRep"
+                ],
+                [
+                    "IsFFE",
+                    "IsInternalRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SUM_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "SUM_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SUM_FFE_LARGE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE",
+                    "IsInternalRep"
+                ],
+                [
+                    "IsFFE",
+                    "IsInternalRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DIFF_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "DIFF_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DIFF_FFE_LARGE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE",
+                    "IsInternalRep"
+                ],
+                [
+                    "IsFFE",
+                    "IsInternalRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PROD_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PROD_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PROD_FFE_LARGE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFFE"
+                ],
+                [
+                    "IsFFE"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "QUO_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "QUO_FFE_LARGE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QUO_FFE_LARGE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ZOp",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ZOp",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ZOp",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRectangularTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRectangularTable)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsRectangularTable: kernel method for a plain list",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "IsPlistRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsRectangularTable: generic",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRectangularTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRectangularTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRectangularTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRectangularTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRectangularTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SmallestGeneratorPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SmallestGeneratorPerm)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "SmallestGeneratorPerm: for internally represented permutation",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SmallestGeneratorPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SmallestGeneratorPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SmallestGeneratorPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SmallestGeneratorPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SmallestGeneratorPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ]
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SmallestMovedPoint: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SmallestMovedPoint)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a collection of permutations",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "SmallestMovedPoint: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "SmallestMovedPoint: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SmallestMovedPoint",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SmallestMovedPoint): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SmallestMovedPoint): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SmallestMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SmallestMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ]
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LargestMovedPoint: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LargestMovedPoint)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "LargestMovedPoint: permutation with memory",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "LargestMovedPoint: straight line program permutation",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "LargestMovedPoint: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "LargestMovedPoint: for a collection of permutations",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "LargestMovedPoint: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "LargestMovedPoint: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "LargestMovedPoint: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "LargestMovedPoint: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "LargestMovedPoint: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "LargestMovedPoint: for an internal permutation",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "LargestMovedPoint: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "LargestMovedPoint: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LargestMovedPoint",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LargestMovedPoint): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LargestMovedPoint): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LargestMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LargestMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ]
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrMovedPoints: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrMovedPoints)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "NrMovedPoints: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "NrMovedPoints: for a collection of permutations",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "NrMovedPoints: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "NrMovedPoints: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "NrMovedPoints: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "NrMovedPoints: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "NrMovedPoints: for a transformation coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "NrMovedPoints: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "NrMovedPoints: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "NrMovedPoints: for a tranformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrMovedPoints",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrMovedPoints): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrMovedPoints): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrMovedPoints)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrMovedPoints)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ]
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MovedPoints: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MovedPoints)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "MovedPoints: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "MovedPoints: for a collection of permutations",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "MovedPoints: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "MovedPoints: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "MovedPoints: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MovedPoints: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "MovedPoints: for a transformation coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "MovedPoints: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "MovedPoints: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "MovedPoints: for a tranformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MovedPoints",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPerm)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList",
+                    "IsEmpty",
+                    "Tester(IsEmpty)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MovedPoints): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MovedPoints): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MovedPoints)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MovedPoints)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SignPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SignPerm)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "SignPerm: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 111
+                },
+                {
+                    "comment": "SignPerm: for a permutation with memory",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "SignPerm: for internally represented permutation",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SignPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SignPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SignPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SignPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SignPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CycleStructurePerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CycleStructurePerm)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "CycleStructurePerm: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 111
+                },
+                {
+                    "comment": "CycleStructurePerm: for a permutation with memory",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "CycleStructurePerm: internal",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "CycleStructurePerm: generic method",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CycleStructurePerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CycleStructurePerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CycleStructurePerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CycleStructurePerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CycleStructurePerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedPerm: for a permutation with memory and a list of integers",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 112
+                },
+                {
+                    "comment": "RestrictedPerm: use kernel method, test",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedPermNC: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 113
+                },
+                {
+                    "comment": "RestrictedPermNC: kernel method",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedPermNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPerm"
+                ],
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DistancePerms: for kernel permutations",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "DistancePerms: for general permutations",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DistancePerms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ],
+                [],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AddRowVector: kernel method for vecffe (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsPlistRep",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsPlistRep",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "AddRowVector: kernel method for plain lists of cyclotomics (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "AddRowVector: For 2 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "AddRowVector: kernel method for GF2 (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "AddRowVector: for two plist vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsIntVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsIntVector"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AddRowVector: for two checking plist vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AddRowVector: for two plist vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AddRowVector: kernel method for GF2 (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AddRowVector: kernel method for small lists (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AddRowVector: generic method (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AddRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "AddRowVector: do nothing if mult is zero",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 10008
+                },
+                {
+                    "comment": "AddRowVector: kernel method for vecffe (3 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsPlistRep",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsPlistRep",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "AddRowVector: kernel method for plain lists of cyclotomics(3 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 97
+                },
+                {
+                    "comment": "AddRowVector: For 2 8 bit vectors and a field element",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "AddRowVector: kernel method for GF2 (3 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "AddRowVector: for two plist vectors, and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsIntVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsIntVector"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AddRowVector: for two checking plist vectors, and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AddRowVector: for two plist vectors, and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AddRowVector: kernel method for small lists (3 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AddRowVector: generic method 3 args",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AddRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "AddRowVector: kernel method for vecffe (5 args -- ignores last 2)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsPlistRep",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsPlistRep",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 141
+                },
+                {
+                    "comment": "AddRowVector: kernel method for plain lists of cyclotomics",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 135
+                },
+                {
+                    "comment": "AddRowVector: For 2 8 bit vectors and a field element and from and to",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 105
+                },
+                {
+                    "comment": "AddRowVector: kernel method for GF2 (5 args, last 2 ignored)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 76
+                },
+                {
+                    "comment": "AddRowVector: for two integer plist vectors, a scalar, and two positions",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsIntVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsIntVector"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "AddRowVector: for two checking plist vectors, a scalar, and two positions",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "AddRowVector: for two plist vectors, a scalar, and two positions",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "AddRowVector: kernel method for small lists",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "AddRowVector: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "AddRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "6args": []
+        },
+        "name": "AddRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AddCoeffs: two 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "AddCoeffs: GF2 vector and 8 bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "AddCoeffs: 8 bit vector and GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "AddCoeffs: for GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "AddCoeffs: for empty list, GF2 vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "AddCoeffs: generic method (2nd arg empty)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "AddCoeffs: generic method (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AddCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "AddCoeffs: two 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "AddCoeffs: GF2 vector and 8 bit vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "AddCoeffs: 8 bit vector and GF2 vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "AddCoeffs: for GF2 vectors and FFE",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "AddCoeffs: for empty list, GF2 vector and FFE",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "AddCoeffs: generic method 3args",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AddCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "AddCoeffs: generic method (5 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AddCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [],
+                        [],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "6args": []
+        },
+        "name": "AddCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MultRowVector: kernel method for vecffe (2 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsPlistRep",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "MultRowVector: Two argument kernel method for plain list of cyclotomics and an integer",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "IsSmallList",
+                            "Tester(IsSmallList)",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "MultRowVector: For an 8 bit vector and an ffe",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "MultRowVector: for GF(2) vector and char 2 scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "MultRowVector: Two argument kernel method for small list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList",
+                            "IsSmallList",
+                            "Tester(IsSmallList)"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "MultRowVector: for a plist vector, and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsIntVector"
+                        ],
+                        []
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "MultRowVector: for a checking plist vector, and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        []
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "MultRowVector: for a plist vector, and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep"
+                        ],
+                        []
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "MultRowVector: two argument generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "MultRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "MultRowVector: for a checking plist vector, a list, a ch. plist vector, a list, a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "MultRowVector: for a plist vector, a list, a plist vector, a list, and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "MultRowVector: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MultRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [],
+                        [],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "6args": []
+        },
+        "name": "MultRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CoeffsMod",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CoeffsMod: call `ReduceCoeffsMod'",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoeffsMod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "MultCoeffs: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "MultCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "6args": []
+        },
+        "name": "MultCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PowerModCoeffs: default, 3 argt",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "PowerModCoeffs: for 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 105
+                },
+                {
+                    "comment": "PowerModCoeffs: for gf2vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 99
+                },
+                {
+                    "comment": "PowerModCoeffs: default five argt method",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "6args": []
+        },
+        "name": "PowerModCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ProductCoeffs: 8 bit vectors, kernel method (2 arg)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "ProductCoeffs: Gf2 vectors, kernel method (2 arg)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ProductCoeffs: call PRODUCT_COEFFS_GENERIC_LISTS with lengths",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ProductCoeffs: 8 bit vectors, kernel method",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "ProductCoeffs: GF2 vectors, kernel method",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "ProductCoeffs: call PRODUCT_COEFFS_GENERIC_LISTS",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProductCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReduceCoeffs: 8 bit vectors, kernel method (2 arg)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "ReduceCoeffs: Gf2 vectors, kernel method (2 arg)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ReduceCoeffs",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ReduceCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ReduceCoeffs: 8 bit vectors, kernel method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "ReduceCoeffs: GF2 vectors, kernel method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "ReduceCoeffs: for float vectors",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFloat)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "CategoryCollections(IsFloat)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "ReduceCoeffs: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ReduceCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReduceCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReduceCoeffsMod",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ReduceCoeffsMod: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ReduceCoeffsMod: generic: list, int,int",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "ReduceCoeffsMod: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ReduceCoeffsMod: generic: list,list,int",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ReduceCoeffsMod: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "ReduceCoeffsMod: generic method (5 args)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ReduceCoeffsMod: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 56
+                }
+            ],
+            "6args": []
+        },
+        "name": "ReduceCoeffsMod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "QuotRemCoeffs: 8 bit vectors, kernel method (2 arg)",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "QuotRemCoeffs: generic, use list lengths",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "QuotRemCoeffs: 8 bit vectors, kernel method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "QuotRemCoeffs: GF2 vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "QuotRemCoeffs: generic",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuotRemCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ValuePol: special code for rational values",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ValuePol: generic",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ValuePol",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RemoveOuterCoeffs: vec8bit and zero",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "RemoveOuterCoeffs: gf2vec and zero",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "RemoveOuterCoeffs: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        []
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "RemoveOuterCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RemoveOuterCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ShiftedCoeffs: empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ShiftedCoeffs: call ShiftRowVektor",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ShiftedCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftShiftRowVector",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 10024
+                },
+                {
+                    "comment": "LeftShiftRowVector: 8bit vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "LeftShiftRowVector: gf2 vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LeftShiftRowVector: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "LeftShiftRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftShiftRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightShiftRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "RightShiftRowVector",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsZeroCyc"
+                        ],
+                        []
+                    ],
+                    "rank": 10023
+                },
+                {
+                    "comment": "RightShiftRowVector: 8bit vector, fill with zeros",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "RightShiftRowVector: gf2 vector, fill with zeros",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "RightShiftRowVector: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "RightShiftRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightShiftRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ShrinkRowVector: 8 bit vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ShrinkRowVector: GF2 vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ShrinkRowVector: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ShrinkRowVector: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ShrinkRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsList",
+                    "CategoryCollections(IsNearAdditiveElementWithZero)",
+                    "CategoryCollections(IsAdditiveElement)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PadCoeffs: 8 bit vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "CategoryCollections(IsNearAdditiveElementWithZero)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "PadCoeffs: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "CategoryCollections(IsNearAdditiveElementWithZero)",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "PadCoeffs: pad with zero",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "CategoryCollections(IsNearAdditiveElementWithZero)",
+                            "CategoryCollections(IsAdditiveElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PadCoeffs: pad with supplied value",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PadCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WeightVecFFE: gf2 vectors",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "WeightVecFFE: generic",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeightVecFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DistanceVecFFE: 8bit-vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "DistanceVecFFE: gf2 vectors",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsList",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "DistanceVecFFE: generic",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DistanceVecFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DistancesDistributionVecFFEsVecFFE: generic",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DistancesDistributionVecFFEsVecFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "CategoryCollections(IsFFE)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DistancesDistributionMatFFEVecFFE: generic",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 114
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DistancesDistributionMatFFEVecFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "CategoryCollections(IsFFE)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "AClosestVectorCombinationsMatFFEVecFFE: generic",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 150
+                }
+            ],
+            "6args": []
+        },
+        "name": "AClosestVectorCombinationsMatFFEVecFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "CategoryCollections(IsFFE)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "AClosestVectorCombinationsMatFFEVecFFECoords: generic",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 150
+                }
+            ],
+            "6args": []
+        },
+        "name": "AClosestVectorCombinationsMatFFEVecFFECoords",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "CategoryCollections(IsFFE)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CosetLeadersMatFFE: generic",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 112
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetLeadersMatFFE",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList",
+                    "CategoryCollections(IsExtAElement)"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                [
+                    "IsExtAElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "AddToListEntries: fast kernel method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList",
+                            "IsPlistRep",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsRange",
+                            "IsRangeRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 100
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddToListEntries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NewInfoClass",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewInfoClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInfoClass"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SetInfoLevel",
+                    "filters": [
+                        [
+                            "IsInfoClass",
+                            "IsInfoClassListRep"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "SetInfoLevel",
+                    "filters": [
+                        [
+                            "IsInfoClass",
+                            "IsInfoClassListRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetInfoLevel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInfoClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InfoLevel",
+                    "filters": [
+                        [
+                            "IsInfoClass",
+                            "IsInfoClassListRep"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InfoLevel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Directory: string",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Directory",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDirectory"
+                ],
+                [
+                    "IsString"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Filename: for a list and a string",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "Filename: for a directory and a string",
+                    "filters": [
+                        [
+                            "IsDirectory"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Filename",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDirectory"
+                ],
+                [
+                    "IsString"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExternalFilename: for a directory list and a string",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ExternalFilename: for a directory and a string",
+                    "filters": [
+                        [
+                            "IsDirectory"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExternalFilename",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Read: string",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Read: input stream",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Read",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReadAsFunction: string",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadAsFunction: input stream",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReadAsFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsEndOfStream: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "IsEndOfStream: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "IsEndOfStream: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsEndOfStream: input text file",
+                    "filters": [
+                        [
+                            "IsInputStream",
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsEndOfStream",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PositionStream: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PositionStream: input text file",
+                    "filters": [
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PositionStream: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionStream",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ]
+            ],
+            [
+                [
+                    "IsInputStream"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReadAll: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReadAll: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReadAll: input text file",
+                    "filters": [
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadAll: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadAll: input stream",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ReadAll: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ReadAll: input text none and limit",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ReadAll: input text file and limit",
+                    "filters": [
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ReadAll: input text string and limit",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ReadAll: input stream, length limit",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReadAll",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReadByte: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReadByte: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReadByte: input text file",
+                    "filters": [
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadByte: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReadByte",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReadLine: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReadLine: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReadLine: input text file",
+                    "filters": [
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadLine: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadLine: generic, call ReadByte",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReadLine",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ],
+                [
+                    "IsBool"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReadAllLine: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ReadAllLine: stream",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ReadAllLine: iostream,function",
+                    "filters": [
+                        [
+                            "IsInputOutputStream"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadAllLine: iostream,boolean",
+                    "filters": [
+                        [
+                            "IsInputOutputStream"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "ReadAllLine: stream,function",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ReadAllLine: stream,boolean",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ReadAllLine: iostream,boolean,function",
+                    "filters": [
+                        [
+                            "IsInputOutputStream"
+                        ],
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReadAllLine: stream,boolean,function",
+                    "filters": [
+                        [
+                            "IsInputStream"
+                        ],
+                        [
+                            "IsBool"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReadAllLine",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RewindStream: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "RewindStream: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "RewindStream: input text stream",
+                    "filters": [
+                        [
+                            "IsInputTextStream"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RewindStream",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInputStream"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SeekPositionStream: input text none",
+                    "filters": [
+                        [
+                            "IsInputTextNone",
+                            "IsInputTextNoneRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "SeekPositionStream: input text file",
+                    "filters": [
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "SeekPositionStream: input text string",
+                    "filters": [
+                        [
+                            "IsInputTextStringRep",
+                            "IsInputTextStream"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SeekPositionStream",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "WriteAll: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "WriteAll: output text none",
+                    "filters": [
+                        [
+                            "IsOutputTextNone",
+                            "IsOutputTextNoneRep"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "WriteAll: output text file",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextFileRep"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "WriteAll: output text string",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextStringRep"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "WriteAll: output stream",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WriteAll",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "WriteByte: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "WriteByte: output text none",
+                    "filters": [
+                        [
+                            "IsOutputTextNone",
+                            "IsOutputTextNoneRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "WriteByte: output text file",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextFileRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "WriteByte: output text string",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextStringRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WriteByte",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "WriteLine: output stream",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WriteLine",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CloseStream: iostream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "CloseStream: output text file",
+                    "filters": [
+                        [
+                            "IsOutputStream",
+                            "IsOutputTextFileRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "CloseStream: input text file",
+                    "filters": [
+                        [
+                            "IsInputStream",
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "CloseStream: non-process streams",
+                    "filters": [
+                        [
+                            "IsPositionalObjectRep",
+                            "IsStream"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "CloseStream: non-process streams",
+                    "filters": [
+                        [
+                            "IsComponentObjectRep",
+                            "IsStream"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CloseStream",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InputTextString: input text stream from string",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InputTextString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InputTextFile: input text stream from file",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InputTextFile",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OutputTextString: error catching method, append not given",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": -9995
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "OutputTextString: output text stream from string",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OutputTextString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OutputTextFile: error catching method, append not given",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": -9995
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "OutputTextFile: output text stream from file",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OutputTextFile",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SetPrintFormattingStatus: output text none",
+                    "filters": [
+                        [
+                            "IsOutputTextNone",
+                            "IsOutputTextNoneRep"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "SetPrintFormattingStatus: for stdout",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "SetPrintFormattingStatus: output text file",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextFileRep"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "SetPrintFormattingStatus: output text string",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextStringRep"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "SetPrintFormattingStatus: for non-text output stream",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPrintFormattingStatus",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrintFormattingStatus: output text none",
+                    "filters": [
+                        [
+                            "IsOutputTextNone",
+                            "IsOutputTextNoneRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PrintFormattingStatus: for stdout",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintFormattingStatus: output text file",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextFileRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintFormattingStatus: output text string",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextStringRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PrintFormattingStatus: for non-text output stream",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrintFormattingStatus",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LogTo: for output file",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "LogTo: for output stream",
+                    "filters": [
+                        [
+                            "IsOutputTextStream"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LogTo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InputLogTo: for output file",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "InputLogTo: for output stream",
+                    "filters": [
+                        [
+                            "IsOutputTextStream"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InputLogTo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OutputLogTo: for output file",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "OutputLogTo: for output stream",
+                    "filters": [
+                        [
+                            "IsOutputTextStream"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OutputLogTo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStream"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FileDescriptorOfStream",
+                    "filters": [
+                        [
+                            "IsInputOutputStream",
+                            "IsInputOutputStreamByPtyRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "FileDescriptorOfStream",
+                    "filters": [
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextFileRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "FileDescriptorOfStream",
+                    "filters": [
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FileDescriptorOfStream",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ImmutableMatrix: field,gf2",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ImmutableMatrix: field,8bit",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ImmutableMatrix: fieldsize,gf2",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ImmutableMatrix: fieldsize,8bit",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ImmutableMatrix: general,2",
+                    "filters": [
+                        [],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ImmutableMatrix: empty",
+                    "filters": [
+                        [],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ImmutableMatrix: transposed empty",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ImmutableMatrix: general,3",
+                    "filters": [
+                        [],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImmutableMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NumberFFVector: 8bit-vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "NumberFFVector: GF2-Vector",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "NumberFFVector: uncompressed vecffe",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumberFFVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRandomSource"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "State: for a real random source",
+                    "filters": [
+                        [
+                            "IsRealRandomSource"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "State",
+                    "filters": [
+                        [
+                            "IsMersenneTwister"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "State",
+                    "filters": [
+                        [
+                            "IsGAPRandomSource"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "State",
+                    "filters": [
+                        [
+                            "IsGlobalRandomSource"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "State",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRandomSource"
+                ]
+            ],
+            [
+                [
+                    "IsRandomSource"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Reset: for a real random source",
+                    "filters": [
+                        [
+                            "IsRealRandomSource"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Reset",
+                    "filters": [
+                        [
+                            "IsRandomSource"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Reset: for a real random source and an object",
+                    "filters": [
+                        [
+                            "IsRealRandomSource"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Reset",
+                    "filters": [
+                        [
+                            "IsMersenneTwister"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Reset",
+                    "filters": [
+                        [
+                            "IsGAPRandomSource"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Reset",
+                    "filters": [
+                        [
+                            "IsGlobalRandomSource"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Reset",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRandomSource"
+                ]
+            ],
+            [
+                [
+                    "IsRandomSource"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Init: for a real random source",
+                    "filters": [
+                        [
+                            "IsRealRandomSource"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Init",
+                    "filters": [
+                        [
+                            "IsMersenneTwister"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Init",
+                    "filters": [
+                        [
+                            "IsGAPRandomSource"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Init",
+                    "filters": [
+                        [
+                            "IsGlobalRandomSource"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Init",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOperation"
+                ]
+            ],
+            [
+                [
+                    "IsOperation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RandomSource",
+                    "filters": [
+                        [
+                            "IsOperation"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "RandomSource",
+                    "filters": [
+                        [
+                            "IsOperation"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RandomSource",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsString"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SplitString: for two strings",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "SplitString: for a string and a character",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SplitString: for three strings",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "SplitString: for a string, a character and a string",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsChar"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "SplitString: for two strings and a character",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "SplitString: for a string and two characters",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsChar"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SplitString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NewFloat: for IsIEEE754FloatRep and string",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewFloat: for IsIEEE754FloatRep and integer",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": -16
+                },
+                {
+                    "comment": "NewFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -16
+                },
+                {
+                    "comment": "NewFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": -16
+                },
+                {
+                    "comment": "NewFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewFloat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MakeFloat: for IsIEEE754FloatRep and integer",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "MakeFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "MakeFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "MakeFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "MakeFloat: for IsIEEE754FloatRep and string",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "MakeFloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MakeFloat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Cos: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Cos)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Cos: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cos",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Cos): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Cos): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Cos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Cos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sin: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Sin)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Sin: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sin",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Sin): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Sin): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Sin)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Sin)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Tan: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Tan)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Tan: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tan",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Tan): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Tan): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Tan)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Tan)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sec: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Sec)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Sec: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sec",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Sec): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Sec): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Sec)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Sec)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Csc: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Csc)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Csc: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Csc",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Csc): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Csc): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Csc)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Csc)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Cot: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Cot)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Cot: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cot",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Cot): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Cot): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Cot)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Cot)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Asin: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Asin)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Asin: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Asin",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Asin): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Asin): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Asin)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Asin)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Acos: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Acos)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Acos: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Acos",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Acos): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Acos): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Acos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Acos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Atan: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Atan)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Atan: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Atan",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Atan): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Atan): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Atan)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Atan)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Cosh: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Cosh)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cosh",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Cosh): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Cosh): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Cosh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Cosh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sinh: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Sinh)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sinh",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Sinh): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Sinh): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Sinh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Sinh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Tanh: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Tanh)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tanh",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Tanh): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Tanh): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Tanh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Tanh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sech: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Sech)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Sech: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sech",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Sech): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Sech): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Sech)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Sech)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Csch: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Csch)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Csch: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Csch",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Csch): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Csch): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Csch)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Csch)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Coth: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Coth)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Coth: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Coth",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Coth): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Coth): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Coth)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Coth)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Asinh: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Asinh)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Asinh",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Asinh): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Asinh): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Asinh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Asinh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Acosh: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Acosh)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Acosh",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Acosh): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Acosh): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Acosh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Acosh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Atanh: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Atanh)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Atanh",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Atanh): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Atanh): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Atanh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Atanh)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Log2: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Log2)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Log2: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Log2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Log2): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Log2): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Log2)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Log2)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Log10: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Log10)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Log10: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Log10",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Log10): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Log10): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Log10)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Log10)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Log1p: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Log1p)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Log1p: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Log1p",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Log1p): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Log1p): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Log1p)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Log1p)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Exp: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Exp)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Exp: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Exp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Exp): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Exp): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Exp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Exp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Exp2: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Exp2)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Exp2: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Exp2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Exp2): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Exp2): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Exp2)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Exp2)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Exp10: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Exp10)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Exp10: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Exp10",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Exp10): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Exp10): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Exp10)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Exp10)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Expm1: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Expm1)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Expm1: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Expm1",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Expm1): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Expm1): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Expm1)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Expm1)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CubeRoot: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CubeRoot)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "CubeRoot: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CubeRoot",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CubeRoot): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CubeRoot): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CubeRoot)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CubeRoot)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Square: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Square)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Square: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Square",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Square): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Square): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Square)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Square)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Ceil: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Ceil)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Ceil: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Ceil: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Ceil",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Ceil): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Ceil): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Ceil)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Ceil)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Floor: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Floor)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Floor: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Floor",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Floor): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Floor): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Floor)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Floor)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Round: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Round)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Round: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Round: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Round",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Round): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Round): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Round)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Round)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Trunc: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Trunc)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Trunc: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Trunc",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Trunc): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Trunc): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Trunc)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Trunc)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Atan2: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Atan2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FrExp: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FrExp)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "FrExp: for macfloat",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "FrExp: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FrExp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FrExp): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FrExp): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FrExp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FrExp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LdExp: for macfloat,int",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LdExp: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LdExp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Argument: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Argument)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Argument: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Argument",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Argument): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Argument): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Argument)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Argument)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ],
+            [
+                [
+                    "IsCyclotomic"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AbsoluteValue: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AbsoluteValue)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "AbsoluteValue: rationals",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AbsoluteValue: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "AbsoluteValue: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbsoluteValue",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsCyclotomic"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AbsoluteValue): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AbsoluteValue): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AbsoluteValue)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AbsoluteValue)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Hypothenuse: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Hypothenuse: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Hypothenuse: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Hypothenuse",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Frac: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Frac)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Frac: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Frac",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Frac): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Frac): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Frac)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Frac)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SinCos: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SinCos)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "SinCos: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SinCos",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SinCos): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SinCos): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SinCos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SinCos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Erf: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Erf)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Erf",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Erf): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Erf): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Erf)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Erf)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Zeta: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Zeta)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Zeta",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Zeta): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Zeta): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Zeta)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Zeta)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Gamma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Gamma)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Gamma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Gamma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Gamma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Gamma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Gamma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComplexI: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComplexI)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComplexI",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComplexI): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComplexI): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComplexI)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComplexI)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrecisionFloat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrecisionFloat)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "PrecisionFloat: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrecisionFloat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrecisionFloat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrecisionFloat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrecisionFloat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrecisionFloat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SignFloat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SignFloat)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "SignFloat: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SignFloat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SignFloat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SignFloat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SignFloat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SignFloat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Sup)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Sup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Sup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Sup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Sup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Inf: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Inf)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Inf",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Inf): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Inf): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Inf)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Inf)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Mid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Mid)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Mid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Mid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Mid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Mid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Mid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AbsoluteDiameter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AbsoluteDiameter)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbsoluteDiameter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AbsoluteDiameter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AbsoluteDiameter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AbsoluteDiameter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AbsoluteDiameter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelativeDiameter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelativeDiameter)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelativeDiameter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelativeDiameter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelativeDiameter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelativeDiameter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelativeDiameter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Overlaps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsDisjoint",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EqFloat: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ],
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "EqFloat: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EqFloat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IncreaseInterval",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BlowupInterval",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BisectInterval",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPInfinity: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPInfinity)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsPInfinity: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPInfinity",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPInfinity): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPInfinity): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPInfinity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPInfinity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNInfinity: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNInfinity)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsNInfinity: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNInfinity",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNInfinity): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNInfinity): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNInfinity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNInfinity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsXInfinity: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsXInfinity)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsXInfinity: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsXInfinity",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsXInfinity): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsXInfinity): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsXInfinity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsXInfinity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNaN: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNaN)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsNaN: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNaN",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNaN): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNaN): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNaN)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNaN)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Cyc: for intervals",
+                    "filters": [
+                        [
+                            "IsFloatInterval"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Cyc: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Cyc: for intervals, degree",
+                    "filters": [
+                        [
+                            "IsFloatInterval"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Cyc: for floats, degree",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cyc",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDirectory"
+                ],
+                [
+                    "IsString"
+                ],
+                [
+                    "IsInputStream"
+                ],
+                [
+                    "IsOutputStream"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "Process",
+                    "filters": [
+                        [
+                            "IsDirectory",
+                            "IsDirectoryRep"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ],
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextFileRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Process",
+                    "filters": [
+                        [
+                            "IsDirectory",
+                            "IsDirectoryRep"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsInputTextNone"
+                        ],
+                        [
+                            "IsOutputTextStream",
+                            "IsOutputTextFileRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Process",
+                    "filters": [
+                        [
+                            "IsDirectory",
+                            "IsDirectoryRep"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsInputTextStream",
+                            "IsInputTextFileRep"
+                        ],
+                        [
+                            "IsOutputTextNone"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Process",
+                    "filters": [
+                        [
+                            "IsDirectory",
+                            "IsDirectoryRep"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsInputTextNone"
+                        ],
+                        [
+                            "IsOutputTextNone"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Process",
+                    "filters": [
+                        [
+                            "IsDirectory",
+                            "IsDirectoryRep"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsInputTextStream"
+                        ],
+                        [
+                            "IsOutputTextStream"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "6args": []
+        },
+        "name": "Process",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectProductElementsFamily: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "DirectProductElementsFamily: for a collection (of families)",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectProductElementsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsDirectProductElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComponentsOfDirectProductElementsFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComponentsOfDirectProductElementsFamily)"
+                        ]
+                    ],
+                    "rank": 20007
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComponentsOfDirectProductElementsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsDirectProductElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComponentsOfDirectProductElementsFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComponentsOfDirectProductElementsFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComponentsOfDirectProductElementsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsDirectProductElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComponentsOfDirectProductElementsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectProductElement: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DirectProductElement: for a direct product elements family, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsDirectProductElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectProductElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsDirectProductElement)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DirectProductElementNC: for a direct product elements family, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsDirectProductElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectProductElementNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EmptyRowVector: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EmptyRowVector)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "EmptyRowVector: for a family",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EmptyRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EmptyRowVector): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EmptyRowVector): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EmptyRowVector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EmptyRowVector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtASet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfExtASet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfExtASet)"
+                        ]
+                    ],
+                    "rank": 20012
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfExtASet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtASet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfExtASet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfExtASet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfExtASet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtASet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfExtASet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtASet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdditivelyActingDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdditivelyActingDomain)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "AdditivelyActingDomain: for additive coset in default repres.",
+                    "filters": [
+                        [
+                            "IsAdditiveCoset",
+                            "IsAdditiveCosetDefaultRep"
+                        ]
+                    ],
+                    "rank": 10014
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditivelyActingDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtASet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdditivelyActingDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdditivelyActingDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdditivelyActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtASet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdditivelyActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsLeftActedOnByRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLeftActedOnByDivisionRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLeftActedOnByDivisionRing)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsLeftActedOnByDivisionRing: method for external left set that is left acted on by a ring",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsLeftActedOnByRing"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftActedOnByDivisionRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsLeftActedOnByRing"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLeftActedOnByDivisionRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLeftActedOnByDivisionRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLeftActedOnByDivisionRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsLeftActedOnByRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLeftActedOnByDivisionRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfExtLSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfExtLSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfExtLSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfExtLSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfExtLSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfExtLSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfExtLSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeftActingDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeftActingDomain)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftActingDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeftActingDomain): method to set also 'IsLeftActedOnByDivisionRing'",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsLeftActedOnByRing"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Setter(LeftActingDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeftActingDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeftActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeftActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfExtRSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfExtRSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfExtRSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfExtRSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfExtRSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfExtRSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfExtRSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RightActingDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RightActingDomain)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightActingDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RightActingDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RightActingDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RightActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RightActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtUSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfExtUSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfExtUSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfExtUSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtUSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfExtUSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfExtUSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfExtUSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtUSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfExtUSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UpperActingDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UpperActingDomain)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UpperActingDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UpperActingDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UpperActingDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UpperActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UpperActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDictionary"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "KnowsDictionary: for lookup sort dictionaries",
+                    "filters": [
+                        [
+                            "IsSortLookupDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "KnowsDictionary: for list lookup dictionaries",
+                    "filters": [
+                        [
+                            "IsListLookupDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "KnowsDictionary: for position dictionaries",
+                    "filters": [
+                        [
+                            "IsPositionDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "KnowsDictionary: for list dictionaries",
+                    "filters": [
+                        [
+                            "IsListDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "KnowsDictionary: for hash tables",
+                    "filters": [
+                        [
+                            "IsHash"
+                        ],
+                        []
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnowsDictionary",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsDictionary"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsDictionary"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AddDictionary: for sort dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsSortDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "AddDictionary: for position dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPositionDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AddDictionary: for list dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsListDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AddDictionary: for hash tables, no value given",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHash"
+                        ],
+                        []
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "AddDictionary: for lookup sort dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsSortLookupDictionary"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "AddDictionary: for hash tables",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHash",
+                            "TableHasIntKeyFun",
+                            "IsSparseHashRep"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AddDictionary: for lookup position dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPositionDictionary"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AddDictionary: for lookup list dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsListLookupDictionary"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AddDictionary: for hash tables",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHash",
+                            "IsSparseHashRep"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 9
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddDictionary",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsDictionary"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RemoveDictionary: for lookup list dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsListLookupDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "RemoveDictionary: for list dictionaries",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsListDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RemoveDictionary",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDictionary"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LookupDictionary: for lookup sort dictionaries",
+                    "filters": [
+                        [
+                            "IsSortLookupDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "LookupDictionary: for hash tables that know their int key",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "TableHasIntKeyFun",
+                            "IsSparseHashRep"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "LookupDictionary: for position dictionaries",
+                    "filters": [
+                        [
+                            "IsPositionDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "LookupDictionary: for list dictionaries",
+                    "filters": [
+                        [
+                            "IsListLookupDictionary"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "LookupDictionary: for hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsSparseHashRep"
+                        ],
+                        []
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LookupDictionary",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListDictionary"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ListKeyEnumerator: for list dictionaries",
+                    "filters": [
+                        [
+                            "IsListDictionary"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ListKeyEnumerator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHash"
+                ],
+                [
+                    "IsString"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PrintHashWithNames: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsSparseHashRep"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PrintHashWithNames: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsDenseHashRep"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrintHashWithNames",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHash"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RandomHashKey: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "RandomHashKey: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsDenseHashRep"
+                        ]
+                    ],
+                    "rank": 107
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RandomHashKey",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHash"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HashKeyEnumerator: for sparse hash tables",
+                    "filters": [
+                        [
+                            "IsHash",
+                            "IsSparseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "HashKeyEnumerator: for dense hash tables",
+                    "filters": [
+                        [
+                            "IsDenseHashRep"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HashKeyEnumerator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DenseIntKey: integers",
+                    "filters": [
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "DenseIntKey: default fail",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DenseIntKey",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SparseIntKey: for finite Gaussian row spaces",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "SparseIntKey: pcgs element lists: i.e. pcgs",
+                    "filters": [
+                        [],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsElementFinitePolycyclicGroup)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SparseIntKey: for matrices over finite field vector spaces",
+                    "filters": [
+                        [],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SparseIntKey: for row spaces over finite fields",
+                    "filters": [
+                        [],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "SparseIntKey: for vector listsover finite field vector spaces",
+                    "filters": [
+                        [],
+                        [
+                            "IsList",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "SparseIntKey: for lists of vectors",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "SparseIntKey: kernel pc group elements",
+                    "filters": [
+                        [],
+                        [
+                            "IsDataObjectRep",
+                            "IsElementFinitePolycyclicGroup",
+                            "IsNBitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "SparseIntKey: permutations, arbitrary domain",
+                    "filters": [
+                        [],
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "SparseIntKey: for an object and transformation",
+                    "filters": [
+                        [],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "SparseIntKey: defaults to DenseIntKey",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SparseIntKey",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHash"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetHashEntryAtLastIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsHash"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetHashEntryAtLastIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsHash"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetHashEntry",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FamilyRange: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FamilyRange)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FamilyRange",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsGeneralMapping)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FamilyRange): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FamilyRange): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FamilyRange)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FamilyRange)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FamilySource: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FamilySource)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FamilySource",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsGeneralMapping)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FamilySource): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FamilySource): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FamilySource)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FamilySource)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FamiliesOfGeneralMappingsAndRanges: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FamiliesOfGeneralMappingsAndRanges)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "FamiliesOfGeneralMappingsAndRanges: for a family (return empty list)",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FamiliesOfGeneralMappingsAndRanges",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FamiliesOfGeneralMappingsAndRanges): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FamiliesOfGeneralMappingsAndRanges): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FamiliesOfGeneralMappingsAndRanges)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FamiliesOfGeneralMappingsAndRanges)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsConstantTimeAccessGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsConstantTimeAccessGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsConstantTimeAccessGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsConstantTimeAccessGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsConstantTimeAccessGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsConstantTimeAccessGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsConstantTimeAccessGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsEndoGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsEndoGeneralMapping: for general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsEndoGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsEndoGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsEndoGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsEndoGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsEndoGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTotal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTotal)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsTotal: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "IsTotal: for ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsTotal: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsTotal: for a composition mapping",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsTotal: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsTotal",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "Tester(InverseGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IsTotal: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTotal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTotal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTotal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTotal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTotal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSingleValued: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsSingleValued: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "IsSingleValued: map from whole fp group or free group to perm, std. gens: test relators",
+                    "filters": [
+                        [
+                            "IsToPermGroupGeneralMappingByImages",
+                            "IsFromFpGroupStdGensGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsSingleValued: for group general mappings of free groups",
+                    "filters": [
+                        [
+                            "Tester(MappingGeneratorsImages)",
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsSingleValued: map from whole fp group or free group, given on std. gens: test relators",
+                    "filters": [
+                        [
+                            "IsFromFpGroupStdGensGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsSingleValued: map from fp group or free group on arbitrary gens: rewrite",
+                    "filters": [
+                        [
+                            "Tester(MappingGeneratorsImages)",
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsSingleValued: for algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsPolynomialRingDefaultGeneratorMapping"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IsSingleValued: for algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "IsSingleValued: for sc ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSCRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsSingleValued: for left module g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsSingleValued",
+                    "filters": [
+                        [
+                            "IsPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsSingleValued: for GMBPCGS: test relations",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByPcgs"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsSingleValued: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsSingleValued: method for a gen. mapping that respects add. and add. inverses",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsSingleValued: method for a gen. mapping that respects mult. and inverses",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsSingleValued: for a composition mapping",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsSingleValued: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsSingleValued",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "Tester(InverseGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IsSingleValued: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSingleValued",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSingleValued): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSingleValued): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSingleValued)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSingleValued)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsInjective: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsInjective)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsInjective: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "IsInjective: for PcpGHBI",
+                    "filters": [
+                        [
+                            "IsFromPcpGHBI",
+                            "IsToPcpGHBI"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "IsInjective: for algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "IsInjective: for a linear action homomorphism",
+                    "filters": [
+                        [
+                            "IsLinearActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsInjective: method for homs from pc group",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsInjective: for a field homomorphism",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsInjective: for ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsInjective: for left module m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsInjective: for left module g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsInjective: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsInjective: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsInjective: for zero mapping",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsInjective: method for a gen. mapping that respects add. and add. inverses",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsInjective: method for a gen. mapping that respects mult. and one",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsInjective: for a mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsInjective: for a composition mapping",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsInjective: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsInjective",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "Tester(InverseGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IsInjective: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInjective",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsInjective): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsInjective): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsInjective)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsInjective)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSurjective: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSurjective)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsSurjective: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "IsSurjective: for a field homomorphism",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsSurjective: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsSurjective: for zero mapping",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsSurjective: for a composition mapping",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsSurjective: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsSurjective",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "Tester(InverseGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IsSurjective: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSurjective",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSurjective): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSurjective): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSurjective)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSurjective)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Range: for default general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsDefaultGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "Range: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Range)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "Range: for operation algebra homomorphism (set full matrix FLMLOR)",
+                    "filters": [
+                        [
+                            "IsOperationAlgebraHomomorphismDefaultRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "Range: surjective blocks homomorphism",
+                    "filters": [
+                        [
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsBlocksHomomorphism"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Range: surjective constituent homomorphism",
+                    "filters": [
+                        [
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsActionHomomorphism",
+                            "IsConstituentHomomorphism"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Range: surjective action homomorphism",
+                    "filters": [
+                        [
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Range: perm subdirect product projection",
+                    "filters": [
+                        [
+                            "IsProjectionSubdirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Range: perm direct product projection",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Range: ophom: S(domain)",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Range",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Range): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Range): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Range)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Range)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Source: for default general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsDefaultGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "Source: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Source)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "Source: perm wreath product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingWreathProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Source: perm direct product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Source: action homomorphism",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Source",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Source): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Source): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Source)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Source)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingRelation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "UnderlyingRelation: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingGeneralMapping): for an underlying relation and a general mapping",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "IsGeneralizedDomain",
+                            "Tester(GeneratorsOfDomain)",
+                            "CategoryCollections(IsDirectProductElement)"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "Setter(UnderlyingGeneralMapping): for an underlying relation and a general mapping",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsCollection",
+                            "Tester(AsList)",
+                            "IsGeneralizedDomain",
+                            "CategoryCollections(IsDirectProductElement)"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "Setter(UnderlyingGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdentityMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdentityMapping)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IdentityMapping: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdentityMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdentityMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdentityMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdentityMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdentityMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InverseGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "InverseGeneralMapping: for nilpotent Lie algebra automorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "InverseGeneralMapping: for group automorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "InverseGeneralMapping: for inner automorphism",
+                    "filters": [
+                        [
+                            "IsInnerAutomorphism",
+                            "Tester(IsInnerAutomorphism)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "InverseGeneralMapping: for ANF automorphism",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "InverseGeneralMapping: for a Frobenius automorphism",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "InverseGeneralMapping: for conjugator automorphism",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "InverseGeneralMapping: for bijective GHBI",
+                    "filters": [
+                        [
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "InverseGeneralMapping: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "InverseGeneralMapping: for an ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "InverseGeneralMapping: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "InverseGeneralMapping: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionWithInverseRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "InverseGeneralMapping: via generators/images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "InverseGeneralMapping",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InverseImmutable)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "InverseGeneralMapping: for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InverseGeneralMapping): transfer the AsGHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages",
+                            "Tester(AsGroupGeneralMappingByImages)"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Setter(InverseGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InverseGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InverseGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InverseGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImagesSource: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImagesSource)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ImagesSource: for zero mapping",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImagesSource: for identity mapping",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImagesSource: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "ImagesSource: for surjective general mapping (delegate to `Range')",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSurjective",
+                            "Tester(IsSurjective)"
+                        ]
+                    ],
+                    "rank": 10009
+                },
+                {
+                    "comment": "ImagesSource: for an algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ImagesSource: actionHomomorphismByBase",
+                    "filters": [
+                        [
+                            "IsActionHomomorphismByBase"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesSource: perm direct product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesSource: blocks homomorphism",
+                    "filters": [
+                        [
+                            "IsBlocksHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesSource: constituent homomorphism",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism",
+                            "IsConstituentHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesSource: for an ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesSource: for a linear g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesSource: for group homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "ImagesSource: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ImagesSource: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ImagesSource: for general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImagesSource",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImagesSource): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImagesSource): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImagesSource)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImagesSource)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PreImagesRange: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PreImagesRange)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "PreImagesRange: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "PreImagesRange: for total general mapping (delegate to `Source')",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)"
+                        ]
+                    ],
+                    "rank": 10009
+                },
+                {
+                    "comment": "PreImagesRange: for an algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PreImagesRange: for an ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesRange: for a linear g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesRange: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PreImagesRange: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "PreImagesRange: for general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImagesRange",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PreImagesRange): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PreImagesRange): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PreImagesRange)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PreImagesRange)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ImagesElm: for zero mapping and object",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImagesElm: for identity mapping and object",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImagesElm: for ANF automorphism and scalar",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "ImagesElm: for embedding of ring into magma ring, and ring element",
+                    "filters": [
+                        [
+                            "IsEmbeddingRingMagmaRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ImagesElm: for binary relations over [1..n] with images list",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ImagesElm: for Frobenius automorphism and source element",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ImagesElm: for magma congruence and element",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ImagesElm: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesElm: for a Green's equivalence",
+                    "filters": [
+                        [
+                            "IsGreensRelation"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesElm: for embedding of magma into magma ring, and mult. element",
+                    "filters": [
+                        [
+                            "IsEmbeddingMagmaMagmaRing"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesElm: for magma congruence and element",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesElm: for magma congruence and element",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesElm: for equivalence relation with partition and element",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "Tester(EquivalenceRelationPartition)"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesElm: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ImagesElm: IsTransformationRepOfEndo",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ],
+                        []
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ImagesElm: method for s.p. gen. mapping respecting add. & add.inv., and element",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ImagesElm: method for s.p. general mapping respecting mult. & inv., and element",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ImagesElm: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionRep"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ImagesElm: for Lie embedding and object",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLieEmbeddingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ImagesElm: for a restricted mapping, and an element",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ImagesElm: for a composition mapping, and an element",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ImagesElm: for an inverse mapping and an element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ImagesElm: for constant time access general mapping, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsConstantTimeAccessGeneralMapping",
+                            "Tester(IsConstantTimeAccessGeneralMapping)"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ImagesElm: for non s.p. general mapping, and element",
+                    "filters": [
+                        [
+                            "IsNonSPGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImagesElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ImagesRepresentative: for zero mapping and object",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImagesRepresentative: for identity mapping and object",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImagesRepresentative: for total GGMBPCGS, and mult.-elm.-with-inverse",
+                    "filters": [
+                        [
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsGroupGeneralMappingByPcgs"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 125
+                },
+                {
+                    "comment": "ImagesRepresentative: for homomorphisms of free groups",
+                    "filters": [
+                        [
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "ImagesRepresentative: for a blow up isomorphism, and a matrix in the source",
+                    "filters": [
+                        [
+                            "IsBlowUpIsomorphism"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "ImagesRepresentative: for an alg. hom. from f. p. algebra, and an element",
+                    "filters": [
+                        [
+                            "IsAlgebraHomomorphismFromFpRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ImagesRepresentative: for an operation algebra homomorphism, and an element",
+                    "filters": [
+                        [
+                            "IsOperationAlgebraHomomorphismDefaultRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ImagesRepresentative: for ANF automorphism and scalar",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "ImagesRepresentative: for FromPcpGHBI",
+                    "filters": [
+                        [
+                            "IsFromPcpGHBI"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ImagesRepresentative: simple tests on equal words to check whether the `generators' are mapped",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ImagesRepresentative: map from fp group or free group, use 'MappedWord'",
+                    "filters": [
+                        [
+                            "IsFromFpGroupStdGensGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ImagesRepresentative: map from (sub)fp group, rewrite",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ImagesRepresentative: for embedding of ring into magma ring, and ring element",
+                    "filters": [
+                        [
+                            "IsEmbeddingRingMagmaRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ImagesRepresentative: for Fp to SCA mapping, and element",
+                    "filters": [
+                        [
+                            "IsFptoSCAMorphism"
+                        ],
+                        [
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ImagesRepresentative",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcgsToPcgsGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ImagesRepresentative: using `RepresentativeAction'",
+                    "filters": [
+                        [
+                            "Tester(ImagesSource)",
+                            "IsActionHomomorphismByBase"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ImagesRepresentative: imprim perm wreath product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingImprimitiveWreathProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ImagesRepresentative: for isom by finite matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsIsomorphismByFinitePolycyclicMatrixGroup",
+                            "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: for isom by matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsIsomorphismByPolycyclicMatrixGroup",
+                            "Tester(IsIsomorphismByPolycyclicMatrixGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: for group by field elems isom",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsMultGroupByFieldElemsIsomorphism",
+                            "Tester(IsMultGroupByFieldElemsIsomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: for unit groups",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsUnitGroupIsomorphism",
+                            "Tester(IsUnitGroupIsomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: restricted perm",
+                    "filters": [
+                        [
+                            "IsActionHomomorphismSubset"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: for action hom that is `ByAsGroup'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages",
+                            "IsActionHomomorphism"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: imprim matrix wreath product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingImprimitiveWreathProductMatrixGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: matrix direct product projection",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductMatrixGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: matrix direct product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductMatrixGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: perm subdirect product projection",
+                    "filters": [
+                        [
+                            "IsProjectionSubdirectProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: perm direct product projection",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: perm direct product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: blocks homomorphism",
+                    "filters": [
+                        [
+                            "IsBlocksHomomorphism"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: Constituent homomorphism",
+                    "filters": [
+                        [
+                            "IsConstituentHomomorphism"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImagesRepresentative: for action hom",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ImagesRepresentative: for Frobenius automorphism and source element",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ImagesRepresentative: for polring g.m.b.i., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsPolynomialRingDefaultGeneratorMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ImagesRepresentative: for algebra g.m.b.i., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ImagesRepresentative",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsFromAffineCrystGroupToPcpGroup",
+                            "Tester(IsFromAffineCrystGroupToPcpGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ImagesRepresentative",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsFromAffineCrystGroupToFpGroup",
+                            "Tester(IsFromAffineCrystGroupToFpGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ImagesRepresentative",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsPointHomomorphism",
+                            "Tester(IsPointHomomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ImagesRepresentative: word decomp hom",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsWordDecompHomomorphism",
+                            "Tester(IsWordDecompHomomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ImagesRepresentative: perm group hom",
+                    "filters": [
+                        [
+                            "IsPermGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ImagesRepresentative: for SC ring g.m.b.i., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "IsSCRingGeneralMappingByImagesDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ImagesRepresentative: for `ByAsGroupGeneralMapping' hom",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesRepresentative: for left module m.b.m., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesRepresentative: for left module g.m.b.i., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImagesRepresentative: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesRepresentative: for group automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesRepresentative: parallel enumeration of source and range",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesRepresentative: for embedding of magma into magma ring, and mult. element",
+                    "filters": [
+                        [
+                            "IsEmbeddingMagmaMagmaRing"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ImagesRepresentative: equivalence relations",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "ImagesRepresentative: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ImagesRepresentative: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionRep"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ImagesRepresentative: for a restricted mapping, and an element",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ImagesRepresentative: for a composition mapping, and an element",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "ImagesRepresentative: for an inverse mapping and an element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ImagesRepresentative: for non s.p. general mapping, and element",
+                    "filters": [
+                        [
+                            "IsNonSPGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ImagesRepresentative: for s.p. general mapping, and element",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImagesRepresentative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ImagesSet: for zero mapping and collection",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10019
+                },
+                {
+                    "comment": "ImagesSet: for identity mapping and collection",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10019
+                },
+                {
+                    "comment": "ImagesSet: constituent homomorphism",
+                    "filters": [
+                        [
+                            "IsConstituentHomomorphism"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(StabChainMutable)"
+                        ]
+                    ],
+                    "rank": 79
+                },
+                {
+                    "comment": "ImagesSet: for blocks homomorphism and perm. group",
+                    "filters": [
+                        [
+                            "IsBlocksHomomorphism"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "ImagesSet: for ANF automorphism and field",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "ImagesSet: for Frobenius automorphism and field contained in the source",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "ImagesSet: for field homomorphism and field",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "ImagesSet: for conjugator isomorphism, and group",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "ImagesSet: method for algebra-with-one hom. and FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "ImagesSet: for polring g.m.b.i., and ring",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsPolynomialRingDefaultGeneratorMapping"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "ImagesSet: method for algebra hom. and FLMLOR",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "ImagesSet: method for injective s.p. mapping respecting mult. & inv., and group",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "ImagesSet: method for s.p. general mapping respecting mult. & inv., and group",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "ImagesSet: method for linear mapping and left module",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ImagesSet: for general mapping, and empty list",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ImagesSet: for a restricted mapping, and an collection",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ImagesSet: for a composition mapping, and an collection",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ImagesSet: for an inverse mapping and a collection",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ImagesSet: for general mapping, and finite collection",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImagesSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ImageElm: for zero mapping and object",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImageElm: for identity mapping and object",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "ImageElm: for ANF automorphism and scalar",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ImageElm: for Fp to SCA mapping, and element",
+                    "filters": [
+                        [
+                            "IsFptoSCAMorphism"
+                        ],
+                        [
+                            "IsElementOfFpAlgebra"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ImageElm: for Frobenius automorphism and source element",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ImageElm: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionRep"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ImageElm: for an inverse mapping and an element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ImageElm: for mapping, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        []
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ImageElm: for general mapping, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImageElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PreImagesElm: for zero mapping and object",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "PreImagesElm: for identity mapping and object",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "PreImagesElm: for embedding of ring into magma ring, and free magma ring element",
+                    "filters": [
+                        [
+                            "IsEmbeddingRingMagmaRing"
+                        ],
+                        [
+                            "IsElementOfFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "PreImagesElm: for ANF automorphism and scalar",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "PreImagesElm: for embedding of magma into magma ring, and free magma ring element",
+                    "filters": [
+                        [
+                            "IsEmbeddingMagmaMagmaRing"
+                        ],
+                        [
+                            "IsElementOfFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImagesElm: for binary rels over [1..n] with images list",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImagesElm: for field homomorphism and element",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesElm: for Lie embedding and Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLieEmbeddingRep"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesElm: equivalence relations with parition and element",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "Tester(EquivalenceRelationPartition)"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PreImagesElm: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionWithInverseRep"
+                        ],
+                        []
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PreImagesElm: method for s.p. gen. mapping respecting add. & add.inv., and element",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PreImagesElm: method for s.p. general mapping respecting mult. & inv., and element",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PreImagesElm: for a restricted mapping, and an element",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PreImagesElm: for a composition mapping, and an element",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PreImagesElm: for an inverse mapping and an element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PreImagesElm: for constant time access general mapping, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsConstantTimeAccessGeneralMapping",
+                            "Tester(IsConstantTimeAccessGeneralMapping)"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PreImagesElm: for general mapping with finite source, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImagesElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsInjective",
+                    "Tester(IsInjective)",
+                    "IsSurjective",
+                    "Tester(IsSurjective)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PreImageElm: for identity mapping and object",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "PreImageElm: for ANF automorphism and scalar",
+                    "filters": [
+                        [
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "PreImageElm: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionWithInverseRep"
+                        ],
+                        []
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PreImageElm: for an inj. & surj. inverse mapping, and an element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "PreImageElm: for inj. & surj. general mapping, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)"
+                        ],
+                        []
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PreImageElm: for general mapping, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImageElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PreImagesRepresentative: for zero mapping and object",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "PreImagesRepresentative: for identity mapping and object",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "PreImagesRepresentative: for an alg. hom. from f. p. algebra, and an element",
+                    "filters": [
+                        [
+                            "IsAlgebraHomomorphismFromFpRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "PreImagesRepresentative: for an operation algebra homomorphism, and an element",
+                    "filters": [
+                        [
+                            "IsOperationAlgebraHomomorphismDefaultRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "PreImagesRepresentative: for a blow up isomorphism, and a matrix in the range",
+                    "filters": [
+                        [
+                            "IsBlowUpIsomorphism"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "PreImagesRepresentative: for embedding of ring into magma ring, and free magma ring element",
+                    "filters": [
+                        [
+                            "IsEmbeddingRingMagmaRing"
+                        ],
+                        [
+                            "IsElementOfFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "PreImagesRepresentative: for ANF automorphism and scalar",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "PreImagesRepresentative: for ToPcpGHBI",
+                    "filters": [
+                        [
+                            "IsToPcpGHBI"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "PreImagesRepresentative: for Fp to SCA mapping, and element",
+                    "filters": [
+                        [
+                            "IsFptoSCAMorphism"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PreImagesRepresentative: AutomGroup Niceomorphism",
+                    "filters": [
+                        [
+                            "IsActionHomomorphismAutomGroup"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "PreImagesRepresentative: IsProjectiveActionHomomorphism",
+                    "filters": [
+                        [
+                            "IsProjectiveActionHomomorphism"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImagesRepresentative: IsLinearActionHomomorphism",
+                    "filters": [
+                        [
+                            "IsLinearActionHomomorphism"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImagesRepresentative: constituent homomorphism",
+                    "filters": [
+                        [
+                            "IsConstituentHomomorphism"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImagesRepresentative: for embedding of magma into magma ring, and free magma ring element",
+                    "filters": [
+                        [
+                            "IsEmbeddingMagmaMagmaRing"
+                        ],
+                        [
+                            "IsElementOfFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImagesRepresentative",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcgsToPcgsGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "PreImagesRepresentative: imprim perm wreath product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingImprimitiveWreathProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PreImagesRepresentative: hom. to standard generators of fp group, using 'MappedWord'",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsToFpGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: imprim matrix wreath product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingImprimitiveWreathProductMatrixGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: matrix direct product projection",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductMatrixGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: matrix direct product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductMatrixGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: perm subdirect product projection",
+                    "filters": [
+                        [
+                            "IsProjectionSubdirectProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: perm direct product projection",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: perm direct product embedding",
+                    "filters": [
+                        [
+                            "IsEmbeddingDirectProductPermGroup"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: blocks homomorphism",
+                    "filters": [
+                        [
+                            "IsBlocksHomomorphism"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PreImagesRepresentative: method for pcgs hom",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsToPcGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PreImagesRepresentative: for algebra g.m.b.i. knowing inverse, and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "Tester(InverseGeneralMapping)",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "PreImagesRepresentative: for homomorphisms of free groups",
+                    "filters": [
+                        [
+                            "IsToFpGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PreImagesRepresentative: for algebra g.m.b.i., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "PreImagesRepresentative",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsPointHomomorphism",
+                            "Tester(IsPointHomomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PreImagesRepresentative: for PBG-Niceo",
+                    "filters": [
+                        [
+                            "IsPreimagesByAsGroupGeneralMappingByImages",
+                            "IsNiceMonomorphism"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesRepresentative",
+                    "filters": [
+                        [
+                            "IsToPermGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesRepresentative: for ring g.m.b.i., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesRepresentative: for left module m.b.m., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesRepresentative: for left module g.m.b.i., and element",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PreImagesRepresentative: for GHBI and mult.-elm.-with-inverse",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PreImagesRepresentative: for PBG-Hom",
+                    "filters": [
+                        [
+                            "IsPreimagesByAsGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PreImagesRepresentative: equivalence relations",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PreImagesRepresentative: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "PreImagesRepresentative: for mapping by function with inverse",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionWithInverseRep"
+                        ],
+                        []
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PreImagesRepresentative: for mapping by function",
+                    "filters": [
+                        [
+                            "IsMappingByFunctionRep"
+                        ],
+                        []
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "PreImagesRepresentative: for a restricted mapping, and an element",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PreImagesRepresentative: for a composition mapping, and an element",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "PreImagesRepresentative: for an inverse mapping and an element",
+                    "filters": [
+                        [
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "PreImagesRepresentative: for total non-s.p. general mapping, and element",
+                    "filters": [
+                        [
+                            "IsNonSPGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "PreImagesRepresentative: for s.p. general mapping, and element",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImagesRepresentative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PreImagesSet: for zero mapping and collection",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10019
+                },
+                {
+                    "comment": "PreImagesSet: for identity mapping and collection",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10019
+                },
+                {
+                    "comment": "PreImagesSet: for PcpGHBI",
+                    "filters": [
+                        [
+                            "IsFromPcpGHBI",
+                            "IsToPcpGHBI"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 89
+                },
+                {
+                    "comment": "PreImagesSet",
+                    "filters": [
+                        [
+                            "IsBlocksHomomorphism"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "PreImagesSet: constituent homomorphism",
+                    "filters": [
+                        [
+                            "IsConstituentHomomorphism"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "PreImagesSet: for ANF automorphism and scalar",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "PreImagesSet: for field homomorphism and field",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "PreImagesSet: map from (sub)group of fp group",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsFromFpGroupGeneralMapping"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "PreImagesSet: for conjugator isomorphism, and group",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "PreImagesSet: method for algebra-with-one hom. and FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "PreImagesSet: method for algebra hom. and FLMLOR",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "PreImagesSet: method for injective s.p. mapping respecting mult. & inv., and group",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "PreImagesSet: method for permgroup homs",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPermGroupGeneralMapping"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "PreImagesSet: method for s.p. general mapping respecting mult. & inv., and group",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "PreImagesSet: method for linear mapping and left module",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "PreImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group",
+                    "filters": [
+                        [
+                            "IsSPGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "PreImagesSet: for general mapping, and empty list",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "PreImagesSet: for a restricted mapping, and an collection",
+                    "filters": [
+                        [
+                            "IsGeneralRestrictedMappingRep"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PreImagesSet: for a composition mapping, and an collection",
+                    "filters": [
+                        [
+                            "IsCompositionMappingRep"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PreImagesSet: for an inverse mapping and a collection",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PreImagesSet: for general mapping, and finite collection",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImagesSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CompositionMapping2: for zero mapping and single-valued gen. mapping that resp. zero",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 10028
+                },
+                {
+                    "comment": "CompositionMapping2: for identity mapping and general mapping",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10025
+                },
+                {
+                    "comment": "CompositionMapping2: for general mapping and identity mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10025
+                },
+                {
+                    "comment": "CompositionMapping2: for general mapping and zero mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 10024
+                },
+                {
+                    "comment": "CompositionMapping2: method for two pc group automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsPcGroupGeneralMappingByImages",
+                            "IsToPcGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "IsPcGroupGeneralMappingByImages",
+                            "IsToPcGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "CompositionMapping2: for two inner automorphisms",
+                    "filters": [
+                        [
+                            "IsInnerAutomorphism",
+                            "Tester(IsInnerAutomorphism)"
+                        ],
+                        [
+                            "IsInnerAutomorphism",
+                            "Tester(IsInnerAutomorphism)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "CompositionMapping2: for two ANF automorphisms",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ],
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "CompositionMapping2: for two Frobenius automorphisms",
+                    "filters": [
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ],
+                        [
+                            "IsFrobeniusAutomorphism"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "CompositionMapping2: for gp. hom. and fp. hom, transferring the coset table",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsFromFpGroupGeneralMappingByImages",
+                            "Tester(CosetTableFpHom)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "CompositionMapping2: for two conjugator automorphisms",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ],
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "CompositionMapping2: fp hom. with perm group hom.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsSurjective",
+                            "Tester(IsSurjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsToFpGroupGeneralMappingByImages"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "CompositionMapping2: for two conjugator isomorphisms",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ],
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "CompositionMapping2: for left module hom. and algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "CompositionMapping2: for left module hom. and linear m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "CompositionMapping2: for action homomorphism with blocks homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsBlocksHomomorphism"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "CompositionMapping2: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CompositionMapping2: for group automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CompositionMapping2: for left module hom. and algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CompositionMapping2: for left module hom. and linear g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "CompositionMapping2: group hom. with perm group hom.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "CompositionMapping2: method for hom2 from pc group",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsGroupGeneralMappingByPcgs"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "CompositionMapping2: for semigroup homomorphism by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsSPGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "IsSemigroupHomomorphismByImagesRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "CompositionMapping2: IsTransformationRepOfEndo, IsTransformationRepOfEndo",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "CompositionMapping2: for gp. hom. and gp. gen. mapp., using `MappingGeneratorsImages'",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "CompositionMapping2: IsTransformationRepOfEndo, IsEndoMapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "CompositionMapping2: IsEndoMapping, IsTransformationRepOfEndo",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "CompositionMapping2: for two general mappings",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CompositionMapping2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ZeroMapping: for collection and additive-magma-with-zero",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedMapping: try if restriction is proper",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 10046
+                },
+                {
+                    "comment": "RestrictedMapping: for mapping that is already restricted",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsGeneralRestrictedMappingRep"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 10015
+                },
+                {
+                    "comment": "RestrictedMapping: action homomorphism",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "RestrictedMapping: injective case: use GeneralRestrictedMapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "RestrictedMapping: create new GHBI",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "RestrictedMapping: use GeneralRestrictedMapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Embedding: generic method for perm semidirect products",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SemidirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "Embedding: perm wreath product",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "Embedding: perm direct product",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "Embedding: LAGUNA: from group to pc-presented normalized unit group of group ring",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNormalizedUnitGroupOfGroupRing",
+                            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "Embedding: pcp wreath product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "Embedding",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "Embedding: of semidirect pc group and integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+                            "Tester(SemidirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "Embedding: of pc group and integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "Embedding: matrix wreath product",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "Embedding: matrix direct product",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "Embedding: for ring and magma ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "Embedding: generic wreath product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)",
+                            "CategoryCollections(IsWreathProductElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Embedding: LAGUNA: from a group to the Lie algebra of the group ring",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "Embedding: free products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FreeProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "Embedding: vectorspace semidirect products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SemidirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "Embedding: of semidirect product and integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SemidirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "Embedding: group direct product and integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "Embedding: for magma and magma ring",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Embedding: for two families, the first with known Lie family",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "Tester(LieFamily)"
+                        ],
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Embedding",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Projection: generic method for perm semidirect products",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SemidirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Projection: perm wreath product",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Projection: of semidirect pc group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+                            "Tester(SemidirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Projection: matrix wreath product",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Projection: generic wreath product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(WreathProductInfo)",
+                            "CategoryCollections(IsWreathProductElement)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "Projection: of semidirect product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SemidirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Projection: perm subdirect product",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SubdirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "Projection: perm direct product",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "Projection",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "Projection: of pc group and integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "Projection: matrix direct product",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "Projection: pc subdirect product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SubdirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "Projection: group direct product and integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Projection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MappingGeneratorsImages: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MappingGeneratorsImages)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "MappingGeneratorsImages: for action hom that is `ByAsGroup'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages",
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "MappingGeneratorsImages: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "MappingGeneratorsImages: for group homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MappingGeneratorsImages:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MappingGeneratorsImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MappingGeneratorsImages): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MappingGeneratorsImages): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MappingGeneratorsImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MappingGeneratorsImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RespectsMultiplication: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RespectsMultiplication)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RespectsMultiplication: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RespectsMultiplication",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RespectsMultiplication): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RespectsMultiplication): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RespectsMultiplication)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RespectsMultiplication)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RespectsOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RespectsOne)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RespectsOne: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RespectsOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RespectsOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RespectsOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RespectsOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RespectsOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RespectsInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RespectsInverses: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RespectsInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RespectsInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RespectsInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RespectsInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RespectsInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KernelOfMultiplicativeGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: method for an injective gen. mapping that respects mult. and one",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for PcpGHBI",
+                    "filters": [
+                        [
+                            "IsFromPcpGHBI",
+                            "IsToPcpGHBI"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: from fp/free group, std. gens., to perm group",
+                    "filters": [
+                        [
+                            "IsToPermGroupGeneralMappingByImages",
+                            "IsFromFpGroupGeneralMapping"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: hom from fp grp",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsFromFpGroupGeneralMapping"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: method for homs from pc group into pc group or perm group",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcGroupGeneralMappingByImages",
+                            "IsToPcGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: matrix direct product projection",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductMatrixGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: perm subdirect product projection",
+                    "filters": [
+                        [
+                            "IsProjectionSubdirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: perm direct product projection",
+                    "filters": [
+                        [
+                            "IsProjectionDirectProductPermGroup"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: blocks homomorphism",
+                    "filters": [
+                        [
+                            "IsBlocksHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for constituent homomorphism",
+                    "filters": [
+                        [
+                            "IsConstituentHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: method for homs from pc group",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPcGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for action homomorphism",
+                    "filters": [
+                        [
+                            "IsActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for perm to perm group homs, compute stab chain, try again",
+                    "filters": [
+                        [
+                            "IsPermGroupGeneralMappingByImages",
+                            "IsToPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: hom by function",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsMappingByFunctionRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsPointHomomorphism",
+                            "Tester(IsPointHomomorphism)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for a restricted mapping that resp. mult. and inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsGeneralRestrictedMappingRep",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for a composition mapping that resp. mult. and inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsCompositionMappingRep",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: method for a finite general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "KernelOfMultiplicativeGeneralMapping: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KernelOfMultiplicativeGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KernelOfMultiplicativeGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KernelOfMultiplicativeGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KernelOfMultiplicativeGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KernelOfMultiplicativeGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoKernelOfMultiplicativeGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: get delayed set attribute values",
+                    "filters": [
+                        [
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: method for a single-valued gen. mapping that respects mult. and one",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: for PcpGHBI",
+                    "filters": [
+                        [
+                            "IsFromPcpGHBI"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: GHBI from fp grp",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping",
+                    "filters": [
+                        [
+                            "IsPermGroupGeneralMappingByImages",
+                            "IsToPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsPointHomomorphism",
+                            "Tester(IsPointHomomorphism)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping",
+                    "filters": [
+                        [
+                            "IsPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: for GMBPCGS: evaluate relations",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByPcgs"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: via `AsGroupGeneralMappingByImages'",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: for a restricted mapping that resp. mult. and inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsGeneralRestrictedMappingRep",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: for a composition mapping that resp. mult. and inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsCompositionMappingRep",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: method for a finite general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsOne",
+                            "Tester(RespectsOne)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "CoKernelOfMultiplicativeGeneralMapping: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoKernelOfMultiplicativeGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoKernelOfMultiplicativeGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoKernelOfMultiplicativeGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoKernelOfMultiplicativeGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoKernelOfMultiplicativeGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RespectsAddition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RespectsAddition)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RespectsAddition: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RespectsAddition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RespectsAddition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RespectsAddition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RespectsAddition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RespectsAddition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RespectsZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RespectsZero: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RespectsZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RespectsZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RespectsZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RespectsZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RespectsZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RespectsAdditiveInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RespectsAdditiveInverses: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RespectsAdditiveInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RespectsAdditiveInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RespectsAdditiveInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RespectsAdditiveInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RespectsAdditiveInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KernelOfAdditiveGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: method for zero mapping",
+                    "filters": [
+                        [
+                            "IsZero",
+                            "Tester(IsZero)",
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 10021
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: method for an injective gen. mapping that respects add. and zero",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for operation algebra hom. with fin. dim. source",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsOperationAlgebraHomomorphismDefaultRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for a field homomorphism",
+                    "filters": [
+                        [
+                            "IsFieldHomomorphism",
+                            "Tester(IsFieldHomomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for left module m.b.m.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for left module g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for a restricted mapping that resp. add. and add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsGeneralRestrictedMappingRep",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for a composition mapping that resp. add. and add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsCompositionMappingRep",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: method for a finite linear mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: method for a finite general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "KernelOfAdditiveGeneralMapping: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KernelOfAdditiveGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KernelOfAdditiveGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KernelOfAdditiveGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KernelOfAdditiveGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KernelOfAdditiveGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoKernelOfAdditiveGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: method for a single-valued gen. mapping that respects add. and zero",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 10013
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: for algebra g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: for ring g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsRingGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: for left module g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: for a restricted mapping that resp. add. and add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsGeneralRestrictedMappingRep",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: for a composition mapping that resp. add. and add.inv.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsCompositionMappingRep",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: method for a finite linear mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: method for a finite general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsZero",
+                            "Tester(RespectsZero)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "CoKernelOfAdditiveGeneralMapping: for an inverse mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsInverseGeneralMappingRep"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoKernelOfAdditiveGeneralMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoKernelOfAdditiveGeneralMapping): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoKernelOfAdditiveGeneralMapping): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoKernelOfAdditiveGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoKernelOfAdditiveGeneralMapping)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RespectsScalarMultiplication: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RespectsScalarMultiplication: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RespectsScalarMultiplication",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RespectsScalarMultiplication): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RespectsScalarMultiplication): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RespectsScalarMultiplication)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RespectsScalarMultiplication)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLinearMapping",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFieldHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFieldHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsFieldHomomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsFieldHomomorphism: method for a general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFieldHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFieldHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFieldHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFieldHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFieldHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransformsMultiplicationIntoAddition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransformsMultiplicationIntoAddition)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformsMultiplicationIntoAddition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransformsMultiplicationIntoAddition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransformsMultiplicationIntoAddition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransformsMultiplicationIntoAddition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransformsMultiplicationIntoAddition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TranformsOneIntoZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TranformsOneIntoZero)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TranformsOneIntoZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TranformsOneIntoZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TranformsOneIntoZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TranformsOneIntoZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TranformsOneIntoZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransformsInversesIntoAdditiveInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransformsInversesIntoAdditiveInverses)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformsInversesIntoAdditiveInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransformsInversesIntoAdditiveInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransformsInversesIntoAdditiveInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransformsInversesIntoAdditiveInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransformsInversesIntoAdditiveInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransformsAdditionIntoMultiplication: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransformsAdditionIntoMultiplication)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformsAdditionIntoMultiplication",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransformsAdditionIntoMultiplication): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransformsAdditionIntoMultiplication): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransformsAdditionIntoMultiplication)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransformsAdditionIntoMultiplication)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransformsZeroIntoOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransformsZeroIntoOne)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformsZeroIntoOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransformsZeroIntoOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransformsZeroIntoOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransformsZeroIntoOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransformsZeroIntoOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransformsAdditiveInversesIntoInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransformsAdditiveInversesIntoInverses)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformsAdditiveInversesIntoInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransformsAdditiveInversesIntoInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransformsAdditiveInversesIntoInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransformsAdditiveInversesIntoInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransformsAdditiveInversesIntoInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Successors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Successors)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "Successors: for a Green's equivalence",
+                    "filters": [
+                        [
+                            "IsGreensRelation"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Successors: for a generic relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Successors: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Successors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Successors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Successors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Successors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Successors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOfBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOfBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "DegreeOfBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOfBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOfBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOfBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOfBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOfBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsReflexiveBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsReflexiveBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsReflexiveBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsReflexiveBinaryRelation: reflexive test binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsReflexiveBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsReflexiveBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsReflexiveBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsReflexiveBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsReflexiveBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsReflexiveBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSymmetricBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSymmetricBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsSymmetricBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsSymmetricBinaryRelation: symmetric test binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsSymmetricBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSymmetricBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSymmetricBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSymmetricBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSymmetricBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSymmetricBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTransitiveBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTransitiveBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsTransitiveBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsTransitiveBinaryRelation: transitive test binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsTransitiveBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTransitiveBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTransitiveBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTransitiveBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTransitiveBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTransitiveBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAntisymmetricBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAntisymmetricBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsAntisymmetricBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsAntisymmetricBinaryRelation: test for Antisymmetry of a binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsAntisymmetricBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAntisymmetricBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAntisymmetricBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAntisymmetricBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAntisymmetricBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAntisymmetricBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPreOrderBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPreOrderBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsPreOrderBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsPreOrderBinaryRelation: test for whether a binary relation is a preorder",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsPreOrderBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPreOrderBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPreOrderBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPreOrderBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPreOrderBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPreOrderBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPartialOrderBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPartialOrderBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsPartialOrderBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsPartialOrderBinaryRelation: test for whether a binary relation is a partial order",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsPartialOrderBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPartialOrderBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPartialOrderBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPartialOrderBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPartialOrderBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPartialOrderBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLatticeOrderBinaryRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLatticeOrderBinaryRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsLatticeOrderBinaryRelation: test for whether a binary relation is a lattice order",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsLatticeOrderBinaryRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLatticeOrderBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLatticeOrderBinaryRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLatticeOrderBinaryRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLatticeOrderBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLatticeOrderBinaryRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsEquivalenceRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsEquivalenceRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsEquivalenceRelation: test for equivalence relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsEquivalenceRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsEquivalenceRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsEquivalenceRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsEquivalenceRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsEquivalenceRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsEquivalenceRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReflexiveClosureBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ReflexiveClosureBinaryRelation: for binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReflexiveClosureBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SymmetricClosureBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "SymmetricClosureBinaryRelation: for binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymmetricClosureBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransitiveClosureBinaryRelation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "TransitiveClosureBinaryRelation: for binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransitiveClosureBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HasseDiagramBinaryRelation: for binary relation",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasseDiagramBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsHasseDiagram: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsHasseDiagram)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "IsHasseDiagram: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsHasseDiagram",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsHasseDiagram): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsHasseDiagram): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsHasseDiagram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsHasseDiagram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PartialOrderOfHasseDiagram: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PartialOrderOfHasseDiagram)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "PartialOrderOfHasseDiagram: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PartialOrderOfHasseDiagram",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PartialOrderOfHasseDiagram): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PartialOrderOfHasseDiagram): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PartialOrderOfHasseDiagram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PartialOrderOfHasseDiagram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StronglyConnectedComponents: for general binary relations",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StronglyConnectedComponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EquivalenceRelationPartition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EquivalenceRelationPartition)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "EquivalenceRelationPartition: for a congruence on a magma",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "EquivalenceRelationPartition: for a Green's equivalence",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "IsGreensRelation"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceRelationPartition: for a right congruence on a magma",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceRelationPartition: for a left congruence on a magma",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceRelationPartition: compute the partition for an arbitrary equiv rel",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "EquivalenceRelationPartition: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EquivalenceRelationPartition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EquivalenceRelationPartition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EquivalenceRelationPartition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EquivalenceRelationPartition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EquivalenceRelationPartition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfEquivalenceRelationPartition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfEquivalenceRelationPartition)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "GeneratorsOfEquivalenceRelationPartition: generators for an equivalence with a partition",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "GeneratorsOfEquivalenceRelationPartition: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfEquivalenceRelationPartition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfEquivalenceRelationPartition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfEquivalenceRelationPartition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfEquivalenceRelationPartition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfEquivalenceRelationPartition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ],
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "JoinEquivalenceRelations: join of two equivalence relations",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "JoinEquivalenceRelations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ],
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MeetEquivalenceRelations: meet of two equivalence relations",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MeetEquivalenceRelations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EquivalenceClassRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EquivalenceClassRelation)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EquivalenceClassRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EquivalenceClassRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EquivalenceClassRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EquivalenceClassRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EquivalenceClassRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EquivalenceClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EquivalenceClasses)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "EquivalenceClasses: for magma congruences",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "EquivalenceClasses: for a Green's J-relation",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "IsGreensJRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "EquivalenceClasses: for a Green's D-relation",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "IsGreensDRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "EquivalenceClasses: for a Green's H-relation",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "IsGreensHRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "EquivalenceClasses: for a Green's L-relation",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "IsGreensLRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "EquivalenceClasses: for a Green's R-relation",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "IsGreensRRelation"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "EquivalenceClasses: wraparound to call 2-argument version",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "EquivalenceClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "EquivalenceClasses: for a generic equivalence relation",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EquivalenceClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EquivalenceClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EquivalenceClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EquivalenceClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EquivalenceClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EquivalenceClassOfElement: for magma congruence with checking",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "EquivalenceClassOfElement: for right magma congruence with checking",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceClassOfElement: for left magma congruence with checking",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceClassOfElement: with checking",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EquivalenceClassOfElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEquivalenceRelation",
+                    "Tester(IsEquivalenceRelation)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EquivalenceClassOfElementNC: for magma congruence with no check",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "EquivalenceClassOfElementNC: for a Green's relation and object",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)",
+                            "IsGreensRelation"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceClassOfElementNC: for magma congruence with no check",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceClassOfElementNC: for magma congruence with no check",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EquivalenceClassOfElementNC: no check",
+                    "filters": [
+                        [
+                            "IsEquivalenceRelation",
+                            "Tester(IsEquivalenceRelation)"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EquivalenceClassOfElementNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MagmaByGenerators: for collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MagmaByGenerators: for family and list",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MagmaWithOneByGenerators: for collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MagmaWithOneByGenerators: for family and list",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaWithOneByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MagmaWithInversesByGenerators: for collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MagmaWithInversesByGenerators: for family and list",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaWithInversesByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsMagma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsMagma)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "AsMagma: for a magma (return the argument)",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 111
+                },
+                {
+                    "comment": "AsMagma: generic method for collections",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsMagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsMagma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsMagma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsSubmagma: generic method for a domain and a collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubmagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfMagma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfMagma)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "GeneratorsOfMagma",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "GeneratorsOfMagma",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "GeneratorsOfMagma",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "GeneratorsOfMagma: for a magma-with-inv. with gens., all elms. of finite order",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFiniteOrderElement)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "GeneratorsOfMagma: for a magma-with-one with generators, all elms. of finite order",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFiniteOrderElement)",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "GeneratorsOfMagma: for a magma-with-inverses with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "GeneratorsOfMagma: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "GeneratorsOfMagma: for a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroup",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "GeneratorsOfMagma: for a magma-with-one with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "GeneratorsOfMagma: generic method for a magma (take domain generators)",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfMagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfMagma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfMagma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfMagmaWithOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithOne",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(GeneratorsOfInverseMonoid)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithOne: for a magma-with-inv. with gens., all elms. of finite order",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFiniteOrderElement)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithOne: for a magma-with-inverses with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithOne: for a magma-with-one with known magma generators (take them)",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagma)"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfMagmaWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfMagmaWithOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfMagmaWithOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfMagmaWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfMagmaWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 20019
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 367
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses: for a subgroup of a free group having a FreeGroupAutomaton",
+                    "filters": [
+                        [
+                            "Tester(FreeGroupAutomaton)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses",
+                    "filters": [
+                        [
+                            "Tester(FreeGeneratorsOfGroup)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses: for whole family f.p. group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses: subgroup fp, via augmented coset table",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses: Schreier generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(ElementTestFunction)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses: for a magma-with-inverses with known magma-with-one gen.s (take them)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "GeneratorsOfMagmaWithInverses: for a magma-with-inverses with known magma generators (take them)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagma)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfMagmaWithInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfMagmaWithInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfMagmaWithInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGeneratorsOfMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a collection of cyclotomics (return false)",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a collection of FFEs",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a collection of free magma ring elements",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsElementOfMagmaRingModuloRelations)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for list of direct product elements",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsDirectProductElement)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a collection of general mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: cosets",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a collection of magma by mult table elements",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for an empty list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IsGeneratorsOfMagmaWithInverses: for a list or collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGeneratorsOfMagmaWithInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGeneratorsOfMagmaWithInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGeneratorsOfMagmaWithInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGeneratorsOfMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGeneratorsOfMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TrivialSubmagmaWithOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TrivialSubmagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "TrivialSubmagmaWithOne: for magma-with-one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TrivialSubmagmaWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TrivialSubmagmaWithOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TrivialSubmagmaWithOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TrivialSubmagmaWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TrivialSubmagmaWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAssociative: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "IsAssociative: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsAssociative: generic method for a (finite dimensional) FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsAssociative: for a magma of nonassoc. words",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsNonassocWord)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsAssociative: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAssociative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAssociative): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAssociative): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAssociative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAssociative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCommutative: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCommutative)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "IsCommutative: finite fp grp",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(Size)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsCommutative: for an associative FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "IsCommutative: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsCommutative: for an associative FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsCommutative: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsCommutative: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsCommutative: generic method for a finite dimensional FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsCommutative: for an associative ring-with-one",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsCommutative: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsCommutative",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsCommutative: for an associative magma with inverses",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "IsCommutative",
+                    "filters": [
+                        [
+                            "Tester(Characteristic)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsAnticommutative",
+                            "Tester(IsAnticommutative)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsCommutative: for an associative ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "IsCommutative: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsCommutative: for associative magma-with-one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsCommutative",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsCommutative: for an associative magma with one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsCommutative",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsCommutative: for an associative magma",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsCommutative: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCommutative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCommutative): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCommutative): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCommutative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCommutative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MultiplicativeNeutralElement: for a magma-with-one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(MultiplicativeNeutralElement)"
+                        ]
+                    ],
+                    "rank": 20015
+                },
+                {
+                    "comment": "MultiplicativeNeutralElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MultiplicativeNeutralElement)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "MultiplicativeNeutralElement",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsFiniteDimensional",
+                            "Tester(IsFiniteDimensional)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "MultiplicativeNeutralElement: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MultiplicativeNeutralElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MultiplicativeNeutralElement): for a magma-with-one",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Setter(MultiplicativeNeutralElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MultiplicativeNeutralElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MultiplicativeNeutralElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MultiplicativeNeutralElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Centre: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Centre)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "Centre: for an associative and commutative magma",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ]
+                    ],
+                    "rank": 10015
+                },
+                {
+                    "comment": "Centre: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Centre: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "Centre: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Centre: for a group ring",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "Centre: for a finite dimensional FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Centre: for an associative magma",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "Centre: generic method for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Centre",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Centre): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Centre): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Centre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Centre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Idempotents: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Idempotents)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "Idempotents: for finite magmas",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Idempotents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Idempotents): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Idempotents): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Idempotents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Idempotents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsCentral: for two associative FLMLORs-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "IsCentral: for two associative FLMLORs",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "IsCentral: for two FLMLORs",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "IsCentral: for two associative rings-with-one",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "IsCentral: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "IsCentral: for two associative rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "IsCentral: for two magmas-with-inverses",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ],
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsCentral: for two magmas-with-one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne"
+                        ],
+                        [
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "IsCentral: for two magmas",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCentral",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentralizerOp",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "CentralizerOp",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CentralizerOp: for two magmas, the first being commutative",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ],
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 10024
+                },
+                {
+                    "comment": "CentralizerOp: for a commutative magma, and a mult. element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 10016
+                },
+                {
+                    "comment": "CentralizerOp: TF method:subgroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingFreeLiftSetup)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 858
+                },
+                {
+                    "comment": "CentralizerOp: handled by nice monomorphism: Subgroup CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "CentralizerOp: TF method:elm",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingFreeLiftSetup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 434
+                },
+                {
+                    "comment": "CentralizerOp: handled by nice monomorphism: subgroup CollElm",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        []
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and FLMLOR",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 121
+                },
+                {
+                    "comment": "CentralizerOp: perm group, perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "CentralizerOp: two AffineCrystGroupsOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "CentralizerOp: two AffineCrystGroupsOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "CentralizerOp: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 102
+                },
+                {
+                    "comment": "CentralizerOp",
+                    "filters": [
+                        [
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)",
+                            "IsIntegerMatrixGroup",
+                            "Tester(IsIntegerMatrixGroup)"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and left module",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 99
+                },
+                {
+                    "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR-with-one, and FLMLOR",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 98
+                },
+                {
+                    "comment": "CentralizerOp: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "CentralizerOp: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR, and FLMLOR",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "CentralizerOp: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR-with-one, and ordinary matrix",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and empty list",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "CentralizerOp: AffineCrystGroupOnLeft and element",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "CentralizerOp: AffineCrystGroupOnRight and element",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR, and ordinary matrix",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "CentralizerOp: for a fin. dim. assoc. algebra and an algebra with parent",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "Tester(ParentAttr)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "CentralizerOp: for a fin. dim. assoc. algebra and an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "CentralizerOp: element in natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "CentralizerOp: element in natural alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "CentralizerOp: perm group,elm",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "CentralizerOp: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "CentralizerOp: for a finite dimensional algebra and a vector space with parent",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "Tester(ParentAttr)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "CentralizerOp: for a finite dimensional algebra and a vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "CentralizerOp: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "CentralizerOp: for an element in a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "CentralizerOp: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "CentralizerOp: pcgs computable group and element",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "CentralizerOp: for an algebra and an element",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        []
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "CentralizerOp: generic method for group and object",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "CentralizerOp: for two magmas",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "CentralizerOp: for a magma, and a mult. element",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "CentralizerOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CentralizerOp: dummy to ignore optional third argument",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 11
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralizerOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentralizerInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CentralizerInParent)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "CentralizerInParent: method that calls the two-argument operation CentralizerOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralizerInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CentralizerInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CentralizerInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CentralizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CentralizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Centralizer",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Centralizer: try to exploit the in-parent attribute CentralizerInParent",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        []
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Centralizer: with given subgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 124
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Centralizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SquareRoots: for prime field and object in Z/pZ",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "SquareRoots: for a field of FFEs, and a FFE",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SquareRoots",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MagmaGeneratorsOfFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MagmaGeneratorsOfFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MagmaGeneratorsOfFamily: for a family of assoc. words",
+                    "filters": [
+                        [
+                            "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "MagmaGeneratorsOfFamily: for a family of free monoid elements",
+                    "filters": [
+                        [
+                            "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "MagmaGeneratorsOfFamily: for a family of free semigroup elements",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "MagmaGeneratorsOfFamily: for a family of free magma elements",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsNonassocWord)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaGeneratorsOfFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MagmaGeneratorsOfFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MagmaGeneratorsOfFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MagmaGeneratorsOfFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MagmaGeneratorsOfFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsLeftMagmaIdeal: generic method for a domain and a collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsLeftMagmaIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftMagmaIdealByGenerators: for a collection of magma elements",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftMagmaIdealByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsRightMagmaIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightMagmaIdealByGenerators: for a collection of magma elements",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightMagmaIdealByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsMagmaIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfMagmaIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfMagmaIdeal)"
+                        ]
+                    ],
+                    "rank": 20018
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfMagmaIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfMagmaIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfMagmaIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfMagmaIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfMagmaIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MagmaIdealByGenerators: for a collection of magma elements",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaIdealByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NaturalHomomorphismByGenerators: for a free monoid and monoid",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "NaturalHomomorphismByGenerators: for an fp monoid and monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ],
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "NaturalHomomorphismByGenerators: for a free semigroup and semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "NaturalHomomorphismByGenerators: for an fp semigroup and semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithZero"
+                ]
+            ],
+            [
+                [
+                    "IsReesMatrixSemigroup",
+                    "Tester(IsReesMatrixSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MultiplicativeZeroOp: for a Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroup",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "MultiplicativeZeroOp: for an element of a magma with zero adjoined",
+                    "filters": [
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MultiplicativeZeroOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithZero"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MultiplicativeZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MultiplicativeZero)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "MultiplicativeZero: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MultiplicativeZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithZero"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MultiplicativeZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MultiplicativeZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MultiplicativeZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithZero"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MultiplicativeZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsMultiplicativeZero: for a semigroup with generators and multiplicative element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsMultiplicativeZero: for magma with multiplicative zero and multiplicative element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(MultiplicativeZero)"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsMultiplicativeZero: for a magma and multiplicative element",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMultiplicativeZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InjectionZeroMagma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InjectionZeroMagma)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "InjectionZeroMagma: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InjectionZeroMagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InjectionZeroMagma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InjectionZeroMagma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InjectionZeroMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InjectionZeroMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithZero",
+                    "IsMagmaWithZeroAdjoinedElementRep"
+                ]
+            ],
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MagmaWithZeroAdjoined: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MagmaWithZeroAdjoined)"
+                        ]
+                    ],
+                    "rank": 20008
+                },
+                {
+                    "comment": "MagmaWithZeroAdjoined: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "MagmaWithZeroAdjoined: for a magma with 0 adjoined element",
+                    "filters": [
+                        [
+                            "IsMagmaWithZeroAdjoinedElementRep"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaWithZeroAdjoined",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithZero",
+                    "IsMagmaWithZeroAdjoinedElementRep"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MagmaWithZeroAdjoined): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MagmaWithZeroAdjoined): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MagmaWithZeroAdjoined)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithZero",
+                    "IsMagmaWithZeroAdjoinedElementRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MagmaWithZeroAdjoined)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithZeroAdjoined"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingInjectionZeroMagma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingInjectionZeroMagma)"
+                        ]
+                    ],
+                    "rank": 20015
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingInjectionZeroMagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithZeroAdjoined"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingInjectionZeroMagma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingInjectionZeroMagma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingInjectionZeroMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithZeroAdjoined"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingInjectionZeroMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratingPairsOfLeftMagmaCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratingPairsOfLeftMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratingPairsOfLeftMagmaCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratingPairsOfLeftMagmaCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratingPairsOfLeftMagmaCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratingPairsOfLeftMagmaCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratingPairsOfLeftMagmaCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ]
+            ],
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PartialClosureOfCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PartialClosureOfCongruence)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PartialClosureOfCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagmaCongruence"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PartialClosureOfCongruence): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PartialClosureOfCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PartialClosureOfCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PartialClosureOfCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftMagmaCongruenceByGeneratingPairs: for a magma and an empty list",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "LeftMagmaCongruenceByGeneratingPairs: for a magma and a list of pairs of its elements",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftMagmaCongruenceByGeneratingPairs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratingPairsOfRightMagmaCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratingPairsOfRightMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratingPairsOfRightMagmaCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratingPairsOfRightMagmaCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratingPairsOfRightMagmaCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratingPairsOfRightMagmaCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratingPairsOfRightMagmaCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightMagmaCongruenceByGeneratingPairs: for a magma and an empty list",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "RightMagmaCongruenceByGeneratingPairs: for a magma and a list of pairs of its elements",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightMagmaCongruenceByGeneratingPairs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MagmaCongruenceByGeneratingPairs: for a magma and an empty list",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "MagmaCongruenceByGeneratingPairs: for a magma and a list of pairs of its elements",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaCongruenceByGeneratingPairs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratingPairsOfMagmaCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratingPairsOfMagmaCongruence)"
+                        ]
+                    ],
+                    "rank": 20029
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratingPairsOfMagmaCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratingPairsOfMagmaCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratingPairsOfMagmaCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratingPairsOfMagmaCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratingPairsOfMagmaCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ],
+                [
+                    "IsMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "JoinMagmaCongruences: for magma congruences",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ],
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "JoinMagmaCongruences",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ],
+                [
+                    "IsMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MeetMagmaCongruences: for magma congruences",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ],
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MeetMagmaCongruences",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SemigroupCongruenceByGeneratingPairs: for a semigroup and an empty list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "SemigroupCongruenceByGeneratingPairs: for a semigroup and a list of pairs of its elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemigroupCongruenceByGeneratingPairs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightSemigroupCongruenceByGeneratingPairs: for a Semigroup and an empty list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "RightSemigroupCongruenceByGeneratingPairs: for a Semigroup and a list of pairs of its elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightSemigroupCongruenceByGeneratingPairs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftSemigroupCongruenceByGeneratingPairs: for a Semigroup and an empty list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "LeftSemigroupCongruenceByGeneratingPairs: for a Semigroup  and a list of pairs of its elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftSemigroupCongruenceByGeneratingPairs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLeftSemigroupCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLeftSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "IsLeftSemigroupCongruence: test whether a left magma congruence is a semigroup a congruence",
+                    "filters": [
+                        [
+                            "IsLeftMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftSemigroupCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLeftSemigroupCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLeftSemigroupCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLeftSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLeftSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRightSemigroupCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRightSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "IsRightSemigroupCongruence: test whether a right magma congruence is a semigroup a congruence",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRightSemigroupCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRightSemigroupCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRightSemigroupCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRightSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRightSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSemigroupCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsSemigroupCongruence: test whether a magma congruence is a semigroup a congruence",
+                    "filters": [
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSemigroupCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSemigroupCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSemigroupCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSemigroupCongruence",
+                    "Tester(IsSemigroupCongruence)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsReesCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsReesCongruence)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsReesCongruence: for a semigroup congruence",
+                    "filters": [
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "IsReesCongruence: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsReesCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSemigroupCongruence",
+                    "Tester(IsSemigroupCongruence)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsReesCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsReesCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsReesCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSemigroupCongruence",
+                    "Tester(IsSemigroupCongruence)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsReesCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InversesOfSemigroupElement: for a semigroup and an element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsAssociativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InversesOfSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemigroupByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemigroupByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSemigroup)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "AsSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 113
+                },
+                {
+                    "comment": "AsSemigroup: generic method for collections",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsSubsemigroup: generic method for a domain and a collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubsemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGeneratorsOfSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGeneratorsOfSemigroup)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsGeneratorsOfSemigroup: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGeneratorsOfSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGeneratorsOfSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGeneratorsOfSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGeneratorsOfSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGeneratorsOfSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CayleyGraphSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CayleyGraphSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "CayleyGraphSemigroup: for generic finite semigroups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "CayleyGraphSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CayleyGraphSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CayleyGraphSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CayleyGraphSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CayleyGraphSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CayleyGraphSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CayleyGraphDualSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CayleyGraphDualSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "CayleyGraphDualSemigroup: for generic finite semigroups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "CayleyGraphDualSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CayleyGraphDualSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CayleyGraphDualSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CayleyGraphDualSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CayleyGraphDualSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CayleyGraphDualSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZeroGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZeroGroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsZeroGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZeroGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZeroGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZeroGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZeroGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZeroGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSimpleSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSimpleSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsSimpleSemigroup: for a subsemigroup of a Rees matrix semigroup with an underlying semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)",
+                            "Tester(UnderlyingSemigroup)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsSimpleSemigroup: for a semigroup with a MultiplicativeNeutralElement",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MultiplicativeNeutralElement)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsSimpleSemigroup: for semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsSimpleSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsSimpleSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSimpleSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSimpleSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSimpleSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSimpleSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSimpleSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZeroSimpleSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZeroSimpleSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsZeroSimpleSemigroup: for a ZeroGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsZeroSimpleSemigroup: for a trivial semigroup",
+                    "filters": [
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "IsZeroSimpleSemigroup: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsZeroSimpleSemigroup: for a semigroup with a MultiplicativeNeutralElement",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MultiplicativeNeutralElement)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsZeroSimpleSemigroup: for a semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsZeroSimpleSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsZeroSimpleSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZeroSimpleSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZeroSimpleSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZeroSimpleSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZeroSimpleSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZeroSimpleSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ANonReesCongruenceOfSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ANonReesCongruenceOfSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "ANonReesCongruenceOfSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ANonReesCongruenceOfSemigroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "ANonReesCongruenceOfSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ANonReesCongruenceOfSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ANonReesCongruenceOfSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ANonReesCongruenceOfSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ANonReesCongruenceOfSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ANonReesCongruenceOfSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsReesCongruenceSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsReesCongruenceSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsReesCongruenceSemigroup: for a (possibly infinite) semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsReesCongruenceSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsReesCongruenceSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsReesCongruenceSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsReesCongruenceSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsReesCongruenceSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsReesCongruenceSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsSemigroupCongruence",
+                    "Tester(IsSemigroupCongruence)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HomomorphismFactorSemigroup: for an fp monoid and a congruence",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ],
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "HomomorphismFactorSemigroup: for a free monoid and a congruence",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "HomomorphismFactorSemigroup: for a free semigroup and a congruence",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "HomomorphismFactorSemigroup: for an fp semigroup and a congruence",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "HomomorphismFactorSemigroup: for a semigroup and a congruence",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HomomorphismFactorSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HomomorphismFactorSemigroupByClosure: for a semigroup and empty list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "HomomorphismFactorSemigroupByClosure: for a semigroup and generating pairs of a congruence",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HomomorphismFactorSemigroupByClosure",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsSemigroupCongruence",
+                    "Tester(IsSemigroupCongruence)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FactorSemigroup: for a semigroup and a congruence",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSemigroupCongruence",
+                            "Tester(IsSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FactorSemigroupByClosure: for a semigroup and empty list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "FactorSemigroupByClosure: for a semigroup and generating pairs of a congruence",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorSemigroupByClosure",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsRegularSemigroupElement: for an inverse semigroup",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ],
+                        [
+                            "IsAssociativeElement"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsRegularSemigroupElement: for generic semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsAssociativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRegularSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRegularSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRegularSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsRegularSemigroup: for a Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroup",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsRegularSemigroup: for generic semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsRegularSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRegularSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRegularSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRegularSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRegularSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRegularSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsInverseSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsInverseSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsInverseSemigroup: for an object",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "IsInverseSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInverseSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsInverseSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsInverseSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DisplaySemigroup: for finite semigroups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DisplaySemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NilpotencyDegree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NilpotencyDegree)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "NilpotencyDegree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NilpotencyDegree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NilpotencyDegree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NilpotencyDegree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NilpotencyDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NilpotencyDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsSubsemigroup: for an inverse semigroup and inverse semigroup with generators",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ],
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "IsSubsemigroup: for semigroup and semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "IsSubsemigroup: for a semigroup and semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubsemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBand: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBand)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsBand: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBand",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBand): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBand): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBand)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBand)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBrandtSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBrandtSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsBrandtSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBrandtSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBrandtSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBrandtSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBrandtSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBrandtSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCliffordSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCliffordSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsCliffordSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCliffordSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCliffordSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCliffordSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCliffordSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCliffordSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCommutativeSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCommutativeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsCommutativeSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCommutativeSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCommutativeSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCommutativeSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCommutativeSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCommutativeSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCompletelyRegularSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCompletelyRegularSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsCompletelyRegularSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCompletelyRegularSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCompletelyRegularSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCompletelyRegularSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCompletelyRegularSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCompletelyRegularSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCompletelySimpleSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCompletelySimpleSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsCompletelySimpleSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCompletelySimpleSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCompletelySimpleSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCompletelySimpleSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCompletelySimpleSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCompletelySimpleSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupAsSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupAsSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsGroupAsSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupAsSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupAsSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupAsSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupAsSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupAsSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIdempotentGenerated: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIdempotentGenerated)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsIdempotentGenerated: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIdempotentGenerated",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIdempotentGenerated): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIdempotentGenerated): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIdempotentGenerated)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIdempotentGenerated)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLeftZeroSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLeftZeroSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsLeftZeroSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftZeroSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLeftZeroSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLeftZeroSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLeftZeroSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLeftZeroSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonogenicSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMonogenicSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsMonogenicSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonogenicSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMonogenicSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMonogenicSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMonogenicSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMonogenicSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonoidAsSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMonoidAsSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsMonoidAsSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonoidAsSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMonoidAsSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMonoidAsSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMonoidAsSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMonoidAsSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpotentSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNilpotentSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsNilpotentSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotentSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNilpotentSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNilpotentSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNilpotentSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNilpotentSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsOrthodoxSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsOrthodoxSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsOrthodoxSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsOrthodoxSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsOrthodoxSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsOrthodoxSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsOrthodoxSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsOrthodoxSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRectangularBand: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRectangularBand)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsRectangularBand: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRectangularBand",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRectangularBand): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRectangularBand): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRectangularBand)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRectangularBand)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRightZeroSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRightZeroSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsRightZeroSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRightZeroSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRightZeroSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRightZeroSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRightZeroSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRightZeroSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSemiband: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSemiband)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsSemiband: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSemiband",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSemiband): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSemiband): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSemiband)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSemiband)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSemilattice: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSemilattice)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsSemilattice: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSemilattice",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSemilattice): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSemilattice): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSemilattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSemilattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZeroSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZeroSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsZeroSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZeroSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZeroSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZeroSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZeroSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZeroSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemigroupViewStringPrefix: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "SemigroupViewStringPrefix: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "SemigroupViewStringPrefix: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemigroupViewStringPrefix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemigroupViewStringSuffix: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "SemigroupViewStringSuffix: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "SemigroupViewStringSuffix: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemigroupViewStringSuffix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLeftSemigroupIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLeftSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsLeftSemigroupIdeal",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsLeftActedOnBySuperset",
+                            "Tester(LeftActingDomain)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftSemigroupIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsMagma"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLeftSemigroupIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLeftSemigroupIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLeftSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLeftSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRightSemigroupIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRightSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsRightSemigroupIdeal",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsRightActedOnBySuperset",
+                            "Tester(RightActingDomain)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRightSemigroupIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRightSemigroupIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRightSemigroupIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRightSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRightSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSemigroupIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "IsSemigroupIdeal",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "Tester(ActingDomain)"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSemigroupIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSemigroupIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSemigroupIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReesCongruenceOfSemigroupIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ReesCongruenceOfSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "ReesCongruenceOfSemigroupIdeal: for a two sided semigroup congruence",
+                    "filters": [
+                        [
+                            "IsLeftActedOnBySuperset",
+                            "IsRightActedOnBySuperset",
+                            "IsMagma",
+                            "IsSemigroupIdeal",
+                            "Tester(IsSemigroupIdeal)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReesCongruenceOfSemigroupIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ReesCongruenceOfSemigroupIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ReesCongruenceOfSemigroupIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ReesCongruenceOfSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLeftActedOnBySuperset",
+                    "IsRightActedOnBySuperset",
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ReesCongruenceOfSemigroupIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MonoidByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MonoidByGenerators: for empty collection and identity",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "MonoidByGenerators: for collection and identity",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MonoidByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsMonoid)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "AsMonoid: for a monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 118
+                },
+                {
+                    "comment": "AsMonoid: for transformation semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "AsMonoid: for a semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AsMonoid: generic method for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsSubmonoid: generic method for a domain and a collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubmonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GroupString: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NameIsomorphismClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NameIsomorphismClass)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NameIsomorphismClass: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NameIsomorphismClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NameIsomorphismClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NameIsomorphismClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NameIsomorphismClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NameIsomorphismClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCyclic: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCyclic)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsCyclic: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "IsCyclic: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "IsCyclic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsCyclic: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsCyclic: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsCyclic: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCyclic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCyclic): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCyclic): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCyclic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCyclic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsElementaryAbelian: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsElementaryAbelian)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsElementaryAbelian: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsElementaryAbelian: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsElementaryAbelian: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsElementaryAbelian: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsElementaryAbelian",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsElementaryAbelian): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsElementaryAbelian): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsElementaryAbelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsElementaryAbelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFinitelyGeneratedGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFinitelyGeneratedGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsFinitelyGeneratedGroup: subgroups of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsFinitelyGeneratedGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsFinitelyGeneratedGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFinitelyGeneratedGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFinitelyGeneratedGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFinitelyGeneratedGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFinitelyGeneratedGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFinitelyGeneratedGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSubsetLocallyFiniteGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSubsetLocallyFiniteGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSubsetLocallyFiniteGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubsetLocallyFiniteGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSubsetLocallyFiniteGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSubsetLocallyFiniteGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSubsetLocallyFiniteGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSubsetLocallyFiniteGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CanComputeIndex",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "CanComputeIndex",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "CanComputeIndex",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "CanComputeIndex: subgroup of full fp groups",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(CosetTableInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "CanComputeIndex: subgroup of full fp groups",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(IndexInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "CanComputeIndex: subgroups fp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(IndexInWholeGroup)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(IndexInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "CanComputeIndex: if sizes can be computed",
+                    "filters": [
+                        [
+                            "CanComputeSize",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CanComputeSize",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "CanComputeIndex: by default impossible unless identical",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanComputeIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KnowsHowToDecompose: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KnowsHowToDecompose)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "KnowsHowToDecompose: group: use GeneratorsOfGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "KnowsHowToDecompose: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "KnowsHowToDecompose: perm group and generators: always true",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "KnowsHowToDecompose: pcp group and generators: always true",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "KnowsHowToDecompose: matrix groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "KnowsHowToDecompose: pc group and generators: always true",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "KnowsHowToDecompose: fp groups: Say yes if finite index",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "KnowsHowToDecompose: trivial group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "KnowsHowToDecompose: generic: just groups of order < 1000",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnowsHowToDecompose",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KnowsHowToDecompose): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KnowsHowToDecompose): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KnowsHowToDecompose)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KnowsHowToDecompose)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsPGroup: for nilpotent groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "IsPGroup: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsPGroup: generic method (check order of the group or of generators if nilpotent)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsPGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimePGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimePGroup)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "PrimePGroup: for direct products",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "PrimePGroup: generic method, check the order of a nontrivial generator",
+                    "filters": [
+                        [
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsPGroup",
+                            "Tester(IsPGroup)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "PrimePGroup: generic method, check the group order",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "PrimePGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "PrimePGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimePGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimePGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimePGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimePGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimePGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PClassPGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PClassPGroup)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "PClassPGroup: for groups with special pcgs",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)",
+                            "Tester(SpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "PClassPGroup: generic method for group",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "PClassPGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PClassPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PClassPGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PClassPGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PClassPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PClassPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankPGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RankPGroup)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "RankPGroup: for groups with special pcgs",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)",
+                            "Tester(SpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "RankPGroup: generic method for group",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "RankPGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RankPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RankPGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RankPGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RankPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RankPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpotentGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNilpotentGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsNilpotentGroup: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "IsNilpotentGroup: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "IsNilpotentGroup: if group size can be computed and is a prime power",
+                    "filters": [
+                        [
+                            "CanComputeSize",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsNilpotentGroup: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsNilpotentGroup: for pcgs computable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "IsNilpotentGroup: for a pcp group with known lower central series",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(LowerCentralSeriesOfGroup)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "IsNilpotentGroup: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsNilpotentGroup: method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsNilpotentGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsNilpotentGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotentGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNilpotentGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNilpotentGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNilpotentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNilpotentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPerfectGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPerfectGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsPerfectGroup: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "IsPerfectGroup: method for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsPerfectGroup",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "IsPerfectGroup: for a (subgroup of a) finitely presented group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsPerfectGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsPerfectGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPerfectGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPerfectGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPerfectGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPerfectGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPerfectGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSporadicSimpleGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSporadicSimpleGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSporadicSimpleGroup: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSporadicSimpleGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSporadicSimpleGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSporadicSimpleGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSporadicSimpleGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSporadicSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSporadicSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSimpleGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSimpleGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSimpleGroup: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "IsSimpleGroup: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsSimpleGroup: for solvable groups",
+                    "filters": [
+                        [
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "IsSimpleGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSimpleGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSimpleGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSimpleGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSimpleGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAlmostSimpleGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAlmostSimpleGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsAlmostSimpleGroup: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsAlmostSimpleGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAlmostSimpleGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAlmostSimpleGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAlmostSimpleGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAlmostSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAlmostSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSupersolvableGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSupersolvableGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSupersolvableGroup: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "IsSupersolvableGroup: method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsSupersolvableGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSupersolvableGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSupersolvableGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSupersolvableGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSupersolvableGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSupersolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSupersolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonomialGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMonomialGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsMonomialGroup: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "IsMonomialGroup: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsMonomialGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonomialGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMonomialGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMonomialGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMonomialGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMonomialGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSolvableGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSolvableGroup: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "IsSolvableGroup: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsSolvableGroup: for AffineCrystGroup, via PointGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "IsSolvableGroup: for rational matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "IsRationalMatrixGroup",
+                            "Tester(IsRationalMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsSolvableGroup: for matrix groups over a finte field (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsSolvableGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsSolvableGroup",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsSolvableGroup: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsSolvableGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSolvableGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSolvableGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSolvableGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSolvableGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPolycyclicGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPolycyclicGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsPolycyclicGroup: for integer matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "IsIntegerMatrixGroup",
+                            "Tester(IsIntegerMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsPolycyclicGroup: for rational matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "IsRationalMatrixGroup",
+                            "Tester(IsRationalMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsPolycyclicGroup: for matrix groups over a finite field (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsPolycyclicGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsPolycyclicGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsPolycyclicGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPolycyclicGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPolycyclicGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPolycyclicGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPolycyclicGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPolycyclicGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AbelianInvariants: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AbelianInvariants)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "AbelianInvariants: for groups of FFE",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "AbelianInvariants: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "AbelianInvariants: for an abelian pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "AbelianInvariants: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "AbelianInvariants: for a finitely presented group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "AbelianInvariants: for a subgroup of a finitely presented group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "AbelianInvariants: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "AbelianInvariants: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "AbelianInvariants: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "AbelianInvariants: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbelianInvariants",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AbelianInvariants): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AbelianInvariants): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AbelianInvariants)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AbelianInvariants)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsInfiniteAbelianizationGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsInfiniteAbelianizationGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsInfiniteAbelianizationGroup: for a finitely presented group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsInfiniteAbelianizationGroup: for a subgroup of a finitely presented group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsInfiniteAbelianizationGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsInfiniteAbelianizationGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInfiniteAbelianizationGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsInfiniteAbelianizationGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsInfiniteAbelianizationGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsInfiniteAbelianizationGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsInfiniteAbelianizationGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsGroup)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "AsGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 133
+                },
+                {
+                    "comment": "AsGroup: for a simple inverse Automaton",
+                    "filters": [
+                        [
+                            "IsSimpleInvAutomatonRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "AsGroup: generic method for collections",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ChiefSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ChiefSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ChiefSeries: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "ChiefSeries: for pcgs computable group refining PcgsElementaryAbelianSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "ChiefSeries: generic method for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ChiefSeries: method for a group (delegate to `ChiefSeriesUnderAction')",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ChiefSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ChiefSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ChiefSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ChiefSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ChiefSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ChiefSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ChiefSeriesUnderAction: method for a pcgs computable group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ChiefSeriesUnderAction: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ChiefSeriesUnderAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ChiefSeriesThrough: generic method for a group and a list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ChiefSeriesThrough: generic method for two groups and a list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 68
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ChiefSeriesThrough",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CommutatorFactorGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CommutatorFactorGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CommutatorFactorGroup: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "CommutatorFactorGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "CommutatorFactorGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CommutatorFactorGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CommutatorFactorGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CommutatorFactorGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CommutatorFactorGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CommutatorFactorGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CompositionSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CompositionSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CompositionSeries: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "CompositionSeries: for simple group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSimpleGroup",
+                            "Tester(IsSimpleGroup)"
+                        ]
+                    ],
+                    "rank": 135
+                },
+                {
+                    "comment": "CompositionSeries: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "CompositionSeries: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "CompositionSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "CompositionSeries: using DerivedSubgroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "CompositionSeries:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "CompositionSeries:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "CompositionSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CompositionSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CompositionSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CompositionSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CompositionSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CompositionSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConjugacyClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConjugacyClasses)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ConjugacyClasses: test options",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20032
+                },
+                {
+                    "comment": "ConjugacyClasses: perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 444
+                },
+                {
+                    "comment": "ConjugacyClasses: TF Method",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingFreeLiftSetup)"
+                        ]
+                    ],
+                    "rank": 429
+                },
+                {
+                    "comment": "ConjugacyClasses: for natural sl",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalSL",
+                            "Tester(IsNaturalSL)"
+                        ]
+                    ],
+                    "rank": 397
+                },
+                {
+                    "comment": "ConjugacyClasses: for natural gl",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "ConjugacyClasses: matrix groups: test naturality",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 391
+                },
+                {
+                    "comment": "ConjugacyClasses: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "ConjugacyClasses: symmetric",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ConjugacyClasses: alternating",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ConjugacyClasses: try solvable method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ConjugacyClasses: for groups: try random search",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ConjugacyClasses:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "ConjugacyClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugacyClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConjugacyClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConjugacyClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConjugacyClassesMaximalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConjugacyClassesMaximalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ConjugacyClassesMaximalSubgroups: use MaximalSubgroupClassReps",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ConjugacyClassesMaximalSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ConjugacyClassesMaximalSubgroups: forAffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugacyClassesMaximalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConjugacyClassesMaximalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConjugacyClassesMaximalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConjugacyClassesMaximalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConjugacyClassesMaximalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "MaximalSubgroups: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "MaximalSubgroups: expand list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "MaximalSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalSubgroupClassReps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalSubgroupClassReps)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: TF method",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingFreeLiftSetup)"
+                        ]
+                    ],
+                    "rank": 429
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: handled by nice monomorphism: subgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: alternating",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: symmetric",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: solvable perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: using lattice",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MaximalSubgroupClassReps: for AffineCrystGroupOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "MaximalSubgroupClassReps: for AffineCrystGroupOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalSubgroupClassReps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalSubgroupClassReps): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalSubgroupClassReps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalSubgroupClassReps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalSubgroupClassReps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PerfectResiduum: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PerfectResiduum)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PerfectResiduum: for solvable groups",
+                    "filters": [
+                        [
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "PerfectResiduum: for perfect groups",
+                    "filters": [
+                        [
+                            "IsPerfectGroup",
+                            "Tester(IsPerfectGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "PerfectResiduum: for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PerfectResiduum: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PerfectResiduum",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PerfectResiduum): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PerfectResiduum): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PerfectResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PerfectResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RepresentativesPerfectSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RepresentativesPerfectSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "RepresentativesPerfectSubgroups: symmetric",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "RepresentativesPerfectSubgroups: alternating",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "RepresentativesPerfectSubgroups: solvable",
+                    "filters": [
+                        [
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "RepresentativesPerfectSubgroups: using Holt/Plesken library",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "RepresentativesPerfectSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativesPerfectSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RepresentativesPerfectSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RepresentativesPerfectSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RepresentativesPerfectSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RepresentativesPerfectSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RepresentativesSimpleSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RepresentativesSimpleSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "RepresentativesSimpleSubgroups: if perfect subs are known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(RepresentativesPerfectSubgroups)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "RepresentativesSimpleSubgroups: using Holt/Plesken library",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "RepresentativesSimpleSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativesSimpleSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RepresentativesSimpleSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RepresentativesSimpleSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RepresentativesSimpleSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RepresentativesSimpleSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConjugacyClassesPerfectSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConjugacyClassesPerfectSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ConjugacyClassesPerfectSubgroups: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ConjugacyClassesPerfectSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugacyClassesPerfectSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConjugacyClassesPerfectSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConjugacyClassesPerfectSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConjugacyClassesPerfectSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConjugacyClassesPerfectSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConjugacyClassesSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConjugacyClassesSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ConjugacyClassesSubgroups: group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ConjugacyClassesSubgroups: lattice",
+                    "filters": [
+                        [
+                            "IsLatticeSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ConjugacyClassesSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugacyClassesSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConjugacyClassesSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConjugacyClassesSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConjugacyClassesSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConjugacyClassesSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LatticeSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LatticeSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "LatticeSubgroups: for a group with table of marks",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(TableOfMarks)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "LatticeSubgroups: for a cyclic group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCyclic",
+                            "Tester(IsCyclic)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "LatticeSubgroups: elementary abelian extension",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "LatticeSubgroups: via radical",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LatticeSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LatticeSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LatticeSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LatticeSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LatticeSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LatticeSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DerivedLength: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DerivedLength)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DerivedLength: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "DerivedLength: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DerivedLength: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DerivedLength",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DerivedLength): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DerivedLength): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DerivedLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DerivedLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HirschLength: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(HirschLength)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "HirschLength",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "HirschLength",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "HirschLength: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "HirschLength: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HirschLength",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(HirschLength): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(HirschLength): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(HirschLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(HirschLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DerivedSeriesOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DerivedSeriesOfGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DerivedSeriesOfGroup: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "DerivedSeriesOfGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DerivedSeriesOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DerivedSeriesOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DerivedSeriesOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DerivedSeriesOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DerivedSeriesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DerivedSeriesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DerivedSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DerivedSubgroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DerivedSubgroup: for a group that knows it is abelian",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ]
+                    ],
+                    "rank": 10041
+                },
+                {
+                    "comment": "DerivedSubgroup: for a group that knows it is perfect",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsPerfectGroup",
+                            "Tester(IsPerfectGroup)"
+                        ]
+                    ],
+                    "rank": 10035
+                },
+                {
+                    "comment": "DerivedSubgroup: handled by nice monomorphism: Subgroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "DerivedSubgroup",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "DerivedSubgroup: permgrps",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "DerivedSubgroup: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "DerivedSubgroup: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "DerivedSubgroup: for a finitely presented group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "DerivedSubgroup: subgroup of a finitely presented group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "DerivedSubgroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DerivedSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DerivedSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DerivedSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DerivedSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DerivedSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DerivedSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalAbelianQuotient: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalAbelianQuotient)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "MaximalAbelianQuotient: whole fp group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "MaximalAbelianQuotient: for subgroups of finitely presented groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "MaximalAbelianQuotient: not fp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "MaximalAbelianQuotient: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalAbelianQuotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalAbelianQuotient): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalAbelianQuotient): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalAbelianQuotient)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalAbelianQuotient)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CommutatorLength: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CommutatorLength)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CommutatorLength: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "CommutatorLength: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "CommutatorLength: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CommutatorLength",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CommutatorLength): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CommutatorLength): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CommutatorLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CommutatorLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DimensionsLoewyFactors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DimensionsLoewyFactors)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DimensionsLoewyFactors: for a group (that must be a finite p-group)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DimensionsLoewyFactors: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DimensionsLoewyFactors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DimensionsLoewyFactors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DimensionsLoewyFactors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DimensionsLoewyFactors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DimensionsLoewyFactors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ElementaryAbelianSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ElementaryAbelianSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ElementaryAbelianSeries: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "ElementaryAbelianSeries: perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "ElementaryAbelianSeries: pcgs computable groups using `PcgsElementaryAbelianSeries'",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "ElementaryAbelianSeries: generic method for groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ElementaryAbelianSeries: list of pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ElementaryAbelianSeries: method for lists",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsFinite",
+                            "Tester(IsFinite)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ElementaryAbelianSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementaryAbelianSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ElementaryAbelianSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ElementaryAbelianSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ElementaryAbelianSeriesLargeSteps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ElementaryAbelianSeriesLargeSteps)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ElementaryAbelianSeriesLargeSteps: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "ElementaryAbelianSeriesLargeSteps: remove spurious factors",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ElementaryAbelianSeriesLargeSteps: remove spurious factors",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "ElementaryAbelianSeriesLargeSteps: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementaryAbelianSeriesLargeSteps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ElementaryAbelianSeriesLargeSteps): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ElementaryAbelianSeriesLargeSteps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ElementaryAbelianSeriesLargeSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ElementaryAbelianSeriesLargeSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Exponent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Exponent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Exponent: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "Exponent: method for abelian groups with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Exponent: solvable group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Exponent: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Exponent: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Exponent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Exponent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Exponent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Exponent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Exponent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Exponent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FittingSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FittingSubgroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "FittingSubgroup: for nilpotent group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)"
+                        ]
+                    ],
+                    "rank": 10039
+                },
+                {
+                    "comment": "FittingSubgroup: handled by nice monomorphism: Subgroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "FittingSubgroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "FittingSubgroup: for ac pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)",
+                            "Tester(AlmostCrystallographicInfo)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "FittingSubgroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "FittingSubgroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "FittingSubgroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "FittingSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FittingSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FittingSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FittingSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FittingSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FittingSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrefrattiniSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrefrattiniSubgroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PrefrattiniSubgroup: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "PrefrattiniSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrefrattiniSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrefrattiniSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrefrattiniSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrefrattiniSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrefrattiniSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FrattiniSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FrattiniSubgroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "FrattiniSubgroup: handled by nice monomorphism: Subgroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "FrattiniSubgroup: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "FrattiniSubgroup: pcgs computable groups using prefrattini and core",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "FrattiniSubgroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "FrattiniSubgroup: Using radical",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "FrattiniSubgroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "FrattiniSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FrattiniSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FrattiniSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FrattiniSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FrattiniSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FrattiniSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InvariantForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InvariantForm)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "InvariantForm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InvariantForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InvariantForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InvariantForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InvariantForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InvariantForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "JenningsSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(JenningsSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "JenningsSeries: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "JenningsSeries: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "JenningsSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "JenningsSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(JenningsSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(JenningsSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(JenningsSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(JenningsSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LowerCentralSeriesOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LowerCentralSeriesOfGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "LowerCentralSeriesOfGroup: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "LowerCentralSeriesOfGroup: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "LowerCentralSeriesOfGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "LowerCentralSeriesOfGroup: fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "LowerCentralSeriesOfGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LowerCentralSeriesOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowerCentralSeriesOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LowerCentralSeriesOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LowerCentralSeriesOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LowerCentralSeriesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LowerCentralSeriesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NilpotencyClassOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NilpotencyClassOfGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NilpotencyClassOfGroup: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NilpotencyClassOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NilpotencyClassOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NilpotencyClassOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NilpotencyClassOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NilpotencyClassOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NilpotencyClassOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalNormalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalNormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "MaximalNormalSubgroups: generic search",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "MaximalNormalSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalNormalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalNormalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalMaximalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalMaximalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NormalMaximalSubgroups: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "NormalMaximalSubgroups: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NormalMaximalSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalMaximalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalMaximalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalMaximalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalMaximalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalMaximalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalNormalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimalNormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "MinimalNormalSubgroups: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 376
+                },
+                {
+                    "comment": "MinimalNormalSubgroups: for solvable groups: use AbelianMinimalNormalSubgroups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "MinimalNormalSubgroups: generic search in NormalSubgroups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(NormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "MinimalNormalSubgroups: compute from conjugacy classes",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "MinimalNormalSubgroups:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "MinimalNormalSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimalNormalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimalNormalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NormalSubgroups: via nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "NormalSubgroups: handled by nice monomorphism: subgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "NormalSubgroups:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "NormalSubgroups: normal complement method for solvable perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "NormalSubgroups: homomorphism principle perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "NormalSubgroups: via IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NormalSubgroups: normal complement method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "NormalSubgroups: homomorphism principle pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "NormalSubgroups: normal complement method for pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "NormalSubgroups: generic class union",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NormalSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrConjugacyClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrConjugacyClasses)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NrConjugacyClasses: for natural SL",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalSL",
+                            "Tester(IsNaturalSL)"
+                        ]
+                    ],
+                    "rank": 397
+                },
+                {
+                    "comment": "NrConjugacyClasses: for natural SU",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSubgroupSL",
+                            "Tester(IsSubgroupSL)",
+                            "IsFullSubgroupGLorSLRespectingSesquilinearForm",
+                            "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "NrConjugacyClasses: for natural GL",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "NrConjugacyClasses: for GU(n,q)",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFullSubgroupGLorSLRespectingSesquilinearForm",
+                            "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"
+                        ]
+                    ],
+                    "rank": 393
+                },
+                {
+                    "comment": "NrConjugacyClasses: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "NrConjugacyClasses",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(ConjugacyClasses)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "NrConjugacyClasses: for a group with known ordinary character table",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(OrdinaryCharacterTable)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "NrConjugacyClasses: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NrConjugacyClasses: for an ordinary character table with underlying group",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "Tester(UnderlyingGroup)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "NrConjugacyClasses: for a Brauer character table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "NrConjugacyClasses: for a character table with known class lengths",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable",
+                            "Tester(SizesConjugacyClasses)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "NrConjugacyClasses: for a character table with known centralizer orders",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable",
+                            "Tester(SizesCentralizers)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "NrConjugacyClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrConjugacyClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrConjugacyClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrConjugacyClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Omega",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "Omega",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Omega",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "Omega",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "Omega",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "Omega",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Omega",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "OmegaOp: for p groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OmegaOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedOmegas: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedOmegas)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedOmegas",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedOmegas: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedOmegas",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedOmegas): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedOmegas): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedOmegas)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedOmegas)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "AgemoOp: PGroups",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 79
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AgemoOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedAgemos: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedAgemos)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedAgemos",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedAgemos: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedAgemos",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedAgemos): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedAgemos): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedAgemos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedAgemos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RadicalGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RadicalGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "RadicalGroup: TF method, use tree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingFreeLiftSetup)"
+                        ]
+                    ],
+                    "rank": 429
+                },
+                {
+                    "comment": "RadicalGroup: handled by nice monomorphism: Subgroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "RadicalGroup: solvable group is its own radical",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 135
+                },
+                {
+                    "comment": "RadicalGroup:  for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "RadicalGroup: factor out Fitting subgroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "RadicalGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "RadicalGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RadicalGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RadicalGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RadicalGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RadicalGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RadicalGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RationalClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RationalClasses)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "RationalClasses: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "RationalClasses: use classes",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "RationalClasses: trial",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "RationalClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RationalClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RationalClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RationalClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RationalClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RationalClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsSmallest: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsSmallest)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "GeneratorsSmallest: matrix group via niceo",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 388
+                },
+                {
+                    "comment": "GeneratorsSmallest: perm group via minimal stab chain",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "GeneratorsSmallest: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "GeneratorsSmallest: group of pc words which is full family",
+                    "filters": [
+                        [
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "GeneratorsSmallest: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "GeneratorsSmallest: for a free monoid",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorsSmallest: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsSmallest",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsSmallest): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsSmallest): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsSmallest)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsSmallest)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LargestElementGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LargestElementGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "LargestElementGroup: matrix group via niceo",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 388
+                },
+                {
+                    "comment": "LargestElementGroup: perm group via minimal stab chain",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "LargestElementGroup: use `EnumeratorSorted'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LargestElementGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LargestElementGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LargestElementGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LargestElementGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LargestElementGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LargestElementGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalGeneratingSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimalGeneratingSet)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "MinimalGeneratingSet",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 367
+                },
+                {
+                    "comment": "MinimalGeneratingSet: cyclic groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCyclic",
+                            "Tester(IsCyclic)"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "MinimalGeneratingSet: compute via Smith normal form",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 91
+                },
+                {
+                    "comment": "MinimalGeneratingSet: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "MinimalGeneratingSet: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "MinimalGeneratingSet: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "MinimalGeneratingSet: solvable group via pc",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "MinimalGeneratingSet: fallback method to inform user",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "MinimalGeneratingSet: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalGeneratingSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimalGeneratingSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimalGeneratingSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimalGeneratingSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimalGeneratingSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SmallGeneratingSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SmallGeneratingSet)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SmallGeneratingSet",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 367
+                },
+                {
+                    "comment": "SmallGeneratingSet: using minimal generating set",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "SmallGeneratingSet: random and generators subset, randsims",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "SmallGeneratingSet: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "SmallGeneratingSet: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SmallGeneratingSet: generators subset",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "SmallGeneratingSet: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SmallGeneratingSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SmallGeneratingSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SmallGeneratingSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SmallGeneratingSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SmallGeneratingSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SupersolvableResiduum: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SupersolvableResiduum)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SupersolvableResiduum: method for finite groups (call `SupersolvableResiduumDefault')",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SupersolvableResiduum: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SupersolvableResiduum",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SupersolvableResiduum): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SupersolvableResiduum): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SupersolvableResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SupersolvableResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComplementSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComplementSystem)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComplementSystem: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ComplementSystem: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComplementSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComplementSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComplementSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComplementSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComplementSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SylowSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SylowSystem)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SylowSystem: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SylowSystem: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SylowSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SylowSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SylowSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SylowSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SylowSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HallSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(HallSystem)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "HallSystem: test whether finite group is solvable",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "HallSystem: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HallSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(HallSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(HallSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(HallSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(HallSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Socle: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Socle)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Socle",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "Socle",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "Socle: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Socle: for finite nilpotent groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "Socle: for finite soluble group, via SolvableSocle",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Socle: for p-groups",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "Socle: from normal subgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Socle:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "Socle: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Socle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Socle): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Socle): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Socle)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Socle)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UpperCentralSeriesOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UpperCentralSeriesOfGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "UpperCentralSeriesOfGroup: handled by nice monomorphism: GroupSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "UpperCentralSeriesOfGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "UpperCentralSeriesOfGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "UpperCentralSeriesOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UpperCentralSeriesOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UpperCentralSeriesOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UpperCentralSeriesOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UpperCentralSeriesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UpperCentralSeriesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EulerianFunction: for a group with table of marks",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(TableOfMarks)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "EulerianFunction: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "EulerianFunction:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "EulerianFunction: for a group, compute table of marks",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EulerianFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsSubgroup: perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "AsSubgroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ClassMultiplicationCoefficient: for an ord. table, and three pos. integers",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 89
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassMultiplicationCoefficient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClosureGroup: for two groups, the bigger conatining the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 10068
+                },
+                {
+                    "comment": "ClosureGroup: method for group that contains the whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10040
+                },
+                {
+                    "comment": "ClosureGroup: handled by nice monomorphism:group CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "ClosureGroup: by niceo",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 373
+                },
+                {
+                    "comment": "ClosureGroup: permgroup, elements",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ]
+                    ],
+                    "rank": 119
+                },
+                {
+                    "comment": "ClosureGroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "ClosureGroup: empty list",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "ClosureGroup: for subgroup of fp group, and subgroup",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "ClosureGroup: groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "ClosureGroup: permgroup, element",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "ClosureGroup: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "ClosureGroup: AffineCrystGroupOnLeft method for group and element",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "ClosureGroup: AffineCrystGroupOnRight method for group and element",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "ClosureGroup: for group and empty element list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "ClosureGroup: subgrp fp: Has coset table",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsSubgroupFpGroup",
+                            "Tester(CosetTableInWholeGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ClosureGroup: subgrp fp: by quotient subgroup",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ClosureGroup: groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "ClosureGroup: groups with cheap membership test",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyTestMembership"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "ClosureGroup: generic method for group and element",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ClosureGroup: for group and element list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ClosureGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ClosureGroup: permgroup, elements, options",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 120
+                },
+                {
+                    "comment": "ClosureGroup: permgroup, permgroup, options",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 117
+                },
+                {
+                    "comment": "ClosureGroup: empty list and options",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 76
+                },
+                {
+                    "comment": "ClosureGroup: permgroup, element, options",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClosureGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CommutatorSubgroup: handled by nice monomorphism:group CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "CommutatorSubgroup: permgroups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "CommutatorSubgroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "CommutatorSubgroup: normal subgroup with whole fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "CommutatorSubgroup: whole fp group with normal subgroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "CommutatorSubgroup: normal subgroup with whole fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "CommutatorSubgroup: groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "CommutatorSubgroup: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CommutatorSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugateGroup: handled by nice monomorphism: group CollElm",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 374
+                },
+                {
+                    "comment": "ConjugateGroup: <P>, <g>",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "ConjugateGroup: method for AffineCrystGroupOnLeft and element",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "ConjugateGroup: method for AffineCrystGroupOnRight and element",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "ConjugateGroup: subgroups of fp group with coset table",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "Tester(CosetTableInWholeGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ConjugateGroup: subgroups of fp group by quotient",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "ConjugateGroup: groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "ConjugateGroup: <G>, <g>",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugateGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "Tester(ParentAttr)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugateSubgroup: for group with parent, and group element",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "ConjugateSubgroup: for group without parent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugateSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugateSubgroups: groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "ConjugateSubgroups: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugateSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CoreOp: handled by nice monomorphism:group CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "CoreOp: subgroups of fp group by quotient",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "CoreOp: subgroups of fp group: use quotient rep",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "CoreOp: pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "CoreOp: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoreOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoreInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoreInParent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CoreInParent: method that calls the two-argument operation CoreOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "CoreInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoreInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoreInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoreInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoreInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoreInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Core: try to exploit the in-parent attribute CoreInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Core",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CosetTable: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CosetTableNormalClosure: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetTableNormalClosure",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FactorGroupNC",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "FactorGroupNC: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorGroupNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalHomomorphism: for a group with natural homomorphism stored",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NaturalHomomorphism: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IndexOp: handled by nice monomorphism: attribute CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "IndexOp: AffineCrystGroupOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "IndexOp: AffineCrystGroupOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "IndexOp: for free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "IndexOp: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "IndexOp: for finitely presented group in whole group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "IndexOp: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "IndexOp: for two character tables",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "IndexOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IndexOp: for free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 101
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndexOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndexInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndexInParent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IndexInParent: method that calls the two-argument operation IndexOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IndexInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndexInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndexInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndexInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndexInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndexInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Index: try to exploit the in-parent attribute IndexInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "Index: for two character tables",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Index",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IndexNC: for two groups with known Size value",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 747
+                },
+                {
+                    "comment": "IndexNC: handled by nice monomorphism: attribute CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "IndexNC: AffineCrystGroupOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "IndexNC: AffineCrystGroupOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "IndexNC: for free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "IndexNC: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "IndexNC: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IndexNC: generic method for two groups (the second one being finite)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "IndexNC: for two character tables",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "IndexNC:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndexNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndexInWholeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndexInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IndexInWholeGroup: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IndexInWholeGroup: for full fp group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IndexInWholeGroup: subgroup fp by quotient",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IndexInWholeGroup: subgroup fp",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IndexInWholeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndexInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndexInWholeGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndexInWholeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndexInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndexInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndependentGeneratorsOfAbelianGroup)"
+                        ]
+                    ],
+                    "rank": 20043
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: for groups of FFE",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 396
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: for perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: for an abelian pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: Use Pcgs and NormalFormIntMat to find the independent generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: For abelian fpgroup, use Smith normal form",
+                    "filters": [
+                        [
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: finite abelian group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "IndependentGeneratorsOfAbelianGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndependentGeneratorsOfAbelianGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndependentGeneratorsOfAbelianGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndependentGeneratorsOfAbelianGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndependentGeneratorsOfAbelianGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndependentGeneratorsOfAbelianGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IndependentGeneratorExponents: for groups of FFE",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 411
+                },
+                {
+                    "comment": "IndependentGeneratorExponents: for an abelian pcp group and an element",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "IndependentGeneratorExponents: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "Tester(DirectProductInfo)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "IndependentGeneratorExponents",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndependentGeneratorExponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IsConjugate: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 144
+                },
+                {
+                    "comment": "IsConjugate: subgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 99
+                },
+                {
+                    "comment": "IsConjugate: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ],
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "IsConjugate: group elements",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsConjugate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsNormalOp: handled by nice monomorphism: attribute CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "IsNormalOp: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "IsNormalOp: subgroups of fp group by quot. rep in full fp grp.",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "IsNormalOp: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormalOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNormalInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNormalInParent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsNormalInParent: method that calls the two-argument operation IsNormalOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsNormalInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormalInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNormalInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNormalInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNormalInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNormalInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsNormal: try to exploit the in-parent attribute IsNormalInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsCharacteristicSubgroup: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCharacteristicSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPNilpotentOp: for a group with special pcgs: test for normal Hall subgroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SpecialPcgs)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IsPNilpotentOp: check if p divides order of hypocentre",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "IsPNilpotentOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPNilpotentOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedIsPNilpotents: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedIsPNilpotents)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedIsPNilpotents: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedIsPNilpotents: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedIsPNilpotents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedIsPNilpotents): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedIsPNilpotents): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedIsPNilpotents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedIsPNilpotents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPNilpotent: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPNilpotent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasIsPNilpotent: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasIsPNilpotent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetIsPNilpotent: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetIsPNilpotent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPSolvableOp: for solvable groups: return true",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 10065
+                },
+                {
+                    "comment": "IsPSolvableOp: generic method: build descending series with abelian or p'-factors",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "IsPSolvableOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPSolvableOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedIsPSolvables: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedIsPSolvables)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedIsPSolvables: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedIsPSolvables: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedIsPSolvables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedIsPSolvables): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedIsPSolvables): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedIsPSolvables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedIsPSolvables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPSolvable: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPSolvable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasIsPSolvable: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasIsPSolvable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetIsPSolvable: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetIsPSolvable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsSubnormal: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubnormal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalClosureOp: handled by nice monomorphism:group CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "NormalClosureOp: subgroup of perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "NormalClosureOp: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "NormalClosureOp: whole fp group with normal subgroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "NormalClosureOp: groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "NormalClosureOp: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "NormalClosureOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalClosureOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalClosureInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalClosureInParent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NormalClosureInParent: method that calls the two-argument operation NormalClosureOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NormalClosureInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalClosureInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalClosureInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalClosureInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalClosureInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalClosureInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalClosure: try to exploit the in-parent attribute NormalClosureInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalClosure",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalIntersection: handled by nice monomorphism:group CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "NormalIntersection: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "NormalIntersection: method for two groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "NormalIntersection: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalIntersection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizerOp",
+                    "filters": [
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NormalizerOp: handled by nice monomorphism: Subgroup CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "NormalizerOp: subgp of natural alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 120
+                },
+                {
+                    "comment": "NormalizerOp: subgp of natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 120
+                },
+                {
+                    "comment": "NormalizerOp: perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "NormalizerOp: two AffineCrystGroupsOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "NormalizerOp: two AffineCrystGroupsOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "NormalizerOp: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "NormalizerOp",
+                    "filters": [
+                        [
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)",
+                            "IsIntegerMatrixGroup",
+                            "Tester(IsIntegerMatrixGroup)"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "NormalizerOp: for a pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "NormalizerOp: in whole group by quot. rep",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "NormalizerOp: subgroups of fp group by quot. rep",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "NormalizerOp: subgroups of fp group: find stabilizing cosets",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "NormalizerOp: for groups with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "NormalizerOp: slightly better orbit algorithm for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "NormalizerOp: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "NormalizerOp: for an element in a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "NormalizerOp: generic method for group and Element",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "NormalizerOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizerInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizerInParent)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "NormalizerInParent: method that calls the two-argument operation NormalizerOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizerInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizerInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Normalizer: try to exploit the in-parent attribute NormalizerInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Normalizer: perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 174
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Normalizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CentralizerModulo: group centralizer via generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 101
+                },
+                {
+                    "comment": "CentralizerModulo: pcgs computable groups, for elm",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "CentralizerModulo:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralizerModulo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PCentralSeriesOp: handled by nice monomorphism: GroupSeries CollOther",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 387
+                },
+                {
+                    "comment": "PCentralSeriesOp: method for pc groups and prime",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "PCentralSeriesOp: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "PCentralSeriesOp",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "PCentralSeriesOp: generic method for group and prime",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PCentralSeriesOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedPCentralSeriess: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedPCentralSeriess)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedPCentralSeriess: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedPCentralSeriess: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedPCentralSeriess",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedPCentralSeriess): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedPCentralSeriess): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedPCentralSeriess)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedPCentralSeriess)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PCentralSeries: pGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PCentralSeries: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasPCentralSeries: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasPCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPCentralSeries: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PRumpOp: for a pcp group and a prime",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "PRumpOp: generic method for group and prime",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PRumpOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedPRumps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedPRumps)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedPRumps: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedPRumps: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedPRumps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedPRumps): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedPRumps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedPRumps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedPRumps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PRump: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PRump",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasPRump: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasPRump",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPRump: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPRump",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PCoreOp: handled by nice monomorphism: subgroup CollOther",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 387
+                },
+                {
+                    "comment": "PCoreOp: for a permutation group, and a positive integer",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "PCoreOp: generic method for group and prime",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PCoreOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedPCores: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedPCores)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedPCores: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedPCores: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedPCores",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedPCores): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedPCores): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedPCores)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedPCores)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PCore: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PCore",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasPCore: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasPCore",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPCore: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPCore",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SubnormalSeriesOp: handled by nice monomorphism: GroupSeries CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "SubnormalSeriesOp: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubnormalSeriesOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SubnormalSeriesInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SubnormalSeriesInParent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SubnormalSeriesInParent: method that calls the two-argument operation SubnormalSeriesOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SubnormalSeriesInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubnormalSeriesInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SubnormalSeriesInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SubnormalSeriesInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SubnormalSeriesInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SubnormalSeriesInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SubnormalSeries: try to exploit the in-parent attribute SubnormalSeriesInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubnormalSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SylowSubgroupOp: Direct construction for natural GL",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNaturalGL",
+                            "Tester(IsNaturalGL)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 414
+                },
+                {
+                    "comment": "SylowSubgroupOp: handled by nice monomorphism: subgroup CollOther",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 387
+                },
+                {
+                    "comment": "SylowSubgroupOp: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 169
+                },
+                {
+                    "comment": "SylowSubgroupOp: symmetric",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "SylowSubgroupOp: alternating",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "SylowSubgroupOp: permutation groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "SylowSubgroupOp",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "SylowSubgroupOp: method for a nilpotent group, and a prime",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "SylowSubgroupOp: generic method for group and prime",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "SylowSubgroupOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SylowSubgroupOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedSylowSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedSylowSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedSylowSubgroups: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedSylowSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedSylowSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedSylowSubgroups): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedSylowSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedSylowSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedSylowSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SylowSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SylowSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasSylowSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasSylowSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetSylowSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetSylowSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SylowComplementOp: test trivial case",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 10063
+                },
+                {
+                    "comment": "SylowComplementOp: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 149
+                },
+                {
+                    "comment": "SylowComplementOp: via IsomoprhismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "SylowComplementOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "SylowComplementOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "SylowComplementOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SylowComplementOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedSylowComplements: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedSylowComplements)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedSylowComplements: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedSylowComplements: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedSylowComplements",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedSylowComplements): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedSylowComplements): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedSylowComplements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedSylowComplements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SylowComplement: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SylowComplement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasSylowComplement: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasSylowComplement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetSylowComplement: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetSylowComplement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HallSubgroupOp: test trivial cases",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 10046
+                },
+                {
+                    "comment": "HallSubgroupOp: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 370
+                },
+                {
+                    "comment": "HallSubgroupOp: pcgs computable groups using special pcgs",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "HallSubgroupOp: via IsomoprhismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "HallSubgroupOp: fitting free",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanComputeFittingFree"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "HallSubgroupOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "HallSubgroupOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "HallSubgroupOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HallSubgroupOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedHallSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedHallSubgroups)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedHallSubgroups: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ComputedHallSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedHallSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedHallSubgroups): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedHallSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedHallSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedHallSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HallSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HallSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasHallSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasHallSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetHallSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 34
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetHallSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NrConjugacyClassesInSupergroup: handled by nice monomorphism: attribute CollColl",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 736
+                },
+                {
+                    "comment": "NrConjugacyClassesInSupergroup: generic method for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrConjugacyClassesInSupergroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Factorization: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Factorization",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "Tester(GeneratorsOfMagmaWithInverses)",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "Tester(GeneratorsOfMagmaWithInverses)",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GrowthFunctionOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GrowthFunctionOfGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "GrowthFunctionOfGroup: finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "GrowthFunctionOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "GrowthFunctionOfGroup: groups and orders",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GrowthFunctionOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "Tester(GeneratorsOfMagmaWithInverses)",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GrowthFunctionOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GrowthFunctionOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GrowthFunctionOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "Tester(GeneratorsOfMagmaWithInverses)",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GrowthFunctionOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ],
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupByGenerators: delegate to `GroupWithGenerators'",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "GroupByGenerators: delegate to `GroupWithGenerators'",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "GroupByGenerators: delegate to `GroupWithGenerators'",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ],
+            [
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupWithGenerators: method for pc elements collection",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "GroupWithGenerators: list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "GroupWithGenerators: for a homogeneous list (of class functions)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "GroupWithGenerators: generic method for collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "GroupWithGenerators: for empty list and trivial character",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "GroupWithGenerators: list of matrices with identity",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "GroupWithGenerators: for list (of class functions) and class function",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "GroupWithGenerators: method for empty pc collection and identity element",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "GroupWithGenerators: method for pc collection and identity element",
+                    "filters": [
+                        [
+                            "IsCollection",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "GroupWithGenerators: method for empty list and element",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "GroupWithGenerators: generic method for collection and identity element",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupWithGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ElementTestFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ElementTestFunction)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ElementTestFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementTestFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ElementTestFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ElementTestFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ElementTestFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ElementTestFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightTransversalOp: for trivial subgroup, call `EnumeratorSorted' for the big group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 202
+                },
+                {
+                    "comment": "RightTransversalOp: for two perm. groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "RightTransversalOp: pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 79
+                },
+                {
+                    "comment": "RightTransversalOp: pc groups",
+                    "filters": [
+                        [
+                            "Tester(Pcgs)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "RightTransversalOp: via coset table",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "RightTransversalOp: generic, use RightCosets",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightTransversalOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RightTransversalInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RightTransversalInParent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "RightTransversalInParent: method that calls the two-argument operation RightTransversalOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "RightTransversalInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightTransversalInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RightTransversalInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RightTransversalInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RightTransversalInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RightTransversalInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightTransversal: try to exploit the in-parent attribute RightTransversalInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightTransversal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IntermediateSubgroups: fp group via quotient subgroups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IntermediateSubgroups: normal case",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "IntermediateSubgroups: blocks for coset operation",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntermediateSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismTypeInfoFiniteSimpleGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismTypeInfoFiniteSimpleGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsomorphismTypeInfoFiniteSimpleGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsomorphismTypeInfoFiniteSimpleGroup: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsomorphismTypeInfoFiniteSimpleGroup",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsomorphismTypeInfoFiniteSimpleGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismTypeInfoFiniteSimpleGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismTypeInfoFiniteSimpleGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismTypeInfoFiniteSimpleGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismTypeInfoFiniteSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismTypeInfoFiniteSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismPcGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismPcGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsomorphismPcGroup: via niceomorphisms",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 377
+                },
+                {
+                    "comment": "IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsomorphismPcGroup: for finitely presented groups that know their size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsomorphismPcGroup: via permutation representation",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsomorphismPcGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "IsomorphismPcGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "IsomorphismPcGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismPcGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismPcGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismPcGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismSpecialPcGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismSpecialPcGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsomorphismSpecialPcGroup: method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsomorphismSpecialPcGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsomorphismSpecialPcGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismSpecialPcGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismSpecialPcGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismSpecialPcGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismSpecialPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismSpecialPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismPermGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismPermGroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismPermGroup: imf matrix groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsImfMatrixGroup"
+                        ]
+                    ],
+                    "rank": 389
+                },
+                {
+                    "comment": "IsomorphismPermGroup: perfect library groups",
+                    "filters": [
+                        [
+                            "IsPerfectLibraryGroup"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "IsomorphismPermGroup: for full finitely presented groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "IsomorphismPermGroup: for subgroups of finitely presented groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "IsomorphismPermGroup: cyclotomic matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "IsomorphismPermGroup: perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "IsomorphismPermGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CanEasilyComputeWithIndependentGensAbelianGroup"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "IsomorphismPermGroup: for finite nilpotent groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "KnowsHowToDecompose",
+                            "Tester(KnowsHowToDecompose)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "IsomorphismPermGroup: matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "IsomorphismPermGroup: via niceomorphisms",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "IsomorphismPermGroup: right regular operation",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsomorphismPermGroup: for a group H-class of a semigroup",
+                    "filters": [
+                        [
+                            "IsGreensHClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IsomorphismPermGroup: for family of fp words",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IsomorphismPermGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "IsomorphismPermGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismPermGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGreensHClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismPermGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismPermGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismPermGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismPermGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismFpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismFpGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsomorphismFpGroup: perfect library groups",
+                    "filters": [
+                        [
+                            "IsPerfectLibraryGroup"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "IsomorphismFpGroup: alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "IsomorphismFpGroup: symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "IsomorphismFpGroup: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "IsomorphismFpGroup: for PointGroup",
+                    "filters": [
+                        [
+                            "IsPointGroup",
+                            "Tester(IsPointGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsomorphismFpGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsomorphismFpGroup: for automorphism groups of free groups",
+                    "filters": [
+                        [
+                            "IsAutomorphismGroupOfFreeGroup"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsomorphismFpGroup: supply name",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsomorphismFpGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsomorphismFpGroup: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 373
+                },
+                {
+                    "comment": "IsomorphismFpGroup: alternating group,name",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "IsomorphismFpGroup: for simple solvable permutation groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSimpleGroup",
+                            "Tester(IsSimpleGroup)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IsomorphismFpGroup: symmetric group,name",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "IsomorphismFpGroup: for simple permutation groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSimpleGroup",
+                            "Tester(IsSimpleGroup)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "IsomorphismFpGroup: for perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "IsomorphismFpGroup: pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsomorphismFpGroup: subgroups of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismFpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismFpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IsomorphismFpGroupByGeneratorsNC: via niceomorphism/w. gens",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 375
+                },
+                {
+                    "comment": "IsomorphismFpGroupByGeneratorsNC: for perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "IsomorphismFpGroupByGeneratorsNC: pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsomorphismFpGroupByGeneratorsNC: subgroups of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsMultiplicativeElementWithInverse)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "IsomorphismFpGroupByGeneratorsNC: via cokernel",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpGroupByGeneratorsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsomorphismFpGroupBySubnormalSeries: for groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsomorphismFpGroupBySubnormalSeries: for groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 65
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpGroupBySubnormalSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismFpGroupByCompositionSeries: supply name",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsomorphismFpGroupByCompositionSeries: for permutation groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "IsomorphismFpGroupByCompositionSeries: pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpGroupByCompositionSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismFpGroupByChiefSeries: supply name",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsomorphismFpGroupByChiefSeries: permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 63
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpGroupByChiefSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimePowerComponents: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimePowerComponents)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "PrimePowerComponents: method for a pc element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithOne"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "PrimePowerComponents: generic method",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimePowerComponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimePowerComponents): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimePowerComponents): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimePowerComponents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimePowerComponents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PrimePowerComponent: generic method",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimePowerComponent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PowerMapOfGroup: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 390
+                },
+                {
+                    "comment": "PowerMapOfGroup: method for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "PowerMapOfGroup: method for a matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "PowerMapOfGroup: method for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 55
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PowerMapOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsInverseSubsemigroup: for a semigroup and a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInverseSubsemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGeneratorsOfInverseSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsGeneratorsOfInverseSemigroup: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsGeneratorsOfInverseSemigroup: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGeneratorsOfInverseSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGeneratorsOfInverseSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGeneratorsOfInverseSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGeneratorsOfInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGeneratorsOfInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfInverseMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfInverseMonoid)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "GeneratorsOfInverseMonoid: for an inverse partial perm monoid with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GeneratorsOfInverseMonoid: for a group with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GeneratorsOfInverseMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfInverseMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfInverseMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfInverseMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfInverseMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfInverseMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfInverseSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "GeneratorsOfInverseSemigroup: for a group with known generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GeneratorsOfInverseSemigroup: for an inverse partial perm semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "GeneratorsOfInverseSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfInverseSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfInverseSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfInverseSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneratorsOfSemigroup",
+                    "Tester(IsGeneratorsOfSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseMonoidByGenerators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsAssociativeElement)"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseMonoidByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneratorsOfSemigroup",
+                    "Tester(IsGeneratorsOfSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseSemigroupByGenerators: for associative element with unique semigroup inverse collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsAssociativeElement)"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseSemigroupByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ],
+                [
+                    "IsGeneratorsOfSemigroup",
+                    "Tester(IsGeneratorsOfSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InverseSubsemigroup: for an inverse semigroup and element collection",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsAssociativeElement)"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseSubsemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ],
+                [
+                    "IsGeneratorsOfSemigroup",
+                    "Tester(IsGeneratorsOfSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InverseSubsemigroupNC: for an inverse semigroup and element collection",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsAssociativeElement)"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseSubsemigroupNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ],
+                [
+                    "IsGeneratorsOfSemigroup",
+                    "Tester(IsGeneratorsOfSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InverseSubmonoid: for an inverse monoid and element collection",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsAssociativeElement)"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseSubmonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsInverseSemigroup",
+                    "Tester(IsInverseSemigroup)"
+                ],
+                [
+                    "IsGeneratorsOfSemigroup",
+                    "Tester(IsGeneratorsOfSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InverseSubmonoidNC: for an inverse monoid and element collection",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ],
+                        [
+                            "CategoryCollections(IsAssociativeElement)"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseSubmonoidNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsInverseSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "AsInverseSemigroup: for an inverse semigroup",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 119
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsInverseSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsInverseSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsInverseSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsInverseMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsInverseMonoid)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "AsInverseMonoid: for an inverse monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 124
+                },
+                {
+                    "comment": "AsInverseMonoid: for an inverse monoid",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 124
+                },
+                {
+                    "comment": "AsInverseMonoid: for an inverse semigroup with known generators",
+                    "filters": [
+                        [
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)",
+                            "Tester(GeneratorsOfInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsInverseMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsInverseMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsInverseMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsInverseMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsInverseMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsInverseSubsemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsInverseSubmonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReverseNaturalPartialOrder: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ReverseNaturalPartialOrder)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "ReverseNaturalPartialOrder: for an inverse partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ReverseNaturalPartialOrder: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReverseNaturalPartialOrder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ReverseNaturalPartialOrder): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ReverseNaturalPartialOrder): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ReverseNaturalPartialOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ReverseNaturalPartialOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalPartialOrder: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalPartialOrder)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "NaturalPartialOrder: for an inverse partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "NaturalPartialOrder: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalPartialOrder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalPartialOrder): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalPartialOrder): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalPartialOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalPartialOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAdditivelyCommutative: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 20012
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAdditivelyCommutative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAdditivelyCommutative): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAdditivelyCommutative): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAdditivelyCommutative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAdditivelyCommutative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NearAdditiveMagmaByGenerators: for collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NearAdditiveMagmaByGenerators: for family and list",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NearAdditiveMagmaByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NearAdditiveMagmaWithZeroByGenerators: for collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NearAdditiveMagmaWithZeroByGenerators: for family and list",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NearAdditiveMagmaWithZeroByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NearAdditiveGroupByGenerators: for collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NearAdditiveGroupByGenerators: for family and list",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NearAdditiveGroupByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfNearAdditiveMagma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfNearAdditiveMagma)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "GeneratorsOfNearAdditiveMagma",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "GeneratorsOfNearAdditiveMagma",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfNearAdditiveMagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfNearAdditiveMagma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfNearAdditiveMagma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfNearAdditiveMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfNearAdditiveMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagmaWithZero"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfNearAdditiveMagmaWithZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "GeneratorsOfNearAdditiveMagmaWithZero",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "GeneratorsOfNearAdditiveMagmaWithZero",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagma)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfNearAdditiveMagmaWithZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagmaWithZero"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfNearAdditiveMagmaWithZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfNearAdditiveMagmaWithZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfNearAdditiveMagmaWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagmaWithZero"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfNearAdditiveMagmaWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfNearAdditiveGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfNearAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GeneratorsOfNearAdditiveGroup",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfNearAdditiveGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfNearAdditiveGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfNearAdditiveGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfNearAdditiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfNearAdditiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagmaWithZero"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TrivialSubnearAdditiveMagmaWithZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TrivialSubnearAdditiveMagmaWithZero)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "TrivialSubnearAdditiveMagmaWithZero: for a FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "TrivialSubnearAdditiveMagmaWithZero: generic method for left modules",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "TrivialSubnearAdditiveMagmaWithZero: for add.-magma-with-zero",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TrivialSubnearAdditiveMagmaWithZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagmaWithZero"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TrivialSubnearAdditiveMagmaWithZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TrivialSubnearAdditiveMagmaWithZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TrivialSubnearAdditiveMagmaWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagmaWithZero"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TrivialSubnearAdditiveMagmaWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdditiveNeutralElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdditiveNeutralElement)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "AdditiveNeutralElement",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditiveNeutralElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdditiveNeutralElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdditiveNeutralElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdditiveNeutralElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdditiveNeutralElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveGroup"
+                ],
+                [
+                    "IsNearAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClosureNearAdditiveGroup: for two add. groups",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ClosureNearAdditiveGroup: for add. group and element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClosureNearAdditiveGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AdditiveCoset: for additive group and additive element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdditiveCoset",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLDistributive: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLDistributive)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLDistributive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLDistributive): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLDistributive): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLDistributive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLDistributive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRDistributive: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRDistributive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRDistributive): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRDistributive): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRDistributive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRDistributive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfSemiring: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfSemiring)"
+                        ]
+                    ],
+                    "rank": 20027
+                },
+                {
+                    "comment": "GeneratorsOfSemiring: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfSemiring",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfSemiring): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfSemiring): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfSemiring)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfSemiring)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfSemiringWithOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfSemiringWithOne)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "GeneratorsOfSemiringWithOne: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfSemiringWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfSemiringWithOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfSemiringWithOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfSemiringWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfSemiringWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveMagmaWithZero",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfSemiringWithZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfSemiringWithZero)"
+                        ]
+                    ],
+                    "rank": 20028
+                },
+                {
+                    "comment": "GeneratorsOfSemiringWithZero: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfSemiringWithZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveMagmaWithZero",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfSemiringWithZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfSemiringWithZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfSemiringWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveMagmaWithZero",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfSemiringWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveMagmaWithZero",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfSemiringWithOneAndZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfSemiringWithOneAndZero)"
+                        ]
+                    ],
+                    "rank": 20030
+                },
+                {
+                    "comment": "GeneratorsOfSemiringWithOneAndZero: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveMagmaWithZero"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfSemiringWithOneAndZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveMagmaWithZero",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfSemiringWithOneAndZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfSemiringWithOneAndZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfSemiringWithOneAndZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveMagmaWithZero",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfSemiringWithOneAndZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSemiring: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSemiring)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSemiring",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSemiring): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSemiring): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSemiring)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSemiring)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSemiringWithOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSemiringWithOne)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSemiringWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSemiringWithOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSemiringWithOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSemiringWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSemiringWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSemiringWithZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSemiringWithZero)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSemiringWithZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSemiringWithZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSemiringWithZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSemiringWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSemiringWithZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSemiringWithOneAndZero: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSemiringWithOneAndZero)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSemiringWithOneAndZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSemiringWithOneAndZero): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSemiringWithOneAndZero): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSemiringWithOneAndZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSemiringWithOneAndZero)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClosureSemiring",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiringByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiringWithOneByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiringWithZeroByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiringWithOneAndZeroByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentralIdempotentsOfSemiring: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CentralIdempotentsOfSemiring)"
+                        ]
+                    ],
+                    "rank": 20027
+                },
+                {
+                    "comment": "CentralIdempotentsOfSemiring: for an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "CentralIdempotentsOfSemiring: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralIdempotentsOfSemiring",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CentralIdempotentsOfSemiring): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CentralIdempotentsOfSemiring): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CentralIdempotentsOfSemiring)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CentralIdempotentsOfSemiring)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsNearRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsNearRing)"
+                        ]
+                    ],
+                    "rank": 20015
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsNearRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsNearRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsNearRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsNearRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsNearRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsRing)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "GeneratorsOfRing: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "GeneratorsOfRing: for a ring-with-one with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRingWithOne)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "GeneratorsOfRing",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(GeneratorsOfNearAdditiveGroup)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "GeneratorsOfRing",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "GeneratorsOfRing: generic method for a two-sided ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "GeneratorsOfRing: generic method for a right ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "GeneratorsOfRing: generic method for a left ideal with known generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "GeneratorsOfRing: for a ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorsOfRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfRingWithOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfRingWithOne)"
+                        ]
+                    ],
+                    "rank": 20031
+                },
+                {
+                    "comment": "GeneratorsOfRingWithOne: for a free magma ring-with-one",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "GeneratorsOfRingWithOne",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "GeneratorsOfRingWithOne",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "GeneratorsOfRingWithOne: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -25
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfRingWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfRingWithOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfRingWithOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfRingWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfRingWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RingByGenerators: method that catches the cases of `Integers' and subrings of `Integers'",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "RingByGenerators: for a list of Lie matrices over a finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))",
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "RingByGenerators: for a collection of FFE",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "RingByGenerators: for a list of matrices over the Cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "RingByGenerators: for a list of matrices over a finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "RingByGenerators: for a list of linear mappings of finite vector spaces",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "RingByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RingByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefaultRingByGenerators: method that catches the cases of `(Gaussian)Integers' and cycl. fields",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for a collection of FFE",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for a list of Lie matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))",
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for a collection over a ring Z/nZ",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for lists of n x n integer matrices",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for a list of matrices over the Cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for a list of matrices over a finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "DefaultRingByGenerators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsRationalFunction)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for a list of linear mappings of vector spaces",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "DefaultRingByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefaultRingByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RingWithOneByGenerators: method that catches the cases of `Integers'",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 10022
+                },
+                {
+                    "comment": "RingWithOneByGenerators: for a collection of FFE",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "RingWithOneByGenerators: for a list of matrices over the Cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "RingWithOneByGenerators: for a list of matrices over a finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "RingWithOneByGenerators: for a list of linear mappings of finite vector spaces",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "RingWithOneByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RingWithOneByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClosureRing: for a ring containing the whole family, and a ring element",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 10036
+                },
+                {
+                    "comment": "ClosureRing: for a ring cont. the whole family, and a collection",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10030
+                },
+                {
+                    "comment": "ClosureRing: for two rings-with-one",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "ClosureRing: for two rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "ClosureRing: for a ring-with-one and a ring element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ClosureRing: for a ring and a ring element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ClosureRing: for ring and collection of elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClosureRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAnticommutative: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAnticommutative)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsAnticommutative: generic method for a (finite dimensional) FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsAnticommutative",
+                    "filters": [
+                        [
+                            "Tester(Characteristic)",
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsAnticommutative: generic method for rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IsAnticommutative: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAnticommutative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAnticommutative): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAnticommutative): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAnticommutative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAnticommutative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIntegralRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIntegralRing)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsIntegralRing",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "IsIntegralRing: for a ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IsIntegralRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIntegralRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIntegralRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIntegralRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIntegralRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIntegralRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsJacobianRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsJacobianRing)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsJacobianRing: for a (finite dimensional) FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsJacobianRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsJacobianRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsJacobianRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsJacobianRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsJacobianRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsJacobianRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZeroSquaredRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsZeroSquaredRing: for a finite dimensional FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsZeroSquaredRing",
+                    "filters": [
+                        [
+                            "Tester(Characteristic)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsAnticommutative",
+                            "Tester(IsAnticommutative)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsZeroSquaredRing: for a ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IsZeroSquaredRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZeroSquaredRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZeroSquaredRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZeroSquaredRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZeroSquaredRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZeroSquaredRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZeroMultiplicationRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZeroMultiplicationRing)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsZeroMultiplicationRing",
+                    "filters": [
+                        [
+                            "Tester(IsTrivial)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsZeroMultiplicationRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZeroMultiplicationRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZeroMultiplicationRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZeroMultiplicationRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZeroMultiplicationRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZeroMultiplicationRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Units: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Units)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "Units: for a full matrix algebra (over a finite field)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "Units: for a finite field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "Units: for a division ring",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "Units: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Units: for full ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Units: zmodnze : for full ring Z/nZ(m)",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZepsObj)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Units: for a (finite) ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Units: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Units",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Units): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Units): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Units)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Units)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Factors",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Factors: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Factors:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Factors: for integers (FactInt)",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Factors: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Factors: for a division ring and a ring element",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Factors: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "Factors: for Z_(pi) and an element thereof (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "Factors: univariate rational polynomial",
+                    "filters": [
+                        [
+                            "IsRationalsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Factors: for a polynomial over a field of cyclotomics",
+                    "filters": [
+                        [
+                            "IsAbelianNumberFieldPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Factors: alg ext polynomial",
+                    "filters": [
+                        [
+                            "IsAlgebraicExtensionPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Factors: polynomial over a finite field",
+                    "filters": [
+                        [
+                            "IsFiniteFieldPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Factors: multivariate, reduce to univariate case",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "Factors: fallback error message",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "Factors:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Factors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsAssociated: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsAssociated: for a division ring, and two ring elements",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "IsAssociated: for ring and two ring elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAssociated",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Associates: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Associates: for a ring and a ring element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Associates",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUnit: LAGUNA: for an element of modular group algebra",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsUnit: zmodnze : for element in Z/nZ(m) (ZModnZepsRep) without given ring",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsUnit: for a Lie object (return `false')",
+                    "filters": [
+                        [
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsUnit: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsUnit: for matrix FLMLOR and matrix",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "IsUnit: for element in Z/nZ (ModulusRep)",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ],
+                        [
+                            "IsZmodnZObj",
+                            "IsModulusRep"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsUnit: for a division ring, and a ring element",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsUnit: LAGUNA: for an element of modular group algebra",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "IsUnit: for Z_(pi) and an element thereof (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsUnit: zmodnze : for element in Z/nZ(m) (ZModnZepsRep) with given ring",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZepsObj)"
+                        ],
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsUnit: for finite Rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsUnit: for a ring with known units and a ring element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(Units)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsUnit: for a ring and a ring element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUnit",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "InterpolatedPolynomial",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 26
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InterpolatedPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Quotient: laurent",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "Quotient: multivar",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Quotient: for two ring elements (delegate to three argument version",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Quotient:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Quotient: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "Quotient: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "Quotient: for a division ring, and two ring elements",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "Quotient: laurent, ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "Quotient: multivar with ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "Quotient: for a ring and two ring elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Quotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StandardAssociate: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "StandardAssociate: for a ring and its zero element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 10036
+                },
+                {
+                    "comment": "StandardAssociate: HNF of n x n integer matrix (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "StandardAssociate: for a division ring and a ring element",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "StandardAssociate: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "StandardAssociate: for Z_(pi) and an element thereof (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "StandardAssociate: for a ring and a ring element (using StandardAssociateUnit)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StandardAssociate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StandardAssociateUnit: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "StandardAssociateUnit: for a ring and its zero element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 10036
+                },
+                {
+                    "comment": "StandardAssociateUnit: for a division ring and a ring element",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "StandardAssociateUnit: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "StandardAssociateUnit: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "StandardAssociateUnit: laurent",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "StandardAssociateUnit: for a polynomial ring and a polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StandardAssociateUnit",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrime: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsPrime: for Gaussian integers and integer",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "IsPrime: for a division ring and a ring element",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "IsPrime: for Gaussian integers and cyclotomic",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsPrime: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrime",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIrreducibleRingElement: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsIrreducibleRingElement: for a division ring and a ring element",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "IsIrreducibleRingElement: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "IsIrreducibleRingElement: for Z_(pi) and an element thereof (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsIrreducibleRingElement: AlgPol",
+                    "filters": [
+                        [
+                            "IsAlgebraicExtensionPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "IsIrreducibleRingElement: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "IsIrreducibleRingElement:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIrreducibleRingElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EuclideanDegree: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "EuclideanDegree: laurent",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "EuclideanDegree: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "EuclideanDegree: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "EuclideanDegree: for a division ring and a ring element",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "EuclideanDegree: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "EuclideanDegree: univariate,ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "EuclideanDegree: laurent,ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EuclideanDegree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EuclideanRemainder: laurent",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "EuclideanRemainder: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "EuclideanRemainder:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "EuclideanRemainder: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "EuclideanRemainder: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "EuclideanRemainder: laurent,ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "EuclideanRemainder: for a Euclidean ring and two ring elements",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "EuclideanRemainder:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EuclideanRemainder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EuclideanQuotient: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "EuclideanQuotient: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "EuclideanQuotient: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "EuclideanQuotient: for a Euclidean ring and two ring elements",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EuclideanQuotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "QuotientRemainder: laurent",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "QuotientRemainder: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "QuotientRemainder:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "QuotientRemainder: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "QuotientRemainder: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ],
+                        [
+                            "IsCyc"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "QuotientRemainder: for a division ring, and two ring elements",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "QuotientRemainder: laurent, ring",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "QuotientRemainder:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuotientRemainder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "QuotientMod: laurent",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "QuotientMod: for three ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "QuotientMod:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "QuotientMod: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "QuotientMod: laurent,ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "QuotientMod: for a Euclidean ring and three ring elements",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "QuotientMod:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuotientMod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PowerMod: laurent",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "PowerMod: for ring element, integer, and ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PowerMod:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "PowerMod: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "PowerMod: laurent,ring ",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "PowerMod: for Euclidean ring, ring element, integer, and ring element",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "PowerMod:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PowerMod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUniqueFactorizationRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GcdOp: univariate polynomials",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsRationalFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "GcdOp: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "GcdOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "GcdOp: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "GcdOp: rational univariate polynomials",
+                    "filters": [
+                        [
+                            "IsEuclideanRing",
+                            "IsRationalsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "GcdOp: for Z_(pi) and two elements thereof (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "GcdOp: univariate polynomials, ring",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "GcdOp: Gcd(Polyring, Pol,Pol)",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "GcdOp: multivariate Gcd based on Groebner bases",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "GcdOp: for a Euclidean ring and two ring elements",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "GcdOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GcdOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GcdRepresentationOp: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "GcdRepresentationOp: for a Euclidean ring and two ring elements",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GcdRepresentationOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUniqueFactorizationRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LcmOp: for two ring elements",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "LcmOp: lattice intersection in Z^n (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 118
+                },
+                {
+                    "comment": "LcmOp: for integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "LcmOp: for Z_(pi) and two elements thereof (ResClasses)",
+                    "filters": [
+                        [
+                            "IsZ_pi",
+                            "Tester(IsZ_pi)"
+                        ],
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "LcmOp: multivariate Lcm based on Groebner bases",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "LcmOp: for a Euclidean ring and two ring elements",
+                    "filters": [
+                        [
+                            "IsUniqueFactorizationRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LcmOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PadicValuation: for rationals",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PadicValuation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGeneralizedCartanMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGeneralizedCartanMatrix)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "IsGeneralizedCartanMatrix: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGeneralizedCartanMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGeneralizedCartanMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGeneralizedCartanMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGeneralizedCartanMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGeneralizedCartanMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsDiagonalMat: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsDiagonalMat: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsDiagonalMat",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsDiagonalMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUpperTriangularMat: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsUpperTriangularMat: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUpperTriangularMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLowerTriangularMat: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsLowerTriangularMat: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLowerTriangularMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaseMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BaseMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "BaseMat: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BaseMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BaseMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BaseMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BaseMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaseMatDestructive: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaseOrthogonalSpaceMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BaseOrthogonalSpaceMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "BaseOrthogonalSpaceMat: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseOrthogonalSpaceMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BaseOrthogonalSpaceMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BaseOrthogonalSpaceMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BaseOrthogonalSpaceMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BaseOrthogonalSpaceMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefaultFieldOfMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DefaultFieldOfMatrix)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "DefaultFieldOfMatrix: method for a compressed matrix over GF(q)",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "DefaultFieldOfMatrix: method for a matrix over GF(2)",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "DefaultFieldOfMatrix: method for a matrix over the cyclotomics",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "DefaultFieldOfMatrix: method for a matrix over a finite field",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "DefaultFieldOfMatrix: default method for a matrix (return `fail')",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefaultFieldOfMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DefaultFieldOfMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DefaultFieldOfMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DefaultFieldOfMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DefaultFieldOfMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DepthOfUpperTriangularMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DepthOfUpperTriangularMatrix)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "DepthOfUpperTriangularMatrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DepthOfUpperTriangularMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DepthOfUpperTriangularMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DepthOfUpperTriangularMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DepthOfUpperTriangularMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DepthOfUpperTriangularMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DeterminantMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DeterminantMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "DeterminantMat: for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeterminantMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DeterminantMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DeterminantMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DeterminantMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DeterminantMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DeterminantMatDestructive: kernel method for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "DeterminantMatDestructive: kernel method for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "DeterminantMatDestructive: non fraction free",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "DeterminantMatDestructive: nonprime residue rings",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "DeterminantMatDestructive: fraction-free method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeterminantMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DeterminantMatDivFree: Division-free method",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeterminantMatDivFree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DimensionsMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DimensionsMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "DimensionsMat: for a matrix with memory",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "DimensionsMat: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "DimensionsMat",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "DimensionsMat: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DimensionsMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DimensionsMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DimensionsMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DimensionsMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DimensionsMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ElementaryDivisorsMat: compatibility method -- supply ring",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ElementaryDivisorsMat: generic method for euclidean rings",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementaryDivisorsMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ElementaryDivisorsTransformationsMat: compatibility method -- supply ring",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ElementaryDivisorsTransformationsMat: over the integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "ElementaryDivisorsTransformationsMat: generic method for euclidean rings",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementaryDivisorsTransformationsMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizedNullspaceMatNT: generic method",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizedNullspaceMatNT",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NullspaceMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NullspaceMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "NullspaceMat: generic method for ordinary matrices",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NullspaceMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NullspaceMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NullspaceMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NullspaceMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NullspaceMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizedNullspaceMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TriangulizedNullspaceMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "TriangulizedNullspaceMat: generic method for ordinary matrices",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizedNullspaceMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TriangulizedNullspaceMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TriangulizedNullspaceMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TriangulizedNullspaceMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TriangulizedNullspaceMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NullspaceMatDestructive: generic method for ordinary matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NullspaceMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizedNullspaceMatDestructive: generic method for ordinary matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizedNullspaceMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GeneralisedEigenvalues: for a matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 81
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneralisedEigenvalues",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GeneralisedEigenspaces: for a matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 81
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneralisedEigenspaces",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Eigenvalues: for a matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "Eigenvalues",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Eigenvalues",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Eigenspaces: for a matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 81
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Eigenspaces",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Eigenvectors: for a matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 81
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Eigenvectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ProjectiveOrder: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ProjectiveOrder)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "ProjectiveOrder: object with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "ProjectiveOrder: ordinary matrix of finite field elements",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ProjectiveOrder: divide and conquer for univariate polynomials",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ProjectiveOrder:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectiveOrder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ProjectiveOrder): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ProjectiveOrder): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ProjectiveOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ProjectiveOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RankMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "RankMat: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "RankMat: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RankMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RankMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RankMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RankMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RankMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankMatDestructive: kernel method for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "RankMatDestructive: kernel method for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "RankMatDestructive: generic method for mutable matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RankMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiEchelonMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemiEchelonMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "SemiEchelonMat: shortcut method for 8bit matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "SemiEchelonMat: shortcut method for GF2 matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "SemiEchelonMat: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemiEchelonMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemiEchelonMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemiEchelonMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemiEchelonMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiEchelonMatDestructive: kernel method for plain lists of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "SemiEchelonMatDestructive: kernel method for plain lists of 8bit vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "SemiEchelonMatDestructive: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiEchelonMatTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemiEchelonMatTransformation)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "SemiEchelonMatTransformation: shortcut method for 8bit matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "SemiEchelonMatTransformation: kernel method for plain lists of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "SemiEchelonMatTransformation: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonMatTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemiEchelonMatTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemiEchelonMatTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemiEchelonMatTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemiEchelonMatTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiEchelonMatTransformationDestructive: kernel method for plain lists of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "SemiEchelonMatTransformationDestructive:  kernel method for plain lists of 8 bit vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "SemiEchelonMatTransformationDestructive: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonMatTransformationDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiEchelonMats: for list of matrices",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonMats",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiEchelonMatsDestructive: for list of matrices",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonMatsDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransposedMatImmutable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransposedMatImmutable)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "TransposedMatImmutable: for a compressed 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "TransposedMatImmutable: GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "TransposedMatImmutable: for an ordinary block matrix",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix",
+                            "IsBlockMatrixRep"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "TransposedMatImmutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "TransposedMatImmutable: generic method for matrices and lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransposedMatImmutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransposedMatImmutable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransposedMatImmutable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransposedMatImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransposedMatImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransposedMatMutable: for a compressed 8 bit matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "TransposedMatMutable: GF2 matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "TransposedMatMutable: generic method",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsRectangularTable",
+                            "Tester(IsRectangularTable)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "TransposedMatMutable: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "TransposedMatMutable: for arbitrary lists of lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransposedMatMutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MutableTransposedMatDestructive: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MutableTransposedMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransposedMatDestructive: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "TransposedMatDestructive: method for empty matrices",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransposedMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonomialMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMonomialMatrix)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "IsMonomialMatrix: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonomialMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMonomialMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMonomialMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMonomialMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMonomialMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InverseMatMod: method for a matrix, and an integer",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "InverseMatMod: generic method for matrix and integer",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseMatMod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "KroneckerProduct: for two 8bit matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 89
+                },
+                {
+                    "comment": "KroneckerProduct: for two 8bit matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "KroneckerProduct: for two gf2 matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "KroneckerProduct: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "KroneckerProduct: for two matrices",
+                    "filters": [
+                        [
+                            "IsMatrixObj"
+                        ],
+                        [
+                            "IsMatrixObj"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KroneckerProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SolutionMatNoCo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SolutionMat: generic method for ordinary matrix and vector",
+                    "filters": [
+                        [
+                            "IsOrdinaryMatrix"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SolutionMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SolutionMatDestructive: generic method",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsOrdinaryMatrix"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SolutionMatDestructive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SumIntersectionMat",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "SumIntersectionMat",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SumIntersectionMat",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SumIntersectionMat",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SumIntersectionMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizedMat: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizedMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizeMat: kernel method for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "TriangulizeMat: method for compressed matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "TriangulizeMat: kernel method for plain list of GF2 vectors",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "IsPlistRep",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "TriangulizeMat: for GF2 matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "TriangulizeMat: for a mutable ordinary matrix over a ring Z/nZ",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "IsOrdinaryMatrix",
+                            "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "TriangulizeMat: generic method for mutable matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "TriangulizeMat: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizeMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UpperSubdiagonal",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UpperSubdiagonal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMutable",
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DiagonalizeMat: over the integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "DiagonalizeMat: method for general Euclidean Ring",
+                    "filters": [
+                        [
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 62
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DiagonalizeMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MutableCopyMat: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "MutableCopyMat: for an 8bit matrix",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "MutableCopyMat: for a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "MutableCopyMat: generic method",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MutableCopyMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TraceMat: generic method",
+                    "filters": [
+                        [
+                            "IsMatrixObj"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "TraceMat: method for lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TraceMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "JordanDecomposition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(JordanDecomposition)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "JordanDecomposition: method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "JordanDecomposition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(JordanDecomposition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(JordanDecomposition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(JordanDecomposition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(JordanDecomposition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacteristicPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CharacteristicPolynomial)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "CharacteristicPolynomial: supply field and indeterminate 1",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CharacteristicPolynomial: supply indeterminate 1",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "CharacteristicPolynomial: supply field",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CharacteristicPolynomial: supply indeterminate 1",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 132
+                },
+                {
+                    "comment": "CharacteristicPolynomial: call `TracePolynomial'",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "CharacteristicPolynomial: check default field, print error if ambiguous",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 103
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "CharacteristicPolynomial: spinning over field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 153
+                },
+                {
+                    "comment": "CharacteristicPolynomial: call `TracePolynomial'",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 133
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacteristicPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CharacteristicPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CharacteristicPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CharacteristicPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CharacteristicPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsOrdinaryMatrix"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CharacteristicPolynomialMatrixNC: spinning over field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 102
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacteristicPolynomialMatrixNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsOrdinaryMatrix"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "MinimalPolynomialMatrixNC: spinning over field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 102
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalPolynomialMatrixNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FieldOfMatrixList: finite field matrices",
+                    "filters": [
+                        [
+                            "IsListOrCollection",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "FieldOfMatrixList: generic: form field",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FieldOfMatrixList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefaultScalarDomainOfMatrixList: finite field matrices",
+                    "filters": [
+                        [
+                            "IsListOrCollection",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "DefaultScalarDomainOfMatrixList: generic: form ring",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefaultScalarDomainOfMatrixList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaseField: for a compressed 8bit matrix",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "BaseField: for a compressed gf2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "BaseField: for a compressed 8bit vector",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "BaseField: for a compressed gf2 vector",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizedIntegerMat: dispatch",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "TriangulizedIntegerMat: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "TriangulizedIntegerMat: empty matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizedIntegerMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizeIntegerMat: dispatch",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "TriangulizeIntegerMat: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizeIntegerMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TriangulizedIntegerMatTransform: dispatch",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "TriangulizedIntegerMatTransform: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "TriangulizedIntegerMatTransform: empty matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TriangulizedIntegerMatTransform",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HermiteNormalFormIntegerMat: dispatch",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "HermiteNormalFormIntegerMat: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "HermiteNormalFormIntegerMat: empty matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HermiteNormalFormIntegerMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HermiteNormalFormIntegerMatTransform: dispatch",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "HermiteNormalFormIntegerMatTransform: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "HermiteNormalFormIntegerMatTransform: empty matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HermiteNormalFormIntegerMatTransform",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SmithNormalFormIntegerMat: dispatch",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "SmithNormalFormIntegerMat: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "SmithNormalFormIntegerMat: empty matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SmithNormalFormIntegerMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SmithNormalFormIntegerMatTransforms: dispatch",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "SmithNormalFormIntegerMatTransforms: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "SmithNormalFormIntegerMatTransforms: empty matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SmithNormalFormIntegerMatTransforms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaseIntMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BaseIntMat)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "BaseIntMat: use HNF",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "BaseIntMat: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseIntMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BaseIntMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BaseIntMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BaseIntMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BaseIntMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BaseIntersectionIntMats: use HNF",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "BaseIntersectionIntMats: emptyR",
+                    "filters": [
+                        [],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "BaseIntersectionIntMats: emptyL",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseIntersectionIntMats",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ComplementIntMat: use HNF and SNF",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "ComplementIntMat: empty submodule",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 59
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComplementIntMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NullspaceIntMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NullspaceIntMat)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "NullspaceIntMat: use HNF",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NullspaceIntMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NullspaceIntMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NullspaceIntMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NullspaceIntMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NullspaceIntMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SolutionIntMat: use HNF",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "SolutionIntMat: empty",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SolutionIntMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                    "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SolutionNullspaceIntMat: use HNF",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SolutionNullspaceIntMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AbelianInvariantsOfList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AbelianInvariantsOfList)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "AbelianInvariantsOfList",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "AbelianInvariantsOfList",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbelianInvariantsOfList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AbelianInvariantsOfList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AbelianInvariantsOfList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AbelianInvariantsOfList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AbelianInvariantsOfList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MatrixByBlockMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MatrixByBlockMatrix)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "MatrixByBlockMatrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MatrixByBlockMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MatrixByBlockMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MatrixByBlockMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MatrixByBlockMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MatrixByBlockMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsTwoSidedIdealOp: for anti-commutative FLMLOR and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsAnticommutative",
+                            "Tester(IsAnticommutative)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsTwoSidedIdealOp: for commutative FLMLOR and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsTwoSidedIdealOp: for FLMLOR and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "IsTwoSidedIdealOp: for rings and subrings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTwoSidedIdealOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTwoSidedIdealInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTwoSidedIdealInParent)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsTwoSidedIdealInParent",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsRightIdealInParent",
+                            "Tester(IsRightIdealInParent)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsTwoSidedIdealInParent",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsLeftIdealInParent",
+                            "Tester(IsLeftIdealInParent)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsTwoSidedIdealInParent: method that calls the two-argument operation IsTwoSidedIdealOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "IsTwoSidedIdealInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTwoSidedIdealInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTwoSidedIdealInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTwoSidedIdealInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTwoSidedIdealInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTwoSidedIdealInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsTwoSidedIdeal: try to exploit the in-parent attribute IsTwoSidedIdealInParent",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTwoSidedIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsLeftIdealOp: for associative FLMLOR and FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IsLeftIdealOp: for associative FLMLOR-with-one and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "IsLeftIdealOp: for associative FLMLOR and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsLeftIdealOp: for SCRings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsLeftIdealOp: for FLMLOR and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftIdealOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLeftIdealInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLeftIdealInParent)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsLeftIdealInParent: method that calls the two-argument operation IsLeftIdealOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "IsLeftIdealInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftIdealInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLeftIdealInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLeftIdealInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLeftIdealInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLeftIdealInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsLeftIdeal: left ideal in ring, naive",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 79
+                },
+                {
+                    "comment": "IsLeftIdeal: try to exploit the in-parent attribute IsLeftIdealInParent",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsRightIdealOp: for associative FLMLOR and FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IsRightIdealOp: for associative FLMLOR-with-one and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "IsRightIdealOp: for associative FLMLOR and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsRightIdealOp: for SCRings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsRightIdealOp: for FLMLOR and free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRightIdealOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRightIdealInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRightIdealInParent)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "IsRightIdealInParent: method that calls the two-argument operation IsRightIdealOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "IsRightIdealInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRightIdealInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRightIdealInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRightIdealInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRightIdealInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRightIdealInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsRightIdeal: try to exploit the in-parent attribute IsRightIdealInParent",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRightIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TwoSidedIdealByGenerators: for Lie algebra and collection of Lie objects",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "TwoSidedIdealByGenerators: for matrix algebra and empty list",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "TwoSidedIdealByGenerators: for Lie algebra and empty list",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "TwoSidedIdealByGenerators: for Gaussian matrix algebra and list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "TwoSidedIdealByGenerators: for non-Gaussian matrix algebra and list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsNonGaussianMatrixSpace"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "TwoSidedIdealByGenerators: for FLMLOR and empty list",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "TwoSidedIdealByGenerators: for FLMLOR and collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "TwoSidedIdealByGenerators: for ring and collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TwoSidedIdealByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftIdealByGenerators: for Lie algebra and collection of Lie objects",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "LeftIdealByGenerators: for matrix algebra and empty list",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "LeftIdealByGenerators: for Lie algebra and empty list",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "LeftIdealByGenerators: for Gaussian matrix algebra and list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "LeftIdealByGenerators: for non-Gaussian matrix algebra and list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsNonGaussianMatrixSpace"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "LeftIdealByGenerators: for FLMLOR and empty list",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "LeftIdealByGenerators: to construct ideals of commutative rings",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "LeftIdealByGenerators: for FLMLOR and collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "LeftIdealByGenerators: for ring and collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftIdealByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightIdealByGenerators: for Lie algebra and collection of Lie objects",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "RightIdealByGenerators: for matrix algebra and empty list",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "RightIdealByGenerators: for Lie algebra and empty list",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "RightIdealByGenerators: for Gaussian matrix algebra and list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "RightIdealByGenerators: for non-Gaussian matrix algebra and list of matrices",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsNonGaussianMatrixSpace"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "RightIdealByGenerators: for FLMLOR and empty list",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "RightIdealByGenerators: to construct ideals of commutative rings",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "RightIdealByGenerators: for FLMLOR and collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "RightIdealByGenerators: for ring and collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightIdealByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfTwoSidedIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfTwoSidedIdeal)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "GeneratorsOfTwoSidedIdeal: for a two-sided ideal with known `GeneratorsOfRightIdeal'",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "GeneratorsOfTwoSidedIdeal: for a two-sided ideal with known `GeneratorsOfLeftIdeal'",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "GeneratorsOfTwoSidedIdeal: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfTwoSidedIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfTwoSidedIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfTwoSidedIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfTwoSidedIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfTwoSidedIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfLeftIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfLeftIdeal)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "GeneratorsOfLeftIdeal: for an ideal with known `GeneratorsOfTwoSidedIdeal'",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "GeneratorsOfLeftIdeal: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfLeftIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfLeftIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfLeftIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfLeftIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfLeftIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfRightIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfRightIdeal)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "GeneratorsOfRightIdeal: for an ideal with known `GeneratorsOfTwoSidedIdeal'",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "GeneratorsOfRightIdeal: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfRightIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfRightIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfRightIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfRightIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfRightIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeftActingRingOfIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeftActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "LeftActingRingOfIdeal: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftActingRingOfIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeftActingRingOfIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeftActingRingOfIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeftActingRingOfIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeftActingRingOfIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RightActingRingOfIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RightActingRingOfIdeal)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "RightActingRingOfIdeal: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightActingRingOfIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RightActingRingOfIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RightActingRingOfIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RightActingRingOfIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RightActingRingOfIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsLeftIdeal: for two FLMLORs",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "AsLeftIdeal: for two rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsLeftIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsRightIdeal: for two FLMLORs",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "AsRightIdeal: for two rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsRightIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsTwoSidedIdeal: for two FLMLORs",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "AsTwoSidedIdeal: for two rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsTwoSidedIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFiniteDimensional: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFiniteDimensional)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "IsFiniteDimensional: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsFiniteDimensional: for a f.p. Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsFiniteDimensional: for a left module of free magma ring elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorRing)",
+                            "CategoryCollections(IsElementOfFreeMagmaRing)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "IsFiniteDimensional: for f.p. algebra",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "IsFiniteDimensional: for a magma ring modulo the span of ``zero''",
+                    "filters": [
+                        [
+                            "IsMagmaRingModuloSpanOfZero"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsFiniteDimensional: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsFiniteDimensional: for an ideal in an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(RightActingRingOfIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsFiniteDimensional: for an ideal in an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsFiniteDimensional: for a space of algebra module elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "IsFiniteDimensional: for a free left module with known dimension",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFiniteDimensional",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFiniteDimensional): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFiniteDimensional): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFiniteDimensional)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFiniteDimensional)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullRowModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "IsFullRowModule: for Gaussian row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsFullRowModule: for non-Gaussian row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsNonGaussianRowSpace"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsFullRowModule: for free left (row) module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsFullRowModule: for arbitrary free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullRowModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullRowModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullRowModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullRowModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullRowModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullMatrixModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "IsFullMatrixModule: for Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsFullMatrixModule: for non-Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsNonGaussianMatrixSpace"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "IsFullMatrixModule: for matrix module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsFullMatrixModule: for arbitrary free left module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullMatrixModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullMatrixModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullMatrixModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullMatrixModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullMatrixModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Dimension: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "Dimension: for full matrix module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Dimension: for full row module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Dimension: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Dimension: for a f.p. Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Dimension: for a magma ring modulo the span of ``zero''",
+                    "filters": [
+                        [
+                            "IsMagmaRingModuloSpanOfZero"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Dimension: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Dimension: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Dimension: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Dimension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Dimension): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Dimension): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Dimension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Dimension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsDistributiveLOpDSum",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 20021
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for FLMLOR with known right ideal generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for FLMLOR with known left ideal generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for a finite field (return the vectors of the canonical basis)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for full matrix module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for full row module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for a magma ring modulo the span of ``zero''",
+                    "filters": [
+                        [
+                            "IsMagmaRingModuloSpanOfZero"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for FLMLOR with known ideal generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for a FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: for a space of algebra module elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsFreeLeftModule",
+                            "Tester(Basis)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorAdditiveGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsDistributiveLOpDSum",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfLeftOperatorAdditiveGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsDistributiveLOpDSum",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfLeftOperatorAdditiveGroup): method that checks for `IsFiniteDimensional'",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Setter(GeneratorsOfLeftOperatorAdditiveGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfLeftOperatorAdditiveGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfLeftOperatorAdditiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsDistributiveLOpDSum",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfLeftOperatorAdditiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet",
+                    "IsDistributiveROpDSum",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfRightOperatorAdditiveGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfRightOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 20021
+                },
+                {
+                    "comment": "GeneratorsOfRightOperatorAdditiveGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtRSet",
+                            "IsDistributiveROpDSum",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfRightOperatorAdditiveGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet",
+                    "IsDistributiveROpDSum",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfRightOperatorAdditiveGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfRightOperatorAdditiveGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfRightOperatorAdditiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtRSet",
+                    "IsDistributiveROpDSum",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfRightOperatorAdditiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsLeftModule: for two division rings",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "AsLeftModule: for division ring and matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "AsLeftModule: method for a division ring and a vector space",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "AsLeftModule:  for a ring and a left module",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "AsLeftModule: generic method for a ring and a collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsLeftModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClosureLeftModule: for two left modules",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ClosureLeftModule: method for a vector space with basis, and a vector",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "Tester(Basis)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ClosureLeftModule: for free left module and vector",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(Basis)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ClosureLeftModule: for left module and vector",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClosureLeftModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftModuleByGenerators: for division ring and matrix over it",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "LeftModuleByGenerators: for ring and collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "LeftModuleByGenerators: for division ring, matrix over it, and row vector",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "LeftModuleByGenerators: for division ring, empty list, and row vector",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 79
+                },
+                {
+                    "comment": "LeftModuleByGenerators: for ring, homogeneous list, and vector",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftModuleByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UseBasis: for a free left module and a homog. list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UseBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRowModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "IsRowModule: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsRowModule: return `false' for objects which are not free left modules",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRowModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRowModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRowModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRowModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRowModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMatrixModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMatrixModule)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "IsMatrixModule: for a free left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsMatrixModule: for a free left module without generators",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsMatrixModule: return `false' for objects which are not free left modules",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMatrixModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMatrixModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMatrixModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMatrixModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMatrixModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DimensionOfVectors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DimensionOfVectors)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "DimensionOfVectors: generic method for left modules",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DimensionOfVectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DimensionOfVectors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DimensionOfVectors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DimensionOfVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DimensionOfVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCanonicalBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCanonicalBasis)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsCanonicalBasis: for a basis handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsBasisByNiceBasis"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsCanonicalBasis: for a basis with replaced left module, and a vector",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisWithReplacedLeftModuleRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsCanonicalBasis: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCanonicalBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCanonicalBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCanonicalBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCanonicalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCanonicalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCanonicalBasisFullRowModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCanonicalBasisFullRowModule)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsCanonicalBasisFullRowModule: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCanonicalBasisFullRowModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCanonicalBasisFullRowModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCanonicalBasisFullRowModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCanonicalBasisFullRowModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCanonicalBasisFullRowModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCanonicalBasisFullMatrixModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCanonicalBasisFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsCanonicalBasisFullMatrixModule: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCanonicalBasisFullMatrixModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCanonicalBasisFullMatrixModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCanonicalBasisFullMatrixModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCanonicalBasisFullMatrixModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCanonicalBasisFullMatrixModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIntegralBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIntegralBasis)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIntegralBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIntegralBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIntegralBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIntegralBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIntegralBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNormalBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNormalBasis)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsNormalBasis: for a basis of a field",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormalBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNormalBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNormalBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNormalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNormalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSemiEchelonized: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSemiEchelonized)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsSemiEchelonized: for basis (of a Gaussian matrix space)",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsSemiEchelonized: for basis of a Gaussian row space",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSemiEchelonized",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSemiEchelonized): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSemiEchelonized): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSemiEchelonized)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSemiEchelonized)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BasisVectors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BasisVectors)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "BasisVectors: for empty basis",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 10018
+                },
+                {
+                    "comment": "BasisVectors: for canonical basis of a full matrix module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisFullMatrixModule",
+                            "Tester(IsCanonicalBasisFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "BasisVectors: for canonical basis of a full row module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisFullRowModule",
+                            "Tester(IsCanonicalBasisFullRowModule)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "BasisVectors: for semi-ech. basis of a Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonBasisOfGaussianMatrixSpaceRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "BasisVectors: for semi-ech. basis of a Gaussian row space",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonBasisOfGaussianRowSpaceRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "BasisVectors: for canon. basis of cyclotomic field of cyclotomics",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisCyclotomicFieldRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "BasisVectors: for basis by nice basis",
+                    "filters": [
+                        [
+                            "IsBasisByNiceBasis"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "BasisVectors: for canon. basis of an algebraic extension",
+                    "filters": [
+                        [
+                            "IsCanonicalBasisAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "BasisVectors: for canonical basis of full s. c. algebra",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasisFullSCAlgebra",
+                            "Tester(IsCanonicalBasisFullSCAlgebra)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "BasisVectors: for a basis with replaced left module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisWithReplacedLeftModuleRep"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "BasisVectors: for pseudo canonical basis of a full hom module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsPseudoCanonicalBasisFullHomModule",
+                            "Tester(IsPseudoCanonicalBasisFullHomModule)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "BasisVectors: for mutable basis with underlying mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaUnderlyingMutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "BasisVectors: for a mutable basis of a Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianMatrixSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "BasisVectors: for a mutable basis of a Gaussian row space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianRowSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "BasisVectors: for mutable basis represented by a nice mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaNiceMutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "BasisVectors: for mutable basis represented by an immutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisByImmutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BasisVectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BasisVectors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BasisVectors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BasisVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BasisVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EnumeratorByBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EnumeratorByBasis)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "EnumeratorByBasis: for enumerator via canonical basis of a full row module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisFullRowModule",
+                            "Tester(IsCanonicalBasisFullRowModule)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "EnumeratorByBasis: for basis of a finite dimensional left module",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EnumeratorByBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EnumeratorByBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EnumeratorByBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EnumeratorByBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EnumeratorByBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StructureConstantsTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StructureConstantsTable)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "StructureConstantsTable: LAGUNA: for a basis of a Lie algebra of a group algebra",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsBasisOfLieAlgebraOfGroupRing",
+                            "Tester(IsBasisOfLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "StructureConstantsTable: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StructureConstantsTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StructureConstantsTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StructureConstantsTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StructureConstantsTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StructureConstantsTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingLeftModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingLeftModule)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingLeftModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingLeftModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingLeftModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingLeftModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingLeftModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Coefficients: for empty basis and vector",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsBasis"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 10025
+                },
+                {
+                    "comment": "Coefficients: for basis of a monomial space, and a vector",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisOfMonomialSpaceRep"
+                        ],
+                        [
+                            "IsMonomialElement",
+                            "IsMonomialElementRep"
+                        ]
+                    ],
+                    "rank": 10019
+                },
+                {
+                    "comment": "Coefficients: for basis of a sparse rowspace, and a vector",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisOfSparseRowSpaceRep"
+                        ],
+                        [
+                            "IsSparseRowSpaceElement"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "Coefficients: for canonical basis of a full matrix module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasisFullMatrixModule",
+                            "Tester(IsCanonicalBasisFullMatrixModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Coefficients: for semi-ech. basis of a Gaussian matrix space, and a matrix",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonBasisOfGaussianMatrixSpaceRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Coefficients: for pseudo can. basis of full hom module, and lin. m.b.m.",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsPseudoCanonicalBasisFullHomModule",
+                            "Tester(IsPseudoCanonicalBasisFullHomModule)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsLinearMappingByMatrixDefaultRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Coefficients: for basis of matrix field",
+                    "filters": [
+                        [
+                            "IsBasisOfMatrixField"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Coefficients: For a FFE in Conway polynomial represntation wrt the canonical basis of its natural field",
+                    "filters": [
+                        [
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsBasisFiniteFieldRep"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Coefficients: for canonical basis of cyclotomic field, and cyclotomic",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisCyclotomicFieldRep"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "Coefficients: for canonical basis of abelian number field, and cyclotomic",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisAbelianNumberFieldRep"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Coefficients: for canon. basis of Gaussian integers, and cyclotomic",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisGaussianIntegersRep"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Coefficients: for canonical basis of a full row module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasisFullRowModule",
+                            "Tester(IsCanonicalBasisFullRowModule)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Coefficients: for the canonical basis of Integers",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisIntegersRep"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Coefficients: for canon. basis of an algebraic extension, and alg. element",
+                    "filters": [
+                        [
+                            "IsCanonicalBasisAlgebraicExtension"
+                        ],
+                        [
+                            "IsAlgebraicElement"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Coefficients: for semi-ech. basis of a Gaussian row space, and a row vector",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonBasisOfGaussianRowSpaceRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Coefficients: for canon. basis of a free magma ring, and a vector",
+                    "filters": [
+                        [
+                            "IsCanonicalBasisFreeMagmaRingRep"
+                        ],
+                        [
+                            "IsElementOfFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Coefficients: for a basis of a finite field, and a scalar",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisFiniteFieldRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Coefficients: for canon. basis of an algebraic extension, and scalar",
+                    "filters": [
+                        [
+                            "IsCanonicalBasisAlgebraicExtension"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Coefficients: for canonical basis of full s. c. algebra",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasisFullSCAlgebra",
+                            "Tester(IsCanonicalBasisFullSCAlgebra)"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Coefficients: for basis handled by nice basis, and vector",
+                    "filters": [
+                        [
+                            "IsBasisByNiceBasis"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Coefficients: for relative basis and vector",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsRelativeBasisDefaultRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Coefficients: method for canonical basis of Rationals",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasis",
+                            "Tester(IsCanonicalBasis)",
+                            "IsCanonicalBasisRationals"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Coefficients: for basis of weight rep elements, and algebra module element",
+                    "filters": [
+                        [
+                            "IsBasisOfWeightRepElementSpace"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsWeightRepElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Coefficients: for basis of a space of algebra module elements, and algebra module element",
+                    "filters": [
+                        [
+                            "IsBasisOfAlgebraModuleElementSpace"
+                        ],
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Coefficients: for a basis with replaced left module, and a vector",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisWithReplacedLeftModuleRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Coefficients: for pseudo canon. basis of a full hom module, and lin. mapping",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsPseudoCanonicalBasisFullHomModule",
+                            "Tester(IsPseudoCanonicalBasisFullHomModule)"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Coefficients",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LinearCombination: for empty basis and empty list",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsBasis"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 10035
+                },
+                {
+                    "comment": "LinearCombination",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonBasisOfGaussianRowSpaceRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "LinearCombination: for canonical basis of full s. c. algebra",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasisFullSCAlgebra",
+                            "Tester(IsCanonicalBasisFullSCAlgebra)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "LinearCombination: for a basis of a finite field, and a hom. list",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisFiniteFieldRep"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "LinearCombination: for a basis with replaced left module, and a hom. list",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsBasisWithReplacedLeftModuleRep"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "LinearCombination: for a basis and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "LinearCombination: for two lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LinearCombination",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SiftedVector: for empty basis and vector",
+                    "filters": [
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)",
+                            "IsBasis"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 10025
+                },
+                {
+                    "comment": "SiftedVector: for semi-ech. basis of Gaussian matrix space, and matrix",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonBasisOfGaussianMatrixSpaceRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "SiftedVector: for mutable basis of Gaussian matrix space, and matrix",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianMatrixSpaceRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SiftedVector: for semi-ech. basis of Gaussian row space, and row vector",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsSemiEchelonBasisOfGaussianRowSpaceRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "SiftedVector: for mutable basis of Gaussian row space, and row vector",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianRowSpaceRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SiftedVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IteratorByBasis: for canonical basis of a full row module",
+                    "filters": [
+                        [
+                            "IsBasis",
+                            "IsCanonicalBasisFullRowModule",
+                            "Tester(IsCanonicalBasisFullRowModule)"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IteratorByBasis: for basis of a finite dimensional left module",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IteratorByBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ],
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Basis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Basis)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "Basis: for a free module of sparse row space elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSparseRowSpaceElement)"
+                        ]
+                    ],
+                    "rank": 10028
+                },
+                {
+                    "comment": "Basis: for a space of monomial elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsMonomialElement)"
+                        ]
+                    ],
+                    "rank": 10028
+                },
+                {
+                    "comment": "Basis: for abelian number field of cyclotomics (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 2065
+                },
+                {
+                    "comment": "Basis: for a finite field (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 2056
+                },
+                {
+                    "comment": "Basis: for an algebraic extension (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 2053
+                },
+                {
+                    "comment": "Basis: for full matrix module (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 2048
+                },
+                {
+                    "comment": "Basis: for full row module (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 2048
+                },
+                {
+                    "comment": "Basis: for Gaussian integers (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ]
+                    ],
+                    "rank": 2042
+                },
+                {
+                    "comment": "Basis: for full s. c. algebra (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSCAlgebraObj)",
+                            "IsFullSCAlgebra",
+                            "Tester(IsFullSCAlgebra)"
+                        ]
+                    ],
+                    "rank": 2041
+                },
+                {
+                    "comment": "Basis: for integers (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": 2039
+                },
+                {
+                    "comment": "Basis: for a free magma ring (delegate to `CanonicalBasis')",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 2036
+                },
+                {
+                    "comment": "Basis: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 125
+                },
+                {
+                    "comment": "Basis: for matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "Basis: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Basis: for an associative FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "Basis: for an associative FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Basis: for a FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Basis: for Gaussian matrix space (construct a semi-echelonized basis)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Basis: for Gaussian row space (construct a semi-echelonized basis)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Basis: for trivial free left module",
+                    "filters": [
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Basis: for a space of weight rep elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsWeightRepElement)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Basis: for a space of algebra module elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Basis: for free module that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Basis",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsFreeLeftModule",
+                            "Tester(CanonicalBasis)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Basis: for an algebra module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Basis: for group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Basis: for a space of monomial elements and a list of tensor elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsMonomialElement)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsMonomialElement)"
+                        ]
+                    ],
+                    "rank": 10048
+                },
+                {
+                    "comment": "Basis: for a free module of sparse row space elements, and list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSparseRowSpaceElement)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 10032
+                },
+                {
+                    "comment": "Basis: for a finite field, and a hom. list",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "Basis: for Gaussian row space and matrix (try semi-echelonized)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "Basis: for a space of weight rep elements and a list of weight rep elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsWeightRepElement)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsWeightRepElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Basis: for a space of algebra module elements and a collection of algebra module elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Basis: for free left module and empty list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "Basis: for Gaussian matrix space and list of matrices (try semi-ech.)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Basis: for free module that is handled by a nice basis, and hom. list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Basis: method returning a relative basis",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Basis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Basis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Basis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Basis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Basis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BasisNC: for a space of monomial elements and a list of monomial elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsMonomialElement)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsMonomialElement)"
+                        ]
+                    ],
+                    "rank": 10048
+                },
+                {
+                    "comment": "BasisNC: for a free module of sparse row space elements, and list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSparseRowSpaceElement)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 10032
+                },
+                {
+                    "comment": "BasisNC: for a finite field, and a hom. list",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "BasisNC: for Gaussian row space and matrix (try semi-echelonized)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "BasisNC: for a space of weight rep elements and a list of weight rep elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsWeightRepElement)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsWeightRepElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "BasisNC: for a space of algebra module elements and a collection of algebra module elements",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "BasisNC: for free left module and empty list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "BasisNC: for Gaussian matrix space and list of matrices (try semi-ech.)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "BasisNC: for free module that is handled by a nice basis, and hom. list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "BasisNC: method returning a relative basis",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BasisNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ],
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiEchelonBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemiEchelonBasis)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "SemiEchelonBasis",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace",
+                            "Tester(CanonicalBasis)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SemiEchelonBasis",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace",
+                            "Tester(CanonicalBasis)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SemiEchelonBasis: for Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "SemiEchelonBasis: for Gaussian row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SemiEchelonBasis: for Gaussian row space and matrix",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "SemiEchelonBasis: for free left module and empty list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "SemiEchelonBasis: for Gaussian matrix space and list of matrices",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemiEchelonBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemiEchelonBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemiEchelonBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemiEchelonBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SemiEchelonBasisNC: for Gaussian row space and matrix",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "SemiEchelonBasisNC: for free left module and empty list",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "SemiEchelonBasisNC: for Gaussian matrix space and list of matrices",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiEchelonBasisNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RelativeBasis: for a basis and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelativeBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RelativeBasisNC: for a basis and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelativeBasisNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasisByNiceBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceBasis)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "NiceBasis: for basis by nice basis",
+                    "filters": [
+                        [
+                            "IsBasisByNiceBasis"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasisByNiceBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasisByNiceBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasisByNiceBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceBasisNC: for basis by nice basis with precomputed basis",
+                    "filters": [
+                        [
+                            "IsBasisByNiceBasis",
+                            "Tester(NiceBasis)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "NiceBasisNC: for basis by nice basis",
+                    "filters": [
+                        [
+                            "IsBasisByNiceBasis"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceBasisNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceFreeLeftModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceFreeLeftModule)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "NiceFreeLeftModule: for commutative FLMLOR that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "NiceFreeLeftModule: for anticommutative FLMLOR that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsAnticommutative",
+                            "Tester(IsAnticommutative)",
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "NiceFreeLeftModule: for associative FLMLOR that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "NiceFreeLeftModule: for FLMLOR that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "NiceFreeLeftModule: for full hom space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule",
+                            "IsFullHomModule",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "NiceFreeLeftModule: for free module that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModule: for generic finite space (use that this is a full row module)",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsGenericFiniteSpace"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceFreeLeftModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceFreeLeftModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceFreeLeftModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceFreeLeftModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceFreeLeftModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule",
+                    "IsHandledByNiceBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceFreeLeftModuleInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceFreeLeftModuleInfo)"
+                        ]
+                    ],
+                    "rank": 20027
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsLinearMappingsModule'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsLinearMappingsModule"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsClassFunctionsSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsClassFunctionsSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsFieldElementsSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFieldElementsSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsCochainsSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsCochainsSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsDirectSumElementsSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsDirectSumElementsSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsLieObjectsModule'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsLieObjectsModule"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsSCAlgebraObjSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSCAlgebraObjSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsSpaceOfUEAElements'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfUEAElements"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsFpAlgebraElementsSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFpAlgebraElementsSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsSpaceOfElementsOfMagmaRing'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfElementsOfMagmaRing"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsNonGaussianMatrixSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsNonGaussianMatrixSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsNonGaussianRowSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsNonGaussianRowSpace"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsSpaceOfRationalFunctions'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfRationalFunctions"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceFreeLeftModuleInfo: for left module in `IsGenericFiniteSpace'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsGenericFiniteSpace"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceFreeLeftModuleInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule",
+                    "IsHandledByNiceBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceFreeLeftModuleInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceFreeLeftModuleInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceFreeLeftModuleInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule",
+                    "IsHandledByNiceBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceFreeLeftModuleInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule",
+                    "IsHandledByNiceBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NiceVector: for left module in `IsLinearMappingsModule', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsLinearMappingsModule"
+                        ],
+                        []
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsClassFunctionsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsClassFunctionsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsFieldElementsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFieldElementsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsCochainsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsCochainsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsDirectSumElementsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsDirectSumElementsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsLieObjectsModule', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsLieObjectsModule"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsSCAlgebraObjSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSCAlgebraObjSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsSpaceOfUEAElements', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfUEAElements"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsFpAlgebraElementsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFpAlgebraElementsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsSpaceOfElementsOfMagmaRing', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfElementsOfMagmaRing"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsNonGaussianMatrixSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsNonGaussianMatrixSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsNonGaussianRowSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsNonGaussianRowSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsSpaceOfRationalFunctions', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfRationalFunctions"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "NiceVector: for left module in `IsGenericFiniteSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsGenericFiniteSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule",
+                    "IsHandledByNiceBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UglyVector: for left module in `IsLinearMappingsModule', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsLinearMappingsModule"
+                        ],
+                        []
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsClassFunctionsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsClassFunctionsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsFieldElementsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFieldElementsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsCochainsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsCochainsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsDirectSumElementsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsDirectSumElementsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsLieObjectsModule', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsLieObjectsModule"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsSCAlgebraObjSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSCAlgebraObjSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsSpaceOfUEAElements', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfUEAElements"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsFpAlgebraElementsSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFpAlgebraElementsSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsSpaceOfElementsOfMagmaRing', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfElementsOfMagmaRing"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsNonGaussianMatrixSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsNonGaussianMatrixSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsNonGaussianRowSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsNonGaussianRowSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsSpaceOfRationalFunctions', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsSpaceOfRationalFunctions"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "UglyVector: for left module in `IsGenericFiniteSpace', and object",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsGenericFiniteSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UglyVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MutableBasis: to construct a mutable basis of a Lie matrix space",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "MutableBasis: method to construct mutable bases of row spaces",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "MutableBasis: for ring and collection of Lie elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "MutableBasis: for ring and collection of s. c. algebra elements",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsSCAlgebraObj)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "MutableBasis: for ring and vectors",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "MutableBasis: to construct mutable bases of Gaussian matrix spaces",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "MutableBasis: generic method for ring and collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "MutableBasis: to construct mutable bases of matrix spaces",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "MutableBasis: method to construct mutable bases of row spaces",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "MutableBasis: for ring, (possibly empty) list, and Lie zero",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "MutableBasis: for ring, (possibly empty) list, and zero element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "MutableBasis: for ring, list and zero",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsAlgebraModuleElement"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "MutableBasis: generic method for ring, list, and object",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 28
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MutableBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutableBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrBasisVectors: for mutable basis represented by a nice mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaNiceMutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "NrBasisVectors: generic method for mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrBasisVectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutableBasis"
+                ]
+            ],
+            [
+                [
+                    "IsMutableBasis"
+                ],
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImmutableBasis: for a mutable basis of a Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianMatrixSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ImmutableBasis: for a mutable basis of a Gaussian row space",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianRowSpaceRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ImmutableBasis: for mutable basis represented by a nice mutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaNiceMutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "ImmutableBasis: for mutable basis represented by an immutable basis",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisByImmutableBasisRep"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ImmutableBasis: for mutable basis, and free left module",
+                    "filters": [
+                        [
+                            "IsMutableBasis"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImmutableBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsMutableBasis"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CloseMutableBasis: for a mut. basis of a Gaussian matrix space, and a matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianMatrixSpaceRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "CloseMutableBasis: for a mut. basis of a Gaussian row space, and a row vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianRowSpaceRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "CloseMutableBasis: for mutable basis with underlying mutable basis, and vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsMutableBasis",
+                            "IsMutableBasisViaUnderlyingMutableBasisRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "CloseMutableBasis: for mutable basis repres. by a nice mutable basis, and vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsMutableBasis",
+                            "IsMutableBasisViaNiceMutableBasisRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "CloseMutableBasis: for mutable basis represented by an immutable basis, and vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsMutableBasis",
+                            "IsMutableBasisByImmutableBasisRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CloseMutableBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutableBasis"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsContainedInSpan: for a mut. basis of a Gaussian matrix space, and a matrix",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianMatrixSpaceRep"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsContainedInSpan: for a mut. basis of a Gaussian row space, and a row vector",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisOfGaussianRowSpaceRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsContainedInSpan: for mutable basis with underlying mutable basis, and vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsMutableBasis",
+                            "IsMutableBasisViaUnderlyingMutableBasisRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "IsContainedInSpan: for mutable basis repres. by a nice mutable basis, and vector",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisViaNiceMutableBasisRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "IsContainedInSpan: for mutable basis represented by an immutable basis, and vector",
+                    "filters": [
+                        [
+                            "IsMutableBasis",
+                            "IsMutableBasisByImmutableBasisRep"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsContainedInSpan",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalBasis)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "CanonicalBasis: for Rationals",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "CanonicalBasis: for cyclotomic field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "CanonicalBasis: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "CanonicalBasis: for matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "CanonicalBasis: for a finite field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "CanonicalBasis: for an algebraic extension",
+                    "filters": [
+                        [
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "CanonicalBasis: for a full row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "CanonicalBasis: for full matrix space",
+                    "filters": [
+                        [
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "CanonicalBasis",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullMatrixModule",
+                            "Tester(IsFullMatrixModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "CanonicalBasis: for a full row module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "CanonicalBasis: LAGUNA: for a Lie algebra of a group algebra",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "CanonicalBasis: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "CanonicalBasis: for Gaussian integers",
+                    "filters": [
+                        [
+                            "IsGaussianIntegers"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "CanonicalBasis: for full s. c. algebras",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSCAlgebraObj)",
+                            "IsFullSCAlgebra",
+                            "Tester(IsFullSCAlgebra)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "CanonicalBasis: for Integers",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "CanonicalBasis: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "CanonicalBasis: for Gaussian row space with known semi-ech. basis",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "Tester(SemiEchelonBasis)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "CanonicalBasis: for algebra module",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "CanonicalBasis: for Gaussian matrix space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "CanonicalBasis: for Gaussian row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "CanonicalBasis: for free module that is handled by a nice basis",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsHandledByNiceBasis"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "CanonicalBasis: default method, return `fail'",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGaussianSpace"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormedRowVectors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormedRowVectors)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "NormedRowVectors: for Gaussian row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormedRowVectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGaussianSpace"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormedRowVectors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormedRowVectors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormedRowVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGaussianSpace"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormedRowVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsSubspace: for a vector space and a collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubspace",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ],
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Subspaces: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Subspaces)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "Subspaces",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "Subspaces: for a vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Subspaces: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -44
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Subspaces: for (Gaussian) full row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "Subspaces: for (Gaussian) full row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "Subspaces: for a vector space, and an integer",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Subspaces",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Subspaces): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Subspaces): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Subspaces)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Subspaces)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGaussianSpace"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrthogonalSpaceInFullRowSpace: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrthogonalSpaceInFullRowSpace)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "OrthogonalSpaceInFullRowSpace: dual space for Gaussian row space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsRowModule",
+                            "Tester(IsRowModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrthogonalSpaceInFullRowSpace",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGaussianSpace"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrthogonalSpaceInFullRowSpace): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrthogonalSpaceInFullRowSpace): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrthogonalSpaceInFullRowSpace)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGaussianSpace"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrthogonalSpaceInFullRowSpace)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsVectorSpaceHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsVectorSpaceHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsVectorSpaceHomomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsVectorSpaceHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsVectorSpaceHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsVectorSpaceHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsVectorSpaceHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsVectorSpaceHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "LeftModuleGeneralMappingByImages: for two free left modules and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftModuleGeneralMappingByImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "LeftModuleHomomorphismByImagesNC: for two left modules and two lists",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 50
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftModuleHomomorphismByImagesNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsLeftModuleGeneralMappingByImages: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsLeftModuleGeneralMappingByImages)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "AsLeftModuleGeneralMappingByImages: for an algebra general mapping by images",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)",
+                            "IsAlgebraGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "AsLeftModuleGeneralMappingByImages: for a linear g.m.b.i.",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)",
+                            "IsLinearGeneralMappingByImagesDefaultRep"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsLeftModuleGeneralMappingByImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsLeftModuleGeneralMappingByImages): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsLeftModuleGeneralMappingByImages): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsLeftModuleGeneralMappingByImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsLeftModuleGeneralMappingByImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "LeftModuleHomomorphismByMatrix: for two bases of free left modules and a matrix",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftModuleHomomorphismByMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NaturalHomomorphismBySubspace: for left module and trivial left module",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 10053
+                },
+                {
+                    "comment": "NaturalHomomorphismBySubspace: for two finite dimensional free left modules",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismBySubspace",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullHomModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullHomModule)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "IsFullHomModule: for space of linear mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullHomModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullHomModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullHomModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullHomModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullHomModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPseudoCanonicalBasisFullHomModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPseudoCanonicalBasisFullHomModule)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsPseudoCanonicalBasisFullHomModule: for a basis of a full hom module",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPseudoCanonicalBasisFullHomModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPseudoCanonicalBasisFullHomModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPseudoCanonicalBasisFullHomModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPseudoCanonicalBasisFullHomModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPseudoCanonicalBasisFullHomModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Hom: for division ring and two free left modules",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 96
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Hom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "End: for division ring and space of linear mappings",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 73
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "End",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ],
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ],
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject"
+                ],
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ScalarProduct: for two class functions",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ScalarProduct: method for two row vectors",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ScalarProduct: generic method",
+                    "filters": [
+                        [
+                            "IsRowVectorObj"
+                        ],
+                        [
+                            "IsRowVectorObj"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ScalarProduct: for left module of class functions, and two class functions",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "ScalarProduct: for character table and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ScalarProduct: for module of class functions, and two values lists",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsClassFunctionsSpace"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ScalarProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Decomposition: for a matrix of cyclotomics, a vector and a depth",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Decomposition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSimpleAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSimpleAlgebra)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "IsSimpleAlgebra: for a Lie algebra in characteristic zero",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsSimpleAlgebra: for an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsSimpleAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSimpleAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSimpleAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSimpleAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSimpleAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSimpleAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfLeftOperatorRing)"
+                        ]
+                    ],
+                    "rank": 20032
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: for FLMLOR with known right ideal generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRightIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: for FLMLOR with known left ideal generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfLeftIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: LAGUNA: for a Lie algebra coming from an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: for a FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: for FLMLOR with known ideal generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfTwoSidedIdeal)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: for a FLMLOR with known left module generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfLeftOperatorRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfLeftOperatorRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfLeftOperatorRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfLeftOperatorRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfLeftOperatorRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfLeftOperatorRingWithOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfLeftOperatorRingWithOne)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRingWithOne: for a FLMLOR-with-one with known left module generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "GeneratorsOfLeftOperatorRingWithOne: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -42
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfLeftOperatorRingWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfLeftOperatorRingWithOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfLeftOperatorRingWithOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfLeftOperatorRingWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfLeftOperatorRingWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PowerSubalgebraSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PowerSubalgebraSeries)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "PowerSubalgebraSeries: for an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "PowerSubalgebraSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PowerSubalgebraSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PowerSubalgebraSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PowerSubalgebraSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PowerSubalgebraSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PowerSubalgebraSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdjointBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdjointBasis)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "AdjointBasis: for a basis of a Lie algebra",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdjointBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdjointBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdjointBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdjointBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdjointBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndicesOfAdjointBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndicesOfAdjointBasis)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicesOfAdjointBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndicesOfAdjointBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndicesOfAdjointBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndicesOfAdjointBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndicesOfAdjointBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RadicalOfAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RadicalOfAlgebra)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "RadicalOfAlgebra: for associative Gaussian matrix algebra",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsMatrixModule",
+                            "Tester(IsMatrixModule)",
+                            "IsGaussianSpace"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "RadicalOfAlgebra: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "RadicalOfAlgebra: for an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "RadicalOfAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RadicalOfAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RadicalOfAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RadicalOfAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RadicalOfAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RadicalOfAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectSumDecomposition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DirectSumDecomposition)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "DirectSumDecomposition: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "DirectSumDecomposition: for semisimple associative algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "DirectSumDecomposition: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectSumDecomposition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DirectSumDecomposition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DirectSumDecomposition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DirectSumDecomposition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DirectSumDecomposition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NullAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NullAlgebra)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "NullAlgebra: for a ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "NullAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NullAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NullAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NullAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NullAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NullAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ProductSpace: for two ideals with same parent",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsTwoSidedIdealInParent",
+                            "Tester(IsTwoSidedIdealInParent)"
+                        ],
+                        [
+                            "Tester(ParentAttr)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsTwoSidedIdealInParent",
+                            "Tester(IsTwoSidedIdealInParent)"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "ProductSpace: for two algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "ProductSpace: for two free left modules",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProductSpace",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectSumOfAlgebras: for list of algebras",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DirectSumOfAlgebras: for two matrix Lie FLMLORs",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 104
+                },
+                {
+                    "comment": "DirectSumOfAlgebras: for two associative matrix FLMLORs",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "DirectSumOfAlgebras: for two algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 72
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectSumOfAlgebras",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsFLMLOR: for a division ring and an algebra",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "AsFLMLOR: for a division ring and a free left module",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "AsFLMLOR: for a ring and a collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsFLMLOR",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsFLMLORWithOne: for a division ring and a algebra-with-one",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "AsFLMLORWithOne: for a division ring and an algebra",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "AsFLMLORWithOne: for a division ring and a free left module",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "AsFLMLORWithOne: for a ring and a collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsFLMLORWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsSubFLMLOR: for an algebra and an algebra-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "AsSubFLMLOR: for two algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 72
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubFLMLOR",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsSubFLMLORWithOne: for an algebra and a algebra-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "AsSubFLMLORWithOne: for two algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 72
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubFLMLORWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClosureLeftOperatorRing: for a FLMLOR containing the whole family, and a ring element",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 10044
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for a left op. ring cont. the whole family, and a collection",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 10033
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for two left operator rings-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for two left operator rings",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for a FLMLOR-with-one with basis, and a ring element",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(Basis)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for a FLMLOR-with-one and a ring element",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for an FLMLOR with basis, and a ring element",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "Tester(Basis)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for a FLMLOR and a ring element",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ClosureLeftOperatorRing: for left operator ring and list of elements",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClosureLeftOperatorRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FLMLORByGenerators: for a field, and a collection of FFE",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 441
+                },
+                {
+                    "comment": "FLMLORByGenerators: for division ring and list of Lie matrices over it",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsLieObject)"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "FLMLORByGenerators: for division ring and list of ordinary matrices over it",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "FLMLORByGenerators: for ring and collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "FLMLORByGenerators: for division ring, list of Lie matrices over it, and Lie matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsLieObject)"
+                        ],
+                        [
+                            "IsLieMatrix",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "FLMLORByGenerators: for division ring, empty list, and Lie matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsLieMatrix",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 101
+                },
+                {
+                    "comment": "FLMLORByGenerators: for division ring, empty list, and square ordinary matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 99
+                },
+                {
+                    "comment": "FLMLORByGenerators: for division ring, list of matrices over it, and ordinary matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "FLMLORByGenerators: for ring, homogeneous list, and ring element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FLMLORByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FLMLORWithOneByGenerators: for a field, and a collection of FFE",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 441
+                },
+                {
+                    "comment": "FLMLORWithOneByGenerators: for division ring and list of ordinary matrices over it",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "FLMLORWithOneByGenerators: for ring and collection",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "FLMLORWithOneByGenerators: for division ring, empty list, and square ordinary matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 99
+                },
+                {
+                    "comment": "FLMLORWithOneByGenerators: for division ring, list of matrices over it, and ordinary matrix",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "FLMLORWithOneByGenerators: for ring, homogeneous list, and ring element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FLMLORWithOneByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieAlgebraByDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieAlgebraByDomain)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "LieAlgebraByDomain: LAGUNA: for an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "LieAlgebraByDomain: for an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "LieAlgebraByDomain: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieAlgebraByDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieAlgebraByDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieAlgebraByDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieAlgebraByDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieAlgebraByDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeviMalcevDecomposition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeviMalcevDecomposition)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "LeviMalcevDecomposition: for an associative or a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "LeviMalcevDecomposition: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeviMalcevDecomposition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeviMalcevDecomposition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeviMalcevDecomposition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeviMalcevDecomposition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeviMalcevDecomposition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsNilpotentElement: for an algebra, and an element",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotentElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Grading: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Grading)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "Grading: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Grading",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Grading): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Grading): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Grading)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Grading)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoefficientsAndMagmaElements: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoefficientsAndMagmaElements)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "CoefficientsAndMagmaElements: for magma ring element in default repr.",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsAndMagmaElements",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoefficientsAndMagmaElements): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoefficientsAndMagmaElements): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoefficientsAndMagmaElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoefficientsAndMagmaElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ZeroCoefficient: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ZeroCoefficient)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "ZeroCoefficient: for magma ring element in default repr.",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroCoefficient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ZeroCoefficient): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ZeroCoefficient): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ZeroCoefficient)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ZeroCoefficient)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfMagmaRingModuloRelations)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalizedElementOfMagmaRingModuloRelations: for family of free Lie algebra elements, and list",
+                    "filters": [
+                        [
+                            "IsFamilyElementOfFreeLieAlgebra"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "NormalizedElementOfMagmaRingModuloRelations: for family of magma rings modulo the span of ``zero'', and list",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloSpanOfZeroFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "NormalizedElementOfMagmaRingModuloRelations: for a family of elements in a *free* magma ring, and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFreeMagmaRing)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizedElementOfMagmaRingModuloRelations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupRing)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "IsGroupRing: for free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingMagma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingMagma)"
+                        ]
+                    ],
+                    "rank": 20039
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingMagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingMagma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingMagma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ElementOfMagmaRing: for family, ring element, and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementOfMagmaRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentationIdeal: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentationIdeal)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "AugmentationIdeal: LAGUNA: for a modular group algebra of a finite group",
+                    "filters": [
+                        [
+                            "IsFModularGroupAlgebra",
+                            "Tester(IsFModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "AugmentationIdeal: for a free magma ring",
+                    "filters": [
+                        [
+                            "IsFreeMagmaRing"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentationIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentationIdeal): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentationIdeal): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentationIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFreeMagmaRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentationIdeal)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule",
+                    "CategoryCollections(IsElementOfFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullFpAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "IsFullFpAlgebra: for f. p. algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "IsFullFpAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsElementOfFpAlgebra)"
+                        ]
+                    ],
+                    "rank": -59
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullFpAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule",
+                    "CategoryCollections(IsElementOfFpAlgebra)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullFpAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullFpAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule",
+                    "CategoryCollections(IsElementOfFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpAlgebra)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ElementOfFpAlgebra: for fp. alg. elms. family with normal form, and ring element",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpAlgebra)",
+                            "Tester(NiceNormalFormByExtRepFunction)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "ElementOfFpAlgebra: for family of fp. alg. elements and ring element",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpAlgebra)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementOfFpAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpAlgebra"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "MappedExpression: for element of f.p. algebra, and two lists of generators",
+                    "filters": [
+                        [
+                            "IsElementOfFpAlgebra"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MappedExpression",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGeneratorsOfFpAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGeneratorsOfFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 20043
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpAlgebra: for a full f.p. algebra",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra",
+                            "IsFullFpAlgebra",
+                            "Tester(IsFullFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGeneratorsOfFpAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGeneratorsOfFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGeneratorsOfFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelatorsOfFpAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelatorsOfFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 20043
+                },
+                {
+                    "comment": "RelatorsOfFpAlgebra: for a full f.p. algebra",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra",
+                            "IsFullFpAlgebra",
+                            "Tester(IsFullFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "RelatorsOfFpAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelatorsOfFpAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelatorsOfFpAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelatorsOfFpAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelatorsOfFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelatorsOfFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeAlgebraOfFpAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeAlgebraOfFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 20043
+                },
+                {
+                    "comment": "FreeAlgebraOfFpAlgebra: for a full f.p. algebra",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra",
+                            "IsFullFpAlgebra",
+                            "Tester(IsFullFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "FreeAlgebraOfFpAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeAlgebraOfFpAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeAlgebraOfFpAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeAlgebraOfFpAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeAlgebraOfFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra",
+                    "IsFullFpAlgebra",
+                    "Tester(IsFullFpAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeAlgebraOfFpAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNormalForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNormalForm)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormalForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNormalForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNormalForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNormalForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNormalForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceNormalFormByExtRepFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceNormalFormByExtRepFunction)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceNormalFormByExtRepFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceNormalFormByExtRepFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceNormalFormByExtRepFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceNormalFormByExtRepFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceNormalFormByExtRepFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceAlgebraMonomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceAlgebraMonomorphism)"
+                        ]
+                    ],
+                    "rank": 20040
+                },
+                {
+                    "comment": "NiceAlgebraMonomorphism: for a full f.p. associative FLMLOR (call `IsomorphismMatrixFLMLOR')",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsSubalgebraFpAlgebra",
+                            "IsFullFpAlgebra",
+                            "Tester(IsFullFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "NiceAlgebraMonomorphism: for a f.p. Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceAlgebraMonomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceAlgebraMonomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceAlgebraMonomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceAlgebraMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubalgebraFpAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceAlgebraMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieAbelian: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieAbelian)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsLieAbelian: LAGUNA: for a Lie algebra of an associative algebra",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsLieAbelian: for a Lie algebra with known basis",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "Tester(Basis)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsLieAbelian: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsLieAbelian: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieAbelian",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieAbelian): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieAbelian): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieAbelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieAbelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieNilpotent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieNilpotent)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsLieNilpotent: LAGUNA: for a Lie algebra of a group ring",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsLieNilpotent: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsLieNilpotent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieNilpotent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieNilpotent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieNilpotent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieNilpotent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieNilpotent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRestrictedLieAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRestrictedLieAlgebra)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsRestrictedLieAlgebra: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsRestrictedLieAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRestrictedLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRestrictedLieAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRestrictedLieAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRestrictedLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRestrictedLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieDerivedSubalgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieDerivedSubalgebra)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieDerivedSubalgebra: LAGUNA: for a Lie algebra of a group ring",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "LieDerivedSubalgebra: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieDerivedSubalgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieDerivedSubalgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieDerivedSubalgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieDerivedSubalgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieDerivedSubalgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieDerivedSubalgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieDerivedSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieDerivedSeries)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieDerivedSeries: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieDerivedSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieDerivedSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieDerivedSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieDerivedSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieDerivedSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieDerivedSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieSolvable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieSolvable)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsLieSolvable: LAGUNA: for a Lie algebra of a group ring",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsLieSolvable: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsLieSolvable: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieSolvable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieSolvable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieSolvable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieSolvable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieSolvable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieLowerCentralSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieLowerCentralSeries)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieLowerCentralSeries: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieLowerCentralSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieLowerCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieLowerCentralSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieLowerCentralSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieLowerCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieLowerCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieUpperCentralSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieUpperCentralSeries)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieUpperCentralSeries: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieUpperCentralSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieUpperCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieUpperCentralSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieUpperCentralSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieUpperCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieUpperCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieCentre: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieCentre)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieCentre: LAGUNA: for a Lie algebra of a group ring",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "LieCentre: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieCentre: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieCentre",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieCentre): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieCentre): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieCentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieCentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RightDerivations: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RightDerivations)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RightDerivations: method for a basis of an algebra",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightDerivations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RightDerivations): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RightDerivations): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RightDerivations)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RightDerivations)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeftDerivations: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeftDerivations)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "LeftDerivations: method for a basis of an algebra",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftDerivations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeftDerivations): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeftDerivations): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeftDerivations)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeftDerivations)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KillingMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KillingMatrix)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "KillingMatrix: for a basis of a Lie algebra",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KillingMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KillingMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KillingMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KillingMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KillingMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CartanSubalgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CartanSubalgebra)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "CartanSubalgebra: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "CartanSubalgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CartanSubalgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CartanSubalgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CartanSubalgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CartanSubalgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CartanSubalgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PthPowerImages: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PthPowerImages)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "PthPowerImages: for a basis of a Lie algebra",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PthPowerImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PthPowerImages): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PthPowerImages): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PthPowerImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PthPowerImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NonNilpotentElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NonNilpotentElement)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "NonNilpotentElement: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "NonNilpotentElement: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NonNilpotentElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NonNilpotentElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NonNilpotentElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NonNilpotentElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NonNilpotentElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AdjointAssociativeAlgebra: for a Lie algebra and a subalgebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 84
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdjointAssociativeAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieNilRadical: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieNilRadical)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieNilRadical: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieNilRadical: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieNilRadical",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieNilRadical): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieNilRadical): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieNilRadical)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieNilRadical)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieSolvableRadical: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieSolvableRadical)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieSolvableRadical: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieSolvableRadical: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieSolvableRadical",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieSolvableRadical): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieSolvableRadical): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieSolvableRadical)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieSolvableRadical)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiSimpleType: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemiSimpleType)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "SemiSimpleType: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SemiSimpleType: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiSimpleType",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemiSimpleType): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemiSimpleType): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemiSimpleType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemiSimpleType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LieCentralizer: for an abelian Lie algebra and a vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "IsLieAbelian",
+                            "Tester(IsLieAbelian)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "LieCentralizer: for a Lie algebra and a vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieCentralizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieCentralizerInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieCentralizerInParent)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieCentralizerInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieCentralizerInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieCentralizerInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieCentralizerInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieCentralizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieCentralizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LieNormalizer: for a Lie algebra and a vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieNormalizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieNormalizerInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieNormalizerInParent)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieNormalizerInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieNormalizerInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieNormalizerInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieNormalizerInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieNormalizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieNormalizerInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AdjointMatrix: for a basis of a Lie algebra, and an element",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdjointMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "KappaPerp: for a Lie algebra and a vector space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KappaPerp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PowerS: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PowerS)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "PowerS: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "PowerS: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PowerS",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PowerS): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PowerS): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PowerS)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PowerS)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsJacobianElement"
+                ]
+            ],
+            [
+                [
+                    "IsJacobianElement"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PthPowerImage: for restricted Lie object",
+                    "filters": [
+                        [
+                            "IsRestrictedJacobianElement",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PthPowerImage: for an element of a restricted Lie algebra",
+                    "filters": [
+                        [
+                            "IsJacobianElement"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PthPowerImage: for restricted Lie object and integer",
+                    "filters": [
+                        [
+                            "IsRestrictedJacobianElement",
+                            "IsLieObject"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "PthPowerImage: for an element of a restricted Lie algebra and an integer",
+                    "filters": [
+                        [
+                            "IsJacobianElement"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PthPowerImage: for a basis of an algebra, and a ring element",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PthPowerImage",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsJacobianElement)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PClosureSubalgebra: for a subalgebra of restricted jacobian elements",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsJacobianElement)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PClosureSubalgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingLieAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingLieAlgebra)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingLieAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingLieAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RootSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RootSystem)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "RootSystem: for a (semisimple) Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "RootSystem: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RootSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RootSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RootSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RootSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RootSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PositiveRoots: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PositiveRoots)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositiveRoots",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PositiveRoots): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PositiveRoots): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PositiveRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PositiveRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NegativeRoots: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NegativeRoots)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NegativeRoots",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NegativeRoots): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NegativeRoots): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NegativeRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NegativeRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PositiveRootVectors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PositiveRootVectors)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositiveRootVectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PositiveRootVectors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PositiveRootVectors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PositiveRootVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PositiveRootVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NegativeRootVectors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NegativeRootVectors)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NegativeRootVectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NegativeRootVectors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NegativeRootVectors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NegativeRootVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NegativeRootVectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SimpleSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SimpleSystem)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SimpleSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SimpleSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SimpleSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SimpleSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SimpleSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CartanMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CartanMatrix)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CartanMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CartanMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CartanMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CartanMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CartanMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BilinearFormMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BilinearFormMat)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "BilinearFormMat: for a root system from a Lie algebra",
+                    "filters": [
+                        [
+                            "IsRootSystemFromLieAlgebra"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BilinearFormMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BilinearFormMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BilinearFormMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BilinearFormMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BilinearFormMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalGenerators)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "CanonicalGenerators: for a root system from a (semisimple) Lie algebra",
+                    "filters": [
+                        [
+                            "IsRootSystemFromLieAlgebra"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystemFromLieAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ChevalleyBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ChevalleyBasis)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "ChevalleyBasis: for a semisimple Lie algebra with a split Cartan subalgebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ChevalleyBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ChevalleyBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ChevalleyBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ChevalleyBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ChevalleyBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ChevalleyBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UniversalEnvelopingAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UniversalEnvelopingAlgebra)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "UniversalEnvelopingAlgebra: for a finite dimensional Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "UniversalEnvelopingAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "UniversalEnvelopingAlgebra: for a finite dimensional Lie algebra and a basis of it",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UniversalEnvelopingAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UniversalEnvelopingAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UniversalEnvelopingAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UniversalEnvelopingAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UniversalEnvelopingAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "JenningsLieAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(JenningsLieAlgebra)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "JenningsLieAlgebra: for a p-group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "JenningsLieAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "JenningsLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(JenningsLieAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(JenningsLieAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(JenningsLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(JenningsLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PCentralLieAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PCentralLieAlgebra)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PCentralLieAlgebra: for a p-group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PCentralLieAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PCentralLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PCentralLieAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PCentralLieAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PCentralLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PCentralLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismOfLieAlgebraFromNilpotentGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule",
+                    "CategoryCollections(IsSCAlgebraObj)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullSCAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullSCAlgebra)"
+                        ]
+                    ],
+                    "rank": 20040
+                },
+                {
+                    "comment": "IsFullSCAlgebra: for s. c. algebra elements collection",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCAlgebraObj)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "IsFullSCAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSCAlgebraObj)"
+                        ]
+                    ],
+                    "rank": -59
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullSCAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule",
+                    "CategoryCollections(IsSCAlgebraObj)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullSCAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullSCAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullSCAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule",
+                    "CategoryCollections(IsSCAlgebraObj)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullSCAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCanonicalBasisFullSCAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCanonicalBasisFullSCAlgebra)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsCanonicalBasisFullSCAlgebra: for a basis",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCanonicalBasisFullSCAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCanonicalBasisFullSCAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCanonicalBasisFullSCAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCanonicalBasisFullSCAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCanonicalBasisFullSCAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AlgebraGeneralMappingByImages: for two FLMLORs and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlgebraGeneralMappingByImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AlgebraHomomorphismByImagesNC: for two FLMLORs and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlgebraHomomorphismByImagesNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AlgebraWithOneGeneralMappingByImages: for two FLMLORs and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlgebraWithOneGeneralMappingByImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AlgebraWithOneHomomorphismByImagesNC: for two FLMLORs and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlgebraWithOneHomomorphismByImagesNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OperationAlgebraHomomorphism: for a FLMLOR and a collection (add `OnRight' argument)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "OperationAlgebraHomomorphism: for a FLMLOR, a free left module with known generators, and a function",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule",
+                            "IsFiniteDimensional",
+                            "Tester(IsFiniteDimensional)",
+                            "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "OperationAlgebraHomomorphism: for a full f.p. associative FLMLOR, a collection, and a function",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsSubalgebraFpAlgebra",
+                            "IsFullFpAlgebra",
+                            "Tester(IsFullFpAlgebra)"
+                        ],
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "OperationAlgebraHomomorphism: for a FLMLOR, a basis, and a function",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsBasis"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OperationAlgebraHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsAddition",
+                    "Tester(RespectsAddition)",
+                    "RespectsAdditiveInverses",
+                    "Tester(RespectsAdditiveInverses)",
+                    "RespectsScalarMultiplication",
+                    "Tester(RespectsScalarMultiplication)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MakePreImagesInfoOperationAlgebraHomomorphism: for an alg. hom. from f. p. algebra",
+                    "filters": [
+                        [
+                            "IsAlgebraHomomorphismFromFpRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "MakePreImagesInfoOperationAlgebraHomomorphism: for an operation algebra homomorphism",
+                    "filters": [
+                        [
+                            "IsOperationAlgebraHomomorphismDefaultRep"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MakePreImagesInfoOperationAlgebraHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismFpFLMLOR: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismFpFLMLOR)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "IsomorphismFpFLMLOR: for f.p. FLMLOR (return the identity mapping)",
+                    "filters": [
+                        [
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 10037
+                },
+                {
+                    "comment": "IsomorphismFpFLMLOR: for a finite dimensional FLMLOR-with-one",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "IsomorphismFpFLMLOR: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": -46
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpFLMLOR",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismFpFLMLOR): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismFpFLMLOR): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismFpFLMLOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismFpFLMLOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismMatrixFLMLOR: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismMatrixFLMLOR)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "IsomorphismMatrixFLMLOR: for a full f.p. associative FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsSubalgebraFpAlgebra",
+                            "IsFullFpAlgebra",
+                            "Tester(IsFullFpAlgebra)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "IsomorphismMatrixFLMLOR: for a matrix FLMLOR",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsomorphismMatrixFLMLOR: for a f.p. FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "IsSubalgebraFpAlgebra"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "IsomorphismMatrixFLMLOR: for a finite dimensional associative FLMLOR with identity",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsomorphismMatrixFLMLOR: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": -46
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismMatrixFLMLOR",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismMatrixFLMLOR): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismMatrixFLMLOR): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismMatrixFLMLOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismMatrixFLMLOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ],
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismSCFLMLOR: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismSCFLMLOR)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsomorphismSCFLMLOR: for s.c. FLMLOR (return the identity mapping)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule",
+                            "CategoryCollections(IsSCAlgebraObj)"
+                        ]
+                    ],
+                    "rank": 10039
+                },
+                {
+                    "comment": "IsomorphismSCFLMLOR: for a finite dimensional FLMLOR (delegate to the method for a basis)",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "IsomorphismSCFLMLOR: for a basis (of a finite dimensional FLMLOR)",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismSCFLMLOR",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismSCFLMLOR): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismSCFLMLOR): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismSCFLMLOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismSCFLMLOR)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsDistributiveLOpDSum",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "RepresentativeLinearOperation: for a matrix FLMLOR, two lists of row vectors, and `OnTuples'",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 95
+                },
+                {
+                    "comment": "RepresentativeLinearOperation: for a matrix FLMLOR, two row vectors, and `OnRight'",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "RepresentativeLinearOperation: for a FLMLOR, two elements in it, and `OnRight'",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "RepresentativeLinearOperation: for a FLMLOR, two tuples of elements in it, and `OnTuples'",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativeLinearOperation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "LieFamily: for family of ring elements",
+                    "filters": [
+                        [
+                            "CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "LieFamily: for a collections family (special case of Lie matrices)",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsCollection)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingFamily)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "UnderlyingFamily",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "UnderlyingFamily",
+                    "filters": [
+                        [
+                            "IsRewritingSystem"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieObject: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieObject)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "LieObject: for a ring element",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieObject",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieObject): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieObject): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieObject)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieObject)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingRingElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingRingElement)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "UnderlyingRingElement: for a Lie object in default representation",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsLieObject"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingRingElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieObject"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingRingElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingRingElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingRingElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingRingElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAlgebraModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "IsAlgebraModule: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -44
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAlgebraModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAlgebraModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLeftAlgebraModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLeftAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "IsLeftAlgebraModule: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -44
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLeftAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLeftAlgebraModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLeftAlgebraModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLeftAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLeftAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRightAlgebraModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRightAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "IsRightAlgebraModule: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -44
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRightAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRightAlgebraModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRightAlgebraModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRightAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRightAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeftActingAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeftActingAlgebra)"
+                        ]
+                    ],
+                    "rank": 20027
+                },
+                {
+                    "comment": "LeftActingAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftActingAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeftActingAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeftActingAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeftActingAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeftActingAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RightActingAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RightActingAlgebra)"
+                        ]
+                    ],
+                    "rank": 20027
+                },
+                {
+                    "comment": "RightActingAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightActingAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RightActingAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RightActingAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RightActingAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RightActingAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ActingAlgebra: for an algebra module",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ActingAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfAlgebraModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 20027
+                },
+                {
+                    "comment": "GeneratorsOfAlgebraModule: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfAlgebraModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfAlgebraModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfAlgebraModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "LeftAlgebraModuleByGenerators: for algebra, function of 2 args, module generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "LeftAlgebraModuleByGenerators: for algebra, function of 2 args, generators, string",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftAlgebraModuleByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "RightAlgebraModuleByGenerators: for algebra, function of 2 args, module generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "RightAlgebraModuleByGenerators: for algebra, function of 2 args, generators, string",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightAlgebraModuleByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "BiAlgebraModuleByGenerators: for 2 algebras, function of 2 args, function of 2 args, module generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 78
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "BiAlgebraModuleByGenerators: for 2 algebras, function of 2 args, function of 2 args, generators, string",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 83
+                }
+            ]
+        },
+        "name": "BiAlgebraModuleByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "LeftAlgebraModule: for algebra, function of 2 args, underlying space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 62
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "RightAlgebraModule: for algebra, function of 2 args, underlying space",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 62
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "BiAlgebraModule: for 2 algebras, function of 2 args, function of 2 args, module generators",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 99
+                }
+            ],
+            "6args": []
+        },
+        "name": "BiAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "CategoryCollections(IsAlgebraModuleElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SubAlgebraModule: for algebra module, and a list of submodule generators",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SubAlgebraModule: for algebra module, and a list of submodule generators, and string",
+                    "filters": [
+                        [
+                            "IsFreeLeftModule",
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsAlgebraModuleElement)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 50
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsAddition",
+                    "Tester(RespectsAddition)",
+                    "RespectsAdditiveInverses",
+                    "Tester(RespectsAdditiveInverses)",
+                    "RespectsScalarMultiplication",
+                    "Tester(RespectsScalarMultiplication)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftModuleByHomomorphismToMatAlg: for an algebra and a homomorphism to a matrix algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftModuleByHomomorphismToMatAlg",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsAddition",
+                    "Tester(RespectsAddition)",
+                    "RespectsAdditiveInverses",
+                    "Tester(RespectsAdditiveInverses)",
+                    "RespectsScalarMultiplication",
+                    "Tester(RespectsScalarMultiplication)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightModuleByHomomorphismToMatAlg: for an algebra and a homomorphism to a matrix algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsAddition",
+                            "Tester(RespectsAddition)",
+                            "RespectsAdditiveInverses",
+                            "Tester(RespectsAdditiveInverses)",
+                            "RespectsScalarMultiplication",
+                            "Tester(RespectsScalarMultiplication)"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightModuleByHomomorphismToMatAlg",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdjointModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdjointModule)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "AdjointModule: for an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "AdjointModule: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdjointModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdjointModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdjointModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdjointModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdjointModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FaithfulModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FaithfulModule)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "FaithfulModule: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "FaithfulModule: for an algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "FaithfulModule: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FaithfulModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FaithfulModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FaithfulModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FaithfulModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FaithfulModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ModuleByRestriction: for an algebra module and a subalgebra",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ModuleByRestriction: for a bi-algebra module and a subalgebra and a subalgebra",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 96
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ModuleByRestriction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NaturalHomomorphismBySubAlgebraModule: for algebra module and a submodule",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismBySubAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasisOfAlgebraModuleElementSpace"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MatrixOfAction: for a basis of an algebra module and an algebra element",
+                    "filters": [
+                        [
+                            "IsBasisOfAlgebraModuleElementSpace"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "MatrixOfAction: for a basis of an algebra module, an algebra element and a side",
+                    "filters": [
+                        [
+                            "IsBasisOfAlgebraModuleElementSpace"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 8
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MatrixOfAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonomialElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConvertToNormalFormMonomialElement: for a symmetric element",
+                    "filters": [
+                        [
+                            "IsSymmetricPowerElement"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ConvertToNormalFormMonomialElement: for a wedge element",
+                    "filters": [
+                        [
+                            "IsWedgeElement"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ConvertToNormalFormMonomialElement: for a tensor element",
+                    "filters": [
+                        [
+                            "IsTensorElement"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConvertToNormalFormMonomialElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TensorProductOp: for a list of finite dimensional vector spaces, and a space (for method selection)",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TensorProductOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TensorProductOfAlgebraModules: for a list of algebra modules",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "TensorProductOfAlgebraModules: for two algebra modules",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TensorProductOfAlgebraModules",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExteriorPower: for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "ExteriorPower: for a vector space and an integer",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExteriorPower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExteriorPowerOfAlgebraModule: for an algebra module and an integer",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExteriorPowerOfAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SymmetricPower: for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "SymmetricPower: for an algebra module and an integer",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymmetricPower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SymmetricPowerOfAlgebraModule: for an algebra module and an integer",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymmetricPowerOfAlgebraModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectSumOfAlgebraModules: for a list of algebra modules",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DirectSumOfAlgebraModules: for two algebra modules",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectSumOfAlgebraModules",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FullSparseRowSpace: for a ring and an integer",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FullSparseRowSpace",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsFreeLeftModule"
+                ],
+                [
+                    "IsFreeLeftModule"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "TranslatorSubalgebra: for an algebra, an algebra module and two subspaces",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 70
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TranslatorSubalgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Cochain: for a module over a Lie algebra, an integer and an object",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cochain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CochainSpace: for a module over a Lie algebra and an integer",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CochainSpace",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Cocycles: for module over a Lie algebra and an integer",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cocycles",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraModule",
+                    "Tester(IsAlgebraModule)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Coboundaries: for module over a Lie algebra and an integer",
+                    "filters": [
+                        [
+                            "IsAlgebraModule",
+                            "Tester(IsAlgebraModule)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Coboundaries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsWeylGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsWeylGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsWeylGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsWeylGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsWeylGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsWeylGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsWeylGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsWeylGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WeylGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WeylGroup)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "WeylGroup: for a root system",
+                    "filters": [
+                        [
+                            "IsRootSystem"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeylGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WeylGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WeylGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WeylGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WeylGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SparseCartanMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SparseCartanMatrix)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "SparseCartanMatrix: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SparseCartanMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SparseCartanMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SparseCartanMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SparseCartanMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SparseCartanMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ApplySimpleReflection: for a sparse Cartan matrix, index and weight",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ApplySimpleReflection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LongestWeylWordPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LongestWeylWordPerm)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "LongestWeylWordPerm: for Weyl group",
+                    "filters": [
+                        [
+                            "IsWeylGroup",
+                            "Tester(IsWeylGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "LongestWeylWordPerm: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LongestWeylWordPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LongestWeylWordPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LongestWeylWordPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LongestWeylWordPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LongestWeylWordPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugateDominantWeight: for Weyl group and weight",
+                    "filters": [
+                        [
+                            "IsWeylGroup",
+                            "Tester(IsWeylGroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugateDominantWeight",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugateDominantWeightWithWord: for Weyl group and weight",
+                    "filters": [
+                        [
+                            "IsWeylGroup",
+                            "Tester(IsWeylGroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugateDominantWeightWithWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWeylGroup",
+                    "Tester(IsWeylGroup)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "WeylOrbitIterator: for weights of a W-orbit",
+                    "filters": [
+                        [
+                            "IsWeylGroup",
+                            "Tester(IsWeylGroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeylOrbitIterator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PositiveRootsAsWeights: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PositiveRootsAsWeights)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "PositiveRootsAsWeights: for a root system",
+                    "filters": [
+                        [
+                            "IsRootSystem"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositiveRootsAsWeights",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PositiveRootsAsWeights): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PositiveRootsAsWeights): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PositiveRootsAsWeights)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PositiveRootsAsWeights)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DominantWeights: for a root system and a dominant weight",
+                    "filters": [
+                        [
+                            "IsRootSystem"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DominantWeights",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRootSystem"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DominantCharacter: for a semisimple Lie algebra and a highest weight",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "DominantCharacter: for a root system and a highest weight",
+                    "filters": [
+                        [
+                            "IsRootSystem"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DominantCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DecomposeTensorProduct: for a semisimple Lie algebra and two dominant weights",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DecomposeTensorProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DimensionOfHighestWeightModule: for a semisimple Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DimensionOfHighestWeightModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LatticeGeneratorsInUEA: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LatticeGeneratorsInUEA)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LatticeGeneratorsInUEA: for semsimple Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LatticeGeneratorsInUEA: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LatticeGeneratorsInUEA",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LatticeGeneratorsInUEA): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LatticeGeneratorsInUEA): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LatticeGeneratorsInUEA)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LatticeGeneratorsInUEA)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HighestWeightModule: for a Lie algebra and a list of non-negative integers",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HighestWeightModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsUEALatticeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeadingUEALatticeMonomial: for an integer and a UEALattice element",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsUEALatticeElement"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingUEALatticeMonomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSearchTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Search: for vector search tables in default representation",
+                    "filters": [
+                        [
+                            "IsVectorSearchTableDefaultRep"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Search",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSearchTable"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Insert: for a vector search table in default representation",
+                    "filters": [
+                        [
+                            "IsVectorSearchTableDefaultRep"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        []
+                    ],
+                    "rank": 9
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Insert",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CoefficientsQadic: for two integers",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsQadic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimeDivisors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimeDivisors)"
+                        ]
+                    ],
+                    "rank": 20021
+                },
+                {
+                    "comment": "PrimeDivisors: for integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimeDivisors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimeDivisors): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimeDivisors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimeDivisors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimeDivisors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PartialFactorization: for integers",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PartialFactorization: try harder (FactInt)",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "PartialFactorization: generic method",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PartialFactorization",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Phi: value of Euler's totient function of an integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Phi",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Lambda: exponent of the group of prime residues modulo an integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Lambda",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Sigma: sum of divisors of an integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Sigma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Tau: number of divisors of an integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tau",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "CategoryCollections(IsSCRingObj)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StandardGeneratorsSubringSCRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StandardGeneratorsSubringSCRing)"
+                        ]
+                    ],
+                    "rank": 20032
+                },
+                {
+                    "comment": "StandardGeneratorsSubringSCRing: for sc rings and their subrings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "StandardGeneratorsSubringSCRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": -26
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StandardGeneratorsSubringSCRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "CategoryCollections(IsSCRingObj)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StandardGeneratorsSubringSCRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StandardGeneratorsSubringSCRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StandardGeneratorsSubringSCRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "CategoryCollections(IsSCRingObj)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StandardGeneratorsSubringSCRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Subrings: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Subrings)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "Subrings: for SC Rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "Subrings: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Subrings",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Subrings): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Subrings): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Subrings)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Subrings)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Ideals: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Ideals)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "Ideals: for SC Rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "Ideals: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Ideals",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Ideals): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Ideals): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Ideals)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Ideals)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DirectSumOp: for SC Rings",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "DirectSumOp: for a list (of rings), and a ring",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectSumOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectSumInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DirectSumInfo)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DirectSumInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectSumInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DirectSumInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DirectSumInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DirectSumInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DirectSumInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "RingGeneralMappingByImages: for two rings and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RingGeneralMappingByImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "RingHomomorphismByImagesNC: for two rings and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RingHomomorphismByImagesNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NaturalHomomorphismByIdeal: for FLMLOR and trivial FLMLOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 10087
+                },
+                {
+                    "comment": "NaturalHomomorphismByIdeal: for free algebra and ideal",
+                    "filters": [
+                        [
+                            "IsMagmaRingModuloRelations"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "NaturalHomomorphismByIdeal: for two finite dimensional FLMLORs",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsFreeLeftModule"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "NaturalHomomorphismByIdeal: sc rings",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsSCRingObj)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "NaturalHomomorphismByIdeal: polynomial rings",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 53
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismByIdeal",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "LucasMod: iterative method",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "LucasMod: recursive version, reduce mod N regularly",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 72
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LucasMod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RationalFunctionsFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RationalFunctionsFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "RationalFunctionsFamily: floats pseudofield",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "RationalFunctionsFamily",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "RationalFunctionsFamily: not UFD ring",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RationalFunctionsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RationalFunctionsFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RationalFunctionsFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RationalFunctionsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RationalFunctionsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoefficientsFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoefficientsFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoefficientsFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoefficientsFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoefficientsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoefficientsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NumeratorOfRationalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NumeratorOfRationalFunction)"
+                        ]
+                    ],
+                    "rank": 20015
+                },
+                {
+                    "comment": "NumeratorOfRationalFunction: univariate using ExtRepNumerator",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "NumeratorOfRationalFunction: call ExtRepNumerator",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumeratorOfRationalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NumeratorOfRationalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NumeratorOfRationalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NumeratorOfRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NumeratorOfRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DenominatorOfRationalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DenominatorOfRationalFunction)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "DenominatorOfRationalFunction: univariate using ExtRepDenominator",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "DenominatorOfRationalFunction: call ExtRepDenominator",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DenominatorOfRationalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DenominatorOfRationalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DenominatorOfRationalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DenominatorOfRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DenominatorOfRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 20015
+                },
+                {
+                    "comment": "IsPolynomial: laurent rep.",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "IsPolynomial: rational function rep.",
+                    "filters": [
+                        [
+                            "IsRationalFunctionDefaultRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IsPolynomial: univariate",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsPolynomial: fallback for non-ratfun",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsPolynomial)"
+                        ]
+                    ],
+                    "rank": 20017
+                },
+                {
+                    "comment": "AsPolynomial: call ExtRepPolynomial",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "AsPolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUnivariateRationalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsUnivariateRationalFunction: ratfun",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUnivariateRationalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsUnivariateRationalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsUnivariateRationalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLaurentPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 20015
+                },
+                {
+                    "comment": "IsLaurentPolynomial: univariate",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsLaurentPolynomial",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsLaurentPolynomial: ratfun",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsLaurentPolynomial: fallback for non-ratfun",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLaurentPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLaurentPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLaurentPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLaurentPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLaurentPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsConstantRationalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsConstantRationalFunction)"
+                        ]
+                    ],
+                    "rank": 20015
+                },
+                {
+                    "comment": "IsConstantRationalFunction: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsConstantRationalFunction: rational function",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsConstantRationalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsConstantRationalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsConstantRationalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsConstantRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsConstantRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExtRepNumeratorRatFun: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExtRepNumeratorRatFun)"
+                        ]
+                    ],
+                    "rank": 20015
+                },
+                {
+                    "comment": "ExtRepNumeratorRatFun: laurent polynomial rep.",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ExtRepNumeratorRatFun: polynomial rep -> ExtRepPolynomialRatFun",
+                    "filters": [
+                        [
+                            "IsPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ExtRepNumeratorRatFun: univariate",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtRepNumeratorRatFun",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExtRepNumeratorRatFun): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExtRepNumeratorRatFun): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExtRepNumeratorRatFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExtRepNumeratorRatFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExtRepDenominatorRatFun: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExtRepDenominatorRatFun)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "ExtRepDenominatorRatFun: laurent polynomial rep.",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsLaurentPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ExtRepDenominatorRatFun: univariate",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ExtRepDenominatorRatFun: polynomial, return constant",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtRepDenominatorRatFun",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExtRepDenominatorRatFun): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExtRepDenominatorRatFun): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExtRepDenominatorRatFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExtRepDenominatorRatFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ZeroCoefficientRatFun: via family",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroCoefficientRatFun",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExtRepPolynomialRatFun: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExtRepPolynomialRatFun)"
+                        ]
+                    ],
+                    "rank": 20017
+                },
+                {
+                    "comment": "ExtRepPolynomialRatFun: laurent polynomial rep.",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsLaurentPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ExtRepPolynomialRatFun: rational function rep.",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsRationalFunctionDefaultRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ExtRepPolynomialRatFun: univariate",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ExtRepPolynomialRatFun: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtRepPolynomialRatFun",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExtRepPolynomialRatFun): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExtRepPolynomialRatFun): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExtRepPolynomialRatFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExtRepPolynomialRatFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLaurentPolynomial",
+                    "Tester(IsLaurentPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoefficientsOfLaurentPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoefficientsOfLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "CoefficientsOfLaurentPolynomial: ratfun",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "CoefficientsOfLaurentPolynomial:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "CoefficientsOfLaurentPolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsOfLaurentPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLaurentPolynomial",
+                    "Tester(IsLaurentPolynomial)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoefficientsOfLaurentPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoefficientsOfLaurentPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoefficientsOfLaurentPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLaurentPolynomial",
+                    "Tester(IsLaurentPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoefficientsOfLaurentPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndeterminateNumberOfUnivariateRationalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndeterminateNumberOfUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "IndeterminateNumberOfUnivariateRationalFunction: ratfun",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IndeterminateNumberOfUnivariateRationalFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndeterminateNumberOfUnivariateRationalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndeterminateNumberOfUnivariateRationalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndeterminateNumberOfUnivariateRationalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndeterminateNumberOfUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndeterminateNumberOfUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "LaurentPolynomialByCoefficients: fam, cof,val",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "LaurentPolynomialByCoefficients: ring",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "LaurentPolynomialByCoefficients: warn about iterated polynomials",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "Tester(CoefficientsFamily)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "LaurentPolynomialByCoefficients: with indeterminate",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LaurentPolynomialByCoefficients",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndeterminateOfUnivariateRationalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndeterminateOfUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "IndeterminateOfUnivariateRationalFunction: use `IndeterminateNumber'",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IndeterminateOfUnivariateRationalFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndeterminateOfUnivariateRationalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndeterminateOfUnivariateRationalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndeterminateOfUnivariateRationalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndeterminateOfUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndeterminateOfUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunctionsFamily"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IndeterminateName: for rational function families",
+                    "filters": [
+                        [
+                            "IsPolynomialFunctionsFamily"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndeterminateName",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunctionsFamily"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasIndeterminateName: for rational function families",
+                    "filters": [
+                        [
+                            "IsPolynomialFunctionsFamily"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasIndeterminateName",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunctionsFamily"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetIndeterminateName: for rational function families",
+                    "filters": [
+                        [
+                            "IsPolynomialFunctionsFamily"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetIndeterminateName",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoefficientsOfUnivariatePolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoefficientsOfUnivariatePolynomial)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "CoefficientsOfUnivariatePolynomial: use laurent coeffs",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "CoefficientsOfUnivariatePolynomial:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "CoefficientsOfUnivariatePolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsOfUnivariatePolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoefficientsOfUnivariatePolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoefficientsOfUnivariatePolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoefficientsOfUnivariatePolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoefficientsOfUnivariatePolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLaurentPolynomial",
+                    "Tester(IsLaurentPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOfLaurentPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOfLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "DegreeOfLaurentPolynomial",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "DegreeOfLaurentPolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOfLaurentPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLaurentPolynomial",
+                    "Tester(IsLaurentPolynomial)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOfLaurentPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOfLaurentPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOfLaurentPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLaurentPolynomial",
+                    "Tester(IsLaurentPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOfLaurentPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UnivariatePolynomialByCoefficients: fam,cof",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "UnivariatePolynomialByCoefficients: ring",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "UnivariatePolynomialByCoefficients: fam, cof,ind",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnivariatePolynomialByCoefficients",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                    "CategoryCollections(IsAdditiveElement)",
+                    "CategoryCollections(IsMultiplicativeElement)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UnivariatePolynomial: ring,cof",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "CategoryCollections(IsMultiplicativeElement)"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "UnivariatePolynomial: ring,empty cof",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "UnivariatePolynomial: ring,cof,indn",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "CategoryCollections(IsMultiplicativeElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "UnivariatePolynomial: ring,cof,indpol",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "CategoryCollections(IsNearAdditiveElementWithInverse)",
+                            "CategoryCollections(IsAdditiveElement)",
+                            "CategoryCollections(IsMultiplicativeElement)"
+                        ],
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "UnivariatePolynomial: ring,empty cof, indnr",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        []
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnivariatePolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoefficientsOfUnivariateRationalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoefficientsOfUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "CoefficientsOfUnivariateRationalFunction: laurent polynomial",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "CoefficientsOfUnivariateRationalFunction: ratfun",
+                    "filters": [
+                        [
+                            "IsRationalFunction",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "CoefficientsOfUnivariateRationalFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsOfUnivariateRationalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoefficientsOfUnivariateRationalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoefficientsOfUnivariateRationalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoefficientsOfUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoefficientsOfUnivariateRationalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "UnivariateRationalFunctionByCoefficients: ring",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "UnivariateRationalFunctionByCoefficients: fam, ncof,dcof,val",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "UnivariateRationalFunctionByCoefficients: ring",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "UnivariateRationalFunctionByCoefficients: with indeterminate",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "6args": []
+        },
+        "name": "UnivariateRationalFunctionByCoefficients",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsFloatRationalFunction"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Value: supply `one'",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Value:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Value: Laurent, ring element, and mult. neutral element",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Value: univariate rational function",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Value: rational function: supply `one'",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "Value: rat.fun., with one",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Value",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeadingMonomial: for a univariate laurent polynomial",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "LeadingMonomial: multivariate polynomials wrt total degree",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingMonomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeadingCoefficient: laurent",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "LeadingCoefficient: multivariate polynomials wrt total degree",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "LeadingCoefficient: multivariate",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingCoefficient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PolynomialCoefficientsOfPolynomial: polynomial,integer",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PolynomialCoefficientsOfPolynomial: polynomial,indet",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PolynomialCoefficientsOfPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DegreeIndeterminate: laurent,indetnr",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "DegreeIndeterminate: pol,indetnr",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DegreeIndeterminate: pol,indet",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeIndeterminate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ],
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Derivative: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Derivative)"
+                        ]
+                    ],
+                    "rank": 20018
+                },
+                {
+                    "comment": "Derivative: for float laurent polynomial",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)",
+                            "IsFloatRationalFunction"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Derivative: Laurent Polynomials",
+                    "filters": [
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Derivative: uratfun,ind",
+                    "filters": [
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Derivative:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "Derivative:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "Derivative: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Derivative: ratfun,inum",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Derivative: poly,ind",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Derivative: ratfun,ind",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Derivative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Derivative): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Derivative): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Derivative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Derivative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Resultant: pol,pol,inum",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Resultant: pol,pol,indet",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Resultant",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ],
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Discriminant: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Discriminant)"
+                        ]
+                    ],
+                    "rank": 20017
+                },
+                {
+                    "comment": "Discriminant: univariate",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "Discriminant:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "Discriminant: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Discriminant: poly,inum",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Discriminant: poly,ind",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Discriminant",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Discriminant): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Discriminant): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Discriminant)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Discriminant)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunctionsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "HeuristicCancelPolynomialsExtRep: rationals",
+                    "filters": [
+                        [
+                            "IsRationalFunctionsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "HeuristicCancelPolynomialsExtRep: ignore",
+                    "filters": [
+                        [
+                            "IsRationalFunctionsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HeuristicCancelPolynomialsExtRep",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ZippedSum",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZippedSum",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ZippedProduct",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZippedProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimeField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimeField)"
+                        ]
+                    ],
+                    "rank": 20052
+                },
+                {
+                    "comment": "PrimeField: for finite field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "PrimeField: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "PrimeField: for a prime field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "PrimeField: for a division ring",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "PrimeField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimeField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimeField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimeField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimeField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimeField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrimeField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 20052
+                },
+                {
+                    "comment": "IsPrimeField: for a division ring",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsPrimeField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimeField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPrimeField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPrimeField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPrimeField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPrimeField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ],
+            [
+                [
+                    "IsNumberFieldByMatrices",
+                    "Tester(IsNumberFieldByMatrices)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefiningPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DefiningPolynomial)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "DefiningPolynomial: for a field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 419
+                },
+                {
+                    "comment": "DefiningPolynomial: for matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "DefiningPolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefiningPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNumberFieldByMatrices",
+                    "Tester(IsNumberFieldByMatrices)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DefiningPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DefiningPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DefiningPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DefiningPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOverPrimeField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOverPrimeField)"
+                        ]
+                    ],
+                    "rank": 20052
+                },
+                {
+                    "comment": "DegreeOverPrimeField: for matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "DegreeOverPrimeField",
+                    "filters": [
+                        [
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "DegreeOverPrimeField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOverPrimeField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOverPrimeField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOverPrimeField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOverPrimeField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOverPrimeField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfDivisionRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfDivisionRing)"
+                        ]
+                    ],
+                    "rank": 20052
+                },
+                {
+                    "comment": "GeneratorsOfDivisionRing: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "GeneratorsOfDivisionRing: for a prime field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "GeneratorsOfDivisionRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfDivisionRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfDivisionRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfDivisionRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfDivisionRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfDivisionRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalBase: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalBase)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "NormalBase: for a field (in characteristic zero)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "NormalBase: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NormalBase: for a finite field and scalar",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "NormalBase: for a field (in characteristic zero), and a scalar",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 62
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalBase",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalBase): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalBase): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalBase)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalBase)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimitiveElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimitiveElement)"
+                        ]
+                    ],
+                    "rank": 20052
+                },
+                {
+                    "comment": "PrimitiveElement: for matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "PrimitiveElement: for a division ring",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "PrimitiveElement: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimitiveElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimitiveElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimitiveElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimitiveElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimitiveElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsFinite",
+                    "Tester(IsFinite)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimitiveRoot: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimitiveRoot)"
+                        ]
+                    ],
+                    "rank": 20058
+                },
+                {
+                    "comment": "PrimitiveRoot",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 432
+                },
+                {
+                    "comment": "PrimitiveRoot: for a finite prime field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "PrimitiveRoot: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimitiveRoot",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsFinite",
+                    "Tester(IsFinite)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimitiveRoot): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimitiveRoot): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimitiveRoot)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsFinite",
+                    "Tester(IsFinite)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimitiveRoot)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RootOfDefiningPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RootOfDefiningPolynomial)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "RootOfDefiningPolynomial: for a small field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 419
+                },
+                {
+                    "comment": "RootOfDefiningPolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RootOfDefiningPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RootOfDefiningPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RootOfDefiningPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RootOfDefiningPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RootOfDefiningPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsDivisionRing: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "AsDivisionRing: for two division rings",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "AsDivisionRing: for a division ring, and a collection",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsDivisionRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClosureDivisionRing: for a division ring containing the whole family, and a scalar",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10062
+                },
+                {
+                    "comment": "ClosureDivisionRing: for division ring and empty list",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ClosureDivisionRing: for a division ring and a scalar",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "ClosureDivisionRing: for division ring and collection of elements",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClosureDivisionRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Subfields: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Subfields)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "Subfields: for finite field of FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "Subfields: for abelian number field of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "Subfields: for finite fields that are not FFEs",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "Subfields: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Subfields",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Subfields): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Subfields): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Subfields)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Subfields)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FieldExtension: for a field of FFEs, and a univ. Laurent polynomial",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 436
+                },
+                {
+                    "comment": "FieldExtension: for field of cyclotomics, and univ. polynomial (degree <= 2)",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "FieldExtension: generic",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FieldExtension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Conjugates: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Conjugates)"
+                        ]
+                    ],
+                    "rank": 20013
+                },
+                {
+                    "comment": "Conjugates: for a scalar (delegate to version with default field)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Conjugates: for a field and a scalar (delegate to version with two fields)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 62
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Conjugates: for two fields of FFEs, and a FFE",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 879
+                },
+                {
+                    "comment": "Conjugates: for Rationals, Rationals, and a rational",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 155
+                },
+                {
+                    "comment": "Conjugates: for cycl. field of cyclotomics, ab. number field, and cyclotomic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 148
+                },
+                {
+                    "comment": "Conjugates: for two abelian number fields of cyclotomics, and cyclotomic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 146
+                },
+                {
+                    "comment": "Conjugates: for two fields and a scalar (call `GaloisGroup')",
+                    "filters": [
+                        [
+                            "IsFieldControlledByGaloisGroup"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 115
+                },
+                {
+                    "comment": "Conjugates: for two fields and a scalar (call `TracePolynomial')",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 114
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Conjugates",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Conjugates): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Conjugates): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Conjugates)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Conjugates)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Norm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Norm)"
+                        ]
+                    ],
+                    "rank": 20013
+                },
+                {
+                    "comment": "Norm: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Norm: for floats",
+                    "filters": [
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Norm: for a scalar (delegate to version with default field)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Norm: for matrix fields",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 10059
+                },
+                {
+                    "comment": "Norm: for a field and a scalar (delegate to version with two fields)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "Norm: for an ordinary character table and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Norm: for two fields of FFEs, and a FFE",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 879
+                },
+                {
+                    "comment": "Norm: for cycl. field of cyclotomics, ab. number field, and cyclotomic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 148
+                },
+                {
+                    "comment": "Norm: for two abelian number fields of cyclotomics, and cyclotomic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 146
+                },
+                {
+                    "comment": "Norm: for two fields and a scalar (use `Conjugates')",
+                    "filters": [
+                        [
+                            "IsFieldControlledByGaloisGroup"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 115
+                },
+                {
+                    "comment": "Norm: for two fields and a scalar (use the trace pol.)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 114
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Norm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Norm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Norm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Norm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Norm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Trace: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Trace)"
+                        ]
+                    ],
+                    "rank": 20013
+                },
+                {
+                    "comment": "Trace: generic method for matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "Trace: for a scalar (delegate to version with default field)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Trace: for a field and a scalar (delegate to version with two fields)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 62
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Trace: for two fields of FFEs, and a FFE",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 879
+                },
+                {
+                    "comment": "Trace: for cycl. field of cyclotomics, ab. number field, and cyclotomic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsCyclotomicField",
+                            "Tester(IsCyclotomicField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 148
+                },
+                {
+                    "comment": "Trace: for two abelian number fields of cyclotomics, and cyclotomic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ],
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 146
+                },
+                {
+                    "comment": "Trace: for two fields and a scalar (use `Conjugates')",
+                    "filters": [
+                        [
+                            "IsFieldControlledByGaloisGroup"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 115
+                },
+                {
+                    "comment": "Trace: for two fields and a scalar (use the trace pol.)",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 114
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Trace",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Trace): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Trace): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Trace)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Trace)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "TracePolynomial: add default indet. 1",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 114
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "TracePolynomial: using minimal polynomial",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 133
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TracePolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ],
+            [
+                [
+                    "IsRationalClassGroupRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GaloisGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GaloisGroup)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "GaloisGroup: for abelian number field ",
+                    "filters": [
+                        [
+                            "IsAbelianNumberField",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "GaloisGroup: for a finite field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "GaloisGroup",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "GaloisGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GaloisGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRationalClassGroupRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GaloisGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GaloisGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GaloisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GaloisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComplexConjugate: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComplexConjugate)"
+                        ]
+                    ],
+                    "rank": 20013
+                },
+                {
+                    "comment": "ComplexConjugate: for a class function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ComplexConjugate: for a quaternion",
+                    "filters": [
+                        [
+                            "IsQuaternion",
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ComplexConjugate: for a cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ComplexConjugate: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ComplexConjugate: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComplexConjugate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComplexConjugate): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComplexConjugate): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComplexConjugate)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComplexConjugate)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RealPart: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RealPart)"
+                        ]
+                    ],
+                    "rank": 20013
+                },
+                {
+                    "comment": "RealPart: for a quaternion",
+                    "filters": [
+                        [
+                            "IsQuaternion",
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "RealPart: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "RealPart: for a scalar",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "RealPart: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RealPart",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RealPart): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RealPart): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RealPart)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RealPart)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImaginaryPart: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImaginaryPart)"
+                        ]
+                    ],
+                    "rank": 20013
+                },
+                {
+                    "comment": "ImaginaryPart: for a quaternion",
+                    "filters": [
+                        [
+                            "IsQuaternion",
+                            "IsSCAlgebraObj"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImaginaryPart: for a cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyc"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ImaginaryPart: for macfloats",
+                    "filters": [
+                        [
+                            "IsIEEE754FloatRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ImaginaryPart: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImaginaryPart",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImaginaryPart): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImaginaryPart): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImaginaryPart)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImaginaryPart)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DivisionRingByGenerators: for collection of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "DivisionRingByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DivisionRingByGenerators: for two coll. of FFEs, the first a field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsFFE)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 441
+                },
+                {
+                    "comment": "DivisionRingByGenerators: for field and collection, both collections of cyclotomics",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "DivisionRingByGenerators: for a division ring, and a collection",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DivisionRingByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FieldOverItselfByGenerators: for a collection of FFEs",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "FieldOverItselfByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FieldOverItselfByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefaultFieldByGenerators: for a collection of FFEs that is a list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "DefaultFieldByGenerators: alg elms",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsAlgebraicElement)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "DefaultFieldByGenerators: for collection of cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "DefaultFieldByGenerators: for a collection",
+                    "filters": [
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DefaultFieldByGenerators: for a finite field, and a collection of FFEs that is a list",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 85
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefaultFieldByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FrobeniusAutomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FrobeniusAutomorphism)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "FrobeniusAutomorphism: for a field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "FrobeniusAutomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FrobeniusAutomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FrobeniusAutomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FrobeniusAutomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FrobeniusAutomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FrobeniusAutomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NthRoot: for a field of FFEs, and a FFE",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsFFE"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 86
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NthRoot",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsZmodnZObjNonprime)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ZmodnZObj: for a positive integer, and an integer -- check small primes",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ZmodnZObj: for family of FFE elements, and integer",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsFFE)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ZmodnZObj: for family of elements in Z/nZ (nonprime), and integer",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsZmodnZObjNonprime)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZmodnZObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsZmodnZObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ModulusOfZmodnZObj: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ModulusOfZmodnZObj)"
+                        ]
+                    ],
+                    "rank": 20017
+                },
+                {
+                    "comment": "ModulusOfZmodnZObj: for element in Z/pZ (prime)",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsZmodnZObj"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ModulusOfZmodnZObj: for FFE",
+                    "filters": [
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ModulusOfZmodnZObj: for element in Z/nZ (nonprime)",
+                    "filters": [
+                        [
+                            "IsZmodnZObjNonprime"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ModulusOfZmodnZObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsZmodnZObj"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ModulusOfZmodnZObj): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ModulusOfZmodnZObj): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ModulusOfZmodnZObj)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsZmodnZObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ModulusOfZmodnZObj)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsZmodnZepsObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Cyclotomic: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Cyclotomic)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "Cyclotomic: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep)",
+                    "filters": [
+                        [
+                            "IsZmodnZepsObj",
+                            "IsZmodnZepsRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cyclotomic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsZmodnZepsObj"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Cyclotomic): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Cyclotomic): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Cyclotomic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsZmodnZepsObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Cyclotomic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRingOfIntegralCyclotomics: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRingOfIntegralCyclotomics)"
+                        ]
+                    ],
+                    "rank": 20031
+                },
+                {
+                    "comment": "IsRingOfIntegralCyclotomics: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -25
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRingOfIntegralCyclotomics",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRingOfIntegralCyclotomics): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRingOfIntegralCyclotomics): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRingOfIntegralCyclotomics)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRingOfIntegralCyclotomics)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCyclotomic"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RoundCyc: Integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "RoundCyc: Rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "RoundCyc: general cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RoundCyc",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCyclotomic"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RoundCycDown: Integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "RoundCycDown: Rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "RoundCycDown: general cyclotomic",
+                    "filters": [
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RoundCycDown",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GaloisMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GaloisMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "GaloisMat: for a matrix of cyclotomics",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsCyclotomic))"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GaloisMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GaloisMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GaloisMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GaloisMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GaloisMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RationalizedMat: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RationalizedMat)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "RationalizedMat: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "RationalizedMat: for an empty list",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RationalizedMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RationalizedMat): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RationalizedMat): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RationalizedMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RationalizedMat)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNumberField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNumberField)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "IsNumberField: for a field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "IsNumberField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNumberField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNumberField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNumberField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNumberField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNumberField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAbelianNumberField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAbelianNumberField)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "IsAbelianNumberField: for a field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "IsAbelianNumberField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAbelianNumberField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAbelianNumberField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAbelianNumberField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAbelianNumberField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAbelianNumberField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCyclotomicField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCyclotomicField)"
+                        ]
+                    ],
+                    "rank": 20054
+                },
+                {
+                    "comment": "IsCyclotomicField: for number fields",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "IsCyclotomicField: for a field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "IsCyclotomicField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -100
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCyclotomicField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCyclotomicField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCyclotomicField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCyclotomicField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCyclotomicField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAbelianNumberField",
+                    "Tester(IsAbelianNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GaloisStabilizer: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GaloisStabilizer)"
+                        ]
+                    ],
+                    "rank": 20059
+                },
+                {
+                    "comment": "GaloisStabilizer: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GaloisStabilizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAbelianNumberField",
+                    "Tester(IsAbelianNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GaloisStabilizer): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GaloisStabilizer): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GaloisStabilizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAbelianNumberField",
+                    "Tester(IsAbelianNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GaloisStabilizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExponentOfPowering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExponentOfPowering)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "ExponentOfPowering: for an identity mapping",
+                    "filters": [
+                        [
+                            "IsOne",
+                            "Tester(IsOne)",
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ExponentOfPowering: for an ANFAutomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsANFAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "ExponentOfPowering: for a mapping (check whether it is the identity mapping)",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ExponentOfPowering: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentOfPowering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExponentOfPowering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExponentOfPowering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExponentOfPowering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExponentOfPowering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Valuation",
+                    "filters": [
+                        [
+                            "IsPadicExtensionNumber"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Valuation",
+                    "filters": [
+                        [
+                            "IsPurePadicNumber"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Valuation: for two integers",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Valuation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsPadicNumber)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PadicNumber: for a pure p-adic family and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPurePadicNumber)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PadicNumber: for a p-adic extension family and a rational",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPadicExtensionNumber)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PadicNumber: for a pure p-adic family and a rational",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPurePadicNumber)"
+                        ],
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PadicNumber: for a p-adic extension family and a list",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsPadicExtensionNumber)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PadicNumber",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPadicNumber"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ShiftedPadicNumber",
+                    "filters": [
+                        [
+                            "IsPadicNumber"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ShiftedPadicNumber",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoefficientsRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoefficientsRing)"
+                        ]
+                    ],
+                    "rank": 20030
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoefficientsRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoefficientsRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoefficientsRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoefficientsRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Indeterminate: number 1",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "Indeterminate: number 1",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Indeterminate: number",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "Indeterminate: number",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Indeterminate: number, name",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Indeterminate: number, avoid",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "Indeterminate: number, name",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Indeterminate: number, avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Indeterminate",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsFloat)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Indeterminate: fam,number",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Indeterminate: number, name, avoid",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Indeterminate: number, name, avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Indeterminate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnivariatePolynomialRing: indet 1",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "UnivariatePolynomialRing: indet number",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "UnivariatePolynomialRing: name",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "UnivariatePolynomialRing: avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "UnivariatePolynomialRing: name,avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnivariatePolynomialRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndeterminatesOfPolynomialRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndeterminatesOfPolynomialRing)"
+                        ]
+                    ],
+                    "rank": 20030
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndeterminatesOfPolynomialRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndeterminatesOfPolynomialRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndeterminatesOfPolynomialRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndeterminatesOfPolynomialRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndeterminatesOfPolynomialRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PolynomialRing",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PolynomialRing: rank",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "PolynomialRing: indetlist",
+                    "filters": [
+                        [
+                            "IsFloatPseudoField"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "PolynomialRing: name",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PolynomialRing: indetlist",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "PolynomialRing: names",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PolynomialRing: rank,avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "PolynomialRing: names,avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PolynomialRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalPolynomial: supply field and indeterminate 1",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MinimalPolynomial: supply field",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "MinimalPolynomial: supply indeterminate 1",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "MinimalPolynomial: spinning over field",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsOrdinaryMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 102
+                },
+                {
+                    "comment": "MinimalPolynomial: for floats",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsFloat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 101
+                },
+                {
+                    "comment": "MinimalPolynomial",
+                    "filters": [
+                        [
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsFFE",
+                            "IsCoeffsModConwayPolRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "MinimalPolynomial: AlgElm",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsAlgebraicElement"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "MinimalPolynomial: finite field, finite field element, and indet. number",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "MinimalPolynomial: for field, scalar, and indet. number",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 81
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FunctionField",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "FunctionField: rank",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "FunctionField: indetlist",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "FunctionField: names",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "FunctionField: rank,avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "FunctionField: names,avoid",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FunctionField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SplittingField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SplittingField)"
+                        ]
+                    ],
+                    "rank": 20017
+                },
+                {
+                    "comment": "SplittingField: use MeatAxe",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "SplittingField: rational polynomials",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "SplittingField: finite field polynomials",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "SplittingField: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SplittingField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SplittingField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SplittingField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SplittingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SplittingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IrrFacsPol: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IrrFacsPol)"
+                        ]
+                    ],
+                    "rank": 20017
+                },
+                {
+                    "comment": "IrrFacsPol",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IrrFacsPol: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IrrFacsPol",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IrrFacsPol): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IrrFacsPol): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IrrFacsPol)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IrrFacsPol)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialRing"
+                ],
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "FactorsSquarefree: univariate rational poly",
+                    "filters": [
+                        [
+                            "IsRationalsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "FactorsSquarefree: for a polynomial over a field of cyclotomics",
+                    "filters": [
+                        [
+                            "IsAbelianNumberFieldPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "FactorsSquarefree: polynomial/alg. ext.",
+                    "filters": [
+                        [
+                            "IsAlgebraicExtensionPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "FactorsSquarefree: univariate polynomial over finite field",
+                    "filters": [
+                        [
+                            "IsFiniteFieldPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorsSquarefree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPrimitivePolynomial: for a (finite) field, and a polynomial",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 65
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimitivePolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimitivePolynomial: univariate polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PrimitivePolynomial: rational polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimitivePolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunctionsFamilyElement",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimizedBombieriNorm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimizedBombieriNorm)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "MinimizedBombieriNorm",
+                    "filters": [
+                        [
+                            "IsRationalFunctionsFamilyElement",
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MinimizedBombieriNorm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsRationalFunctionsFamilyElement"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimizedBombieriNorm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunctionsFamilyElement",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimizedBombieriNorm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimizedBombieriNorm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimizedBombieriNorm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunctionsFamilyElement",
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimizedBombieriNorm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AlgebraicElementsFamilies: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AlgebraicElementsFamilies)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "AlgebraicElementsFamilies",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "AlgebraicElementsFamilies: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlgebraicElementsFamilies",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AlgebraicElementsFamilies): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AlgebraicElementsFamilies): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AlgebraicElementsFamilies)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AlgebraicElementsFamilies)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AlgebraicElementsFamily: generic",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlgebraicElementsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AlgebraicExtension: generic",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "AlgebraicExtension:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "AlgebraicExtension: with name",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 76
+                },
+                {
+                    "comment": "AlgebraicExtension:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsRationalFunction"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlgebraicExtension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaxNumeratorCoeffAlgElm: algebraic element",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement",
+                            "IsKroneckerConstRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MaxNumeratorCoeffAlgElm: algebraic element",
+                    "filters": [
+                        [
+                            "IsAlgebraicElement",
+                            "IsAlgBFRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MaxNumeratorCoeffAlgElm: rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaxNumeratorCoeffAlgElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraicExtension"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefectApproximation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DefectApproximation)"
+                        ]
+                    ],
+                    "rank": 20055
+                },
+                {
+                    "comment": "DefectApproximation: Algebraic Extension",
+                    "filters": [
+                        [
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 53
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefectApproximation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraicExtension"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DefectApproximation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DefectApproximation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DefectApproximation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAlgebraicExtension"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DefectApproximation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [],
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Unknown: for positive integer",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Unknown",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWord"
+                ],
+                [
+                    "CategoryCollections(IsWord)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "MappedWord: for a straight line program word, and two lists",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 123
+                },
+                {
+                    "comment": "MappedWord: for fp group element",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsElementOfFpGroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "MappedWord: for a letter assoc. word, a homogeneous list, and a list",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "MappedWord: for a syllable assoc. word, a homogeneous list, and a list",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "MappedWord: for a nonassoc. word, a homogeneous list, and a list",
+                    "filters": [
+                        [
+                            "IsNonassocWord"
+                        ],
+                        [
+                            "CategoryCollections(IsNonassocWord)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "MappedWord: empty generators list",
+                    "filters": [
+                        [],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MappedWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections((IsWord and IsAssociativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFreeSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20021
+                },
+                {
+                    "comment": "IsFreeSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFreeSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections((IsWord and IsAssociativeElement))"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFreeSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFreeSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFreeSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections((IsWord and IsAssociativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFreeSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFreeMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFreeMonoid)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "IsFreeMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                        ]
+                    ],
+                    "rank": -4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFreeMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFreeMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFreeMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFreeMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFreeMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AssignGeneratorVariables: default method for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "AssignGeneratorVariables: default method for a LOR",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsDistributiveLOpDSum",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "AssignGeneratorVariables: default method for a ring",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(GeneratorsOfRing)"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AssignGeneratorVariables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Subword: for a straight line program word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 145
+                },
+                {
+                    "comment": "Subword: for letter associative word and two positions",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Subword: for syllable associative word and two positions",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Subword",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionWord: for two associative words,start at 1",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PositionWord: for two associative words and a positive integer, using letters",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "PositionWord: for two associative words and a positive integer, using syllables",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ],
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SubstitutedWord: for assoc. word, two positive integers, and assoc. word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SubstitutedWord: for three associative words",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubstitutedWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "EliminatedWord: for three associative words, using the external rep.",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EliminatedWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExponentSumWord: letter rep as.word, gen",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ExponentSumWord: syllable rep as.word, gen",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentSumWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NumberSyllables: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NumberSyllables)"
+                        ]
+                    ],
+                    "rank": 20008
+                },
+                {
+                    "comment": "NumberSyllables: for a straight line program word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 109
+                },
+                {
+                    "comment": "NumberSyllables: for an inf. bits assoc. word",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "NumberSyllables: for a 32 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "NumberSyllables: for a 16 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "NumberSyllables: for an 8 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "NumberSyllables: assoc word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "NumberSyllables: for an assoc. word in syllable rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumberSyllables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NumberSyllables): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NumberSyllables): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NumberSyllables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NumberSyllables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExponentSyllable: for a straight line program word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "ExponentSyllable: for an inf. bits assoc. word, and a pos. integer",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExponentSyllable: for a 32 bits assoc. word, and pos. integer",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExponentSyllable: for a 16 bits assoc. word, and pos. integer",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExponentSyllable: for an 8 bits assoc. word, and a pos. integer",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExponentSyllable: assoc word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ExponentSyllable: for an assoc. word in syllable rep, and a positive integer",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentSyllable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GeneratorSyllable: for a straight line program word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "GeneratorSyllable: for a 32 bits assoc. word, and pos. integer",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "GeneratorSyllable: assoc word in B letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsBLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorSyllable: assoc word in W letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsWLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorSyllable: for an inf. bits assoc. word, and an integer",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorSyllable: for a 16 bits assoc. word, and integer",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorSyllable: for an 8 bits assoc. word, and an integer",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GeneratorSyllable: for an assoc. word in syllable rep, and a positive integer",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorSyllable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SubSyllables: for associative word and two positions, using ext rep.",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubSyllables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LetterRepAssocWord: for a straight line program word",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 109
+                },
+                {
+                    "comment": "LetterRepAssocWord: B letter rep",
+                    "filters": [
+                        [
+                            "IsBLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "LetterRepAssocWord: W letter rep",
+                    "filters": [
+                        [
+                            "IsWLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "LetterRepAssocWord: syllable rep",
+                    "filters": [
+                        [
+                            "IsSyllableAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "LetterRepAssocWord: letter rep,gens",
+                    "filters": [
+                        [
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "LetterRepAssocWord: syllable rep, generators",
+                    "filters": [
+                        [
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LetterRepAssocWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AssocWordByLetterRep: B letter words family",
+                    "filters": [
+                        [
+                            "IsBLetterWordsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AssocWordByLetterRep: W letter words family",
+                    "filters": [
+                        [
+                            "IsWLetterWordsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AssocWordByLetterRep: family, list: syllables",
+                    "filters": [
+                        [
+                            "IsSyllableWordsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "AssocWordByLetterRep: letter words family",
+                    "filters": [
+                        [
+                            "IsLetterWordsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "AssocWordByLetterRep: family, list, gens: syllables",
+                    "filters": [
+                        [
+                            "IsSyllableWordsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AssocWordByLetterRep",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SyllableRepAssocWord: assoc word in syllable rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "SyllableRepAssocWord: assoc word: via extrep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SyllableRepAssocWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExponentSums: for an inf. bits assoc. word",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExponentSums: for a 32 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExponentSums: for a 16 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExponentSums: for an 8 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "ExponentSums: assoc word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ExponentSums: for a group and an assoc. word in syllable rep",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ExponentSums: for an inf. bits assoc. word, and two integers",
+                    "filters": [
+                        [
+                            "IsInfBitsAssocWord"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ExponentSums: for a 32 bits assoc. word",
+                    "filters": [
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExponentSums: for a 16 bits assoc. word, and two integers",
+                    "filters": [
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExponentSums: for an 8 bits assoc. word, and two integers",
+                    "filters": [
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExponentSums: assoc word in letter rep,ints",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentSums",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RenumberedWord: associative words in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "RenumberedWord: associative words in syllable rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsSyllableAssocWordRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RenumberedWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaseDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BaseDomain)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "BaseDomain: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "BaseDomain: for an 8bit matrix",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "BaseDomain: for a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "BaseDomain: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "BaseDomain: for an 8bit vector",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "BaseDomain: for a gf2 vector",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BaseDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BaseDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BaseDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BaseDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PositionLastNonZero: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "PositionLastNonZero: for a matrix obj",
+                    "filters": [
+                        [
+                            "IsMatrixObj"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "PositionLastNonZero: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "PositionLastNonZero: for a row vector obj",
+                    "filters": [
+                        [
+                            "IsRowVectorObj"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PositionLastNonZero: for a plist matrix, and a position",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PositionLastNonZero: for a matrix obj, and an index",
+                    "filters": [
+                        [
+                            "IsMatrixObj"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionLastNonZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsRowListMatrix"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Unpack: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Unpack: for an 8bit matrix",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Unpack: for a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Unpack: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Unpack: for an 8bit vector",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "Unpack: for a gf2 vector",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Unpack",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExtractSubVector: generic method",
+                    "filters": [
+                        [
+                            "IsRowVectorObj"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtractSubVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ZeroVector: for an integer and a plist matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ZeroVector: for an int and an 8bit matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ZeroVector: for an int and a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ZeroVector: for an integer and a plist vector",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ZeroVector: for an int and an 8bit vector",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ZeroVector: for an int and a gf2 vector",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Vector: for a plist of finite field elements and an 8bitvector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "Vector: for a list of gf2 elements and a gf2 vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "Vector: for a plain list and a plist vector",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsPlistRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Vector: for a list and a plist vector",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Vector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConstructingFilter: for a checking plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ConstructingFilter: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ConstructingFilter: for an 8bit matrix",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ConstructingFilter: for a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "ConstructingFilter: for a checking plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "ConstructingFilter: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ConstructingFilter: for an 8bit vector",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ConstructingFilter: for a gf2 vector",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConstructingFilter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CompatibleMatrix: for a plist vector",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "CompatibleMatrix: for an 8bit vector",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "CompatibleMatrix: for a gf2 vector",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CompatibleMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NewRowVector: for Is8BitVectorRep, GF(q), and a list",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -11
+                },
+                {
+                    "comment": "NewRowVector: for IsGF2VectorRep, GF(2), and a list",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -11
+                },
+                {
+                    "comment": "NewRowVector: for IsPlistVectorRep, a ring, and a list",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -12
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewRowVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NewZeroVector: for Is8BitVectorRep, GF(q), and an int",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -11
+                },
+                {
+                    "comment": "NewZeroVector: for IsGF2VectorRep, GF(2), and an int",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -11
+                },
+                {
+                    "comment": "NewZeroVector: for IsPlistVectorRep, a ring, and an int",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -12
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewZeroVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ],
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ChangedBaseDomain: for an 8bit matrix and a finite field",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "ChangedBaseDomain: for a gf2 matrix and a finite field",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "ChangedBaseDomain: for an 8bit vector and a finite field",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ChangedBaseDomain: for a gf2 vector and a finite field",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ChangedBaseDomain: for a checking plist matrix, and a domain",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ChangedBaseDomain: for a plist matrix, and a domain",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "ChangedBaseDomain: for a checking plist vector, and a domain",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ChangedBaseDomain: for a plist vector, and a domain",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ChangedBaseDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsRandomSource"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsMatrixObj"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsRandomSource"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Randomize: for a mutable plist matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Randomize: for a mutable 8bit matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Randomize: for a mutable gf2 matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Randomize: for a mutable plist vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Randomize: for a mutable 8bit vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "Randomize: for a mutable gf2 vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Randomize: for a mutable 8bit matrix, and a random source",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsRandomSource"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Randomize: for a mutable gf2 matrix, and a random source",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsRandomSource"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Randomize: for a mutable 8bit vector and a random source",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsRandomSource"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Randomize: for a mutable gf2 vector and a random source",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsRandomSource"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Randomize",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsMutable",
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "CopySubVector: for two gf2 vectors, and two ranges",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsRange"
+                        ],
+                        [
+                            "IsRange"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "CopySubVector: for two plist vectors and two lists",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep",
+                            "IsCheckingVector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "CopySubVector: for two plist vectors and two lists",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "CopySubVector: for two 8bit vectors, and two lists",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsMutable",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "CopySubVector: for two gf2 vectors, and two lists",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CopySubVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WeightOfVector: for an 8bit vector",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "WeightOfVector: for a gf2 vector",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "WeightOfVector: generic method",
+                    "filters": [
+                        [
+                            "IsRowVectorObj"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeightOfVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DistanceOfVectors: for two 8bit vectors",
+                    "filters": [
+                        [
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "DistanceOfVectors: for two gf2 vectors",
+                    "filters": [
+                        [
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "DistanceOfVectors: generic method",
+                    "filters": [
+                        [
+                            "IsRowVectorObj"
+                        ],
+                        [
+                            "IsRowVectorObj"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DistanceOfVectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RowLength: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RowLength)"
+                        ]
+                    ],
+                    "rank": 20015
+                },
+                {
+                    "comment": "RowLength: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "RowLength: for an 8bit matrix",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "RowLength: for a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RowLength",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RowLength): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RowLength): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RowLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RowLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExtractSubMatrix: for a plist matrix, and two lists",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ExtractSubMatrix: for an 8bit matrix, and two lists",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ExtractSubMatrix: for a gf2 matrix, and two lists",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtractSubMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": [
+                {
+                    "comment": "CopySubMatrix: for two gf2 matrices, two lists and two ranges",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRange"
+                        ],
+                        [
+                            "IsRange"
+                        ]
+                    ],
+                    "rank": 94
+                },
+                {
+                    "comment": "CopySubMatrix: for a plist matrix and a checking plist matrix and four lists",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "CopySubMatrix: for two plist matrices and four lists",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "CopySubMatrix: for two 8bit matrices, and four lists",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "CopySubMatrix: for two gf2 matrices, and four lists",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ]
+        },
+        "name": "CopySubMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "MatElm: for a plist matrix and two positions",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "MatElm: for an 8bit matrix and two integers",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "MatElm: for a gf2 matrix and two integers",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 53
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MatElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SetMatElm: for an 8bit matrix, two integers, and a ffe",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "SetMatElm: for a gf2 matrix, two integers, and a ffe",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "SetMatElm: for a checking plist matrix, two positions, and an object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "SetMatElm: for a plist matrix, two positions, and an object",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 54
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetMatElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ],
+            [
+                [
+                    "IsMutable",
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AddMatrix: for two row list matrices",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsRowListMatrix"
+                        ],
+                        [
+                            "IsRowListMatrix"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "AddMatrix: for two row list matrices and a scalar",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsRowListMatrix"
+                        ],
+                        [
+                            "IsRowListMatrix"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MultMatrix: for a row list matrix",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsRowListMatrix"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MultMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ProductTransposedMatMat: generic method",
+                    "filters": [
+                        [
+                            "IsMatrixObj"
+                        ],
+                        [
+                            "IsMatrixObj"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProductTransposedMatMat",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ZeroMatrix: for two integers and a plist matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "ZeroMatrix: for a compressed 8bit matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "ZeroMatrix: for a compressed gf2 matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZeroMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "NewZeroMatrix: for Is8BitMatrixRep, GF(q), and two ints",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewZeroMatrix: for IsGF2MatrixRep, GF(2), and two ints",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewZeroMatrix: for IsPlistMatrixRep, a ring, and two ints",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewZeroMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IdentityMatrix: for an integer and a plist matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IdentityMatrix: for a compressed 8bit matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IdentityMatrix: for a compressed gf2 matrix",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdentityMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NewIdentityMatrix: for Is8BitMatrixRep, GF(q), and an int",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewIdentityMatrix: for IsGF2MatrixRep, GF(2), and an int",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewIdentityMatrix: for IsPlistMatrixRep, a ring, and an int",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewIdentityMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CompanionMatrix: for a polynomial and a matrix",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsMatrixObj"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CompanionMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NewCompanionMatrix: for IsPlistMatrixRep, a polynomial and a ring",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewCompanionMatrix: for Is8BitMatrixRep, a polynomial and a ring",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewCompanionMatrix: for IsGF2MatrixRep, a polynomial and a ring",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewCompanionMatrix: for IsPlistMatrixRep and IsCheckingMatrix, a polynomial and a ring",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewCompanionMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Matrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Matrix)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "Matrix: for a Rees 0-matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Matrix: for a Rees matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Matrix: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Matrix: generic convenience method with 2 args",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMatrixObj"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Matrix: for a list and a plist matrix",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Matrix: for a list of vecs, an integer, and an 8bit mat",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Matrix: for a list of vecs, an integer, and a gf2 mat",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Matrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "NewMatrix: for Is8BitMatrixRep, GF(q), an int, and a list",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewMatrix: for IsGF2MatrixRep, GF(2), an int, and a list",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -15
+                },
+                {
+                    "comment": "NewMatrix: for IsPlistMatrixRep, a ring, an int, and a list",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep",
+                            "IsCheckingMatrix"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CompatibleVector: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "CompatibleVector: for an 8bit matrix",
+                    "filters": [
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "CompatibleVector: for a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CompatibleVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMatrixObj"
+                ],
+                [
+                    "IsRowVectorObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Unfold: for a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistMatrixRep"
+                        ],
+                        [
+                            "IsPlistVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Unfold: for a matrix object, and a vector object",
+                    "filters": [
+                        [
+                            "IsMatrixObj"
+                        ],
+                        [
+                            "IsRowVectorObj"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Unfold",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRowVectorObj"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsMatrixObj"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Fold: for a plist vector, a positive int, and a plist matrix",
+                    "filters": [
+                        [
+                            "IsPlistVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsPlistMatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Fold: for an 8bit vector, a positive int, and an 8bit matrix",
+                    "filters": [
+                        [
+                            "IsRowVectorObj",
+                            "Is8BitVectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "Is8BitMatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Fold: for a gf2 vector, a positive int, and a gf2 matrix",
+                    "filters": [
+                        [
+                            "IsRowVectorObj",
+                            "IsGF2VectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsGF2MatrixRep"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Fold: for a vector, a positive int, and a matrix",
+                    "filters": [
+                        [
+                            "IsRowVectorObj"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsMatrixObj"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Fold",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBuiltFromAdditiveMagmaWithInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBuiltFromAdditiveMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBuiltFromAdditiveMagmaWithInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBuiltFromAdditiveMagmaWithInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBuiltFromAdditiveMagmaWithInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBuiltFromAdditiveMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBuiltFromAdditiveMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBuiltFromMagma: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBuiltFromMagma)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBuiltFromMagma",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBuiltFromMagma): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBuiltFromMagma): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBuiltFromMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBuiltFromMagma)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBuiltFromMagmaWithOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBuiltFromMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBuiltFromMagmaWithOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBuiltFromMagmaWithOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBuiltFromMagmaWithOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBuiltFromMagmaWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBuiltFromMagmaWithOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBuiltFromMagmaWithInverses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBuiltFromMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBuiltFromMagmaWithInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBuiltFromMagmaWithInverses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBuiltFromMagmaWithInverses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBuiltFromMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBuiltFromMagmaWithInverses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBuiltFromGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBuiltFromGroup)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBuiltFromGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBuiltFromGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBuiltFromGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBuiltFromGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBuiltFromGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBuiltFromSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBuiltFromSemigroup)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBuiltFromSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBuiltFromSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBuiltFromSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBuiltFromSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBuiltFromSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBuiltFromMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBuiltFromMonoid)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBuiltFromMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBuiltFromMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBuiltFromMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBuiltFromMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBuiltFromMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemigroupOfRewritingSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemigroupOfRewritingSystem)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "SemigroupOfRewritingSystem: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromSemigroup",
+                            "Tester(IsBuiltFromSemigroup)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemigroupOfRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemigroupOfRewritingSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemigroupOfRewritingSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemigroupOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemigroupOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MonoidOfRewritingSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MonoidOfRewritingSystem)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "MonoidOfRewritingSystem: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMonoid",
+                            "Tester(IsBuiltFromMonoid)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MonoidOfRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MonoidOfRewritingSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MonoidOfRewritingSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MonoidOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MonoidOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeStructureOfRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConfluentRws: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConfluentRws)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConfluentRws",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConfluentRws): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConfluentRws): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConfluentRws)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConfluentRws)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsOfRws: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsOfRws)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "GeneratorsOfRws",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "GeneratorsOfRws",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "GeneratorsOfRws: for a monoid rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMonoid",
+                            "Tester(IsBuiltFromMonoid)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "GeneratorsOfRws: for a monoid rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromSemigroup",
+                            "Tester(IsBuiltFromSemigroup)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfRws",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsOfRws)",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Setter(GeneratorsOfRws): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsOfRws): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsOfRws)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsOfRws)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NumberGeneratorsOfRws: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NumberGeneratorsOfRws)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "NumberGeneratorsOfRws",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "NumberGeneratorsOfRws",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "NumberGeneratorsOfRws",
+                    "filters": [
+                        [
+                            "IsRewritingSystem"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumberGeneratorsOfRws",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NumberGeneratorsOfRws)",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Setter(NumberGeneratorsOfRws): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NumberGeneratorsOfRws): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NumberGeneratorsOfRws)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NumberGeneratorsOfRws)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Rules: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Rules)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "Rules",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Rules: Deep Thought",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Rules: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Rules",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Rules): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Rules): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Rules)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Rules)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrderingOfRewritingSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrderingOfRewritingSystem)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "OrderingOfRewritingSystem: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrderingOfRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrderingOfRewritingSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrderingOfRewritingSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrderingOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrderingOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsConfluent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsConfluent)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsConfluent: for pc group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsConfluent: method for finite polycylic rewriting systems",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsConfluent: FromTheLeftCollector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsConfluent: generic method for polycyclic rewriting systems",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IsConfluent: for a monoid or a semigroup rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsConfluent",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsConfluent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsConfluent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsConfluent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsConfluent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsConfluent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsReduced: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsReduced)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "IsReduced: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsReduced",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsReduced): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsReduced): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsReduced)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsReduced)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddRule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AddRuleReduced: for a Knuth Bendix rewriting system and a rule",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddRuleReduced",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AddGenerators",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsRewritingSystem"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MakeConfluent: for Knuth Bendix Rewriting System",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsBuiltFromMonoid",
+                            "Tester(IsBuiltFromMonoid)",
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "MakeConfluent: for Knuth Bendix Rewriting System",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsBuiltFromSemigroup",
+                            "Tester(IsBuiltFromSemigroup)",
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MakeConfluent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReduceRules",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ReduceRules: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReduceRules",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsRewritingSystem"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReduceRules",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReducedAdditiveInverse: ReducedForm",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromAdditiveMagmaWithInverses",
+                            "Tester(IsBuiltFromAdditiveMagmaWithInverses)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedAdditiveInverse",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedComm",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedComm",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedComm",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedComm: DeepThoughtReducedComm",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ReducedComm: ReducedLeftQuotient/ReducedProduct",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedComm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedConjugate: DeepThoughtReducedConjugate",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ReducedConjugate: ReducedLeftQuotient/ReducedProduct",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedConjugate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsAdditiveElement"
+                ],
+                [
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedDifference: ReducedSum/ReducedAdditiveInverse",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromAdditiveMagmaWithInverses",
+                            "Tester(IsBuiltFromAdditiveMagmaWithInverses)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedDifference",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReducedForm",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ReducedForm",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ReducedForm",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ReducedForm: CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ReducedForm: for a monoid rewriting system and a word on the underlying free monoid",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMonoid",
+                            "Tester(IsBuiltFromMonoid)"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ReducedForm: for a semigroup rewriting system and a word on the underlying free semigroup",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromSemigroup",
+                            "Tester(IsBuiltFromSemigroup)"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsReducedForm: for a rewriting system and an object",
+                    "filters": [
+                        [
+                            "IsRewritingSystem"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsReducedForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReducedInverse",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ReducedInverse: DeepThoughtReducedInverse",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ReducedInverse: ReducedForm",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMagmaWithInverses",
+                            "Tester(IsBuiltFromMagmaWithInverses)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedInverse",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedLeftQuotient",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedLeftQuotient",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedLeftQuotient",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedLeftQuotient: DeepThoughtReducedLeftQuotient",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ReducedLeftQuotient: ReducedProduct/ReducedInverse",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMagmaWithInverses",
+                            "Tester(IsBuiltFromMagmaWithInverses)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedLeftQuotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReducedOne",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "ReducedOne: ReducedForm",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMagmaWithOne",
+                            "Tester(IsBuiltFromMagmaWithOne)"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ReducedOne: ReducedForm",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromAdditiveMagmaWithInverses",
+                            "Tester(IsBuiltFromAdditiveMagmaWithInverses)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedPower",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "ReducedPower",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "ReducedPower",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "IsInt",
+                            "IsSmallIntRep"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "ReducedPower: DeepThoughtReducedPower",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ReducedPower: ReducedInverse/CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ReducedPower: ReducedProduct/ReducedInverse",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedPower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedProduct",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedProduct",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedProduct",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedProduct: DeepThoughtReducedProduct",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ReducedProduct: ReducedForm",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMagma",
+                            "Tester(IsBuiltFromMagma)"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedQuotient",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedQuotient",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedQuotient",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ReducedQuotient: DeepThoughtReducedQuotient",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ReducedQuotient: ReducedProduct/ReducedInverse",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMagmaWithInverses",
+                            "Tester(IsBuiltFromMagmaWithInverses)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedQuotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                [
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedScalarProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                [
+                    "IsAdditiveElement"
+                ],
+                [
+                    "IsAdditiveElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedSum: ReducedForm",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromAdditiveMagmaWithInverses",
+                            "Tester(IsBuiltFromAdditiveMagmaWithInverses)"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ],
+                        [
+                            "IsAdditiveElement"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedSum",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedZero",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ],
+            [
+                [
+                    "IsGeneralPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelativeOrders: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelativeOrders)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "RelativeOrders: fp",
+                    "filters": [
+                        [
+                            "IsModuloPcgsFpGroupRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "RelativeOrders: pc series",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "RelativeOrders",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "RelativeOrders: Method for Deep Thought",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "RelativeOrders: from-the-left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelativeOrders",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGeneralPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelativeOrders): setting orders for prime orders pcgs",
+                    "filters": [
+                        [
+                            "IsComponentObjectRep",
+                            "IsAttributeStoringRep",
+                            "IsPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "Tester(IsFiniteOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Setter(RelativeOrders): setting orders and checking for prime orders",
+                    "filters": [
+                        [
+                            "IsComponentObjectRep",
+                            "IsAttributeStoringRep",
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Setter(RelativeOrders)",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "Setter(RelativeOrders): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelativeOrders): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelativeOrders)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelativeOrders)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OutdatePolycyclicCollector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OutdatePolycyclicCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UpdatePolycyclicCollector: combinatorial collector rep",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsCombinatorialCollectorRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "UpdatePolycyclicCollector",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "UpdatePolycyclicCollector",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "UpdatePolycyclicCollector: FromTheLeftCollector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UpdatePolycyclicCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CollectWord",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CollectWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "CollectWordOrFail: DeepThought",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "CollectWordOrFail: FTL collector with Hall polynomials, exponent vector, gen-exp-pairs",
+                    "filters": [
+                        [
+                            "IsUpToDatePolycyclicCollector",
+                            "IsFromTheLeftCollectorRep",
+                            "IsPolynomialCollector",
+                            "Tester(IsPolynomialCollector)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "CollectWordOrFail: CombinatorialFromTheLeftCollector",
+                    "filters": [
+                        [
+                            "IsUpToDatePolycyclicCollector",
+                            "IsFromTheLeftCollectorRep",
+                            "IsWeightedCollector",
+                            "Tester(IsWeightedCollector)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "CollectWordOrFail: FromTheLeftCollector",
+                    "filters": [
+                        [
+                            "IsUpToDatePolycyclicCollector",
+                            "IsFromTheLeftCollectorRep",
+                            "UseLibraryCollector",
+                            "Tester(UseLibraryCollector)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector",
+                            "IsUpToDatePolycyclicCollector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "CollectWordOrFail: FromTheLeftCollector",
+                    "filters": [
+                        [
+                            "IsUpToDatePolycyclicCollector",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "CollectWordOrFail",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "CollectWordOrFail: FromTheLeftCollector (outdated)",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 17
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CollectWordOrFail",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NonTrivialRightHandSides",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NonTrivialRightHandSides",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ObjByExponents",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ObjByExponents: DeepThought",
+                    "filters": [
+                        [
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "ObjByExponents",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ObjByExponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SetCommutator: from-the-left collector, words",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "SetCommutator: for from-the-left collector, words as lists",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "SetCommutator: integers",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerConjugateCollector"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "SetCommutator: elements",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetCommutator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SetCommutatorNC: integers",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerConjugateCollector"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "SetCommutatorNC: elements",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerConjugateCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetCommutatorNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetCommutatorANC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SetConjugate: combinatorial collector rep",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsCombinatorialCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "SetConjugate",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "SetConjugate",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "SetConjugate: from-the-left collector, words",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "SetConjugate",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerCommutatorCollector"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "SetConjugate: for from-the-left collector, words as lists",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "SetConjugate",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetConjugate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SetConjugateNC",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "SetConjugateNC",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerCommutatorCollector"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "SetConjugateNC: for from-the-left collector, words as lists",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "SetConjugateNC",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetConjugateNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SetConjugateANC: pow conj single collector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetConjugateANC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPower: combinatorial collector rep",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsCombinatorialCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "SetPower",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SetPower",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "SetPower: from-the-left collector, word",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "SetPower: for from-the-left collector, word as list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "SetPower",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPowerNC",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SetPowerNC: for from-the-left collector, word as list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "SetPowerNC",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPowerNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPowerANC: pow conj single collector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPowerANC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetRelativeOrder",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "SetRelativeOrder: for from-the-left collector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "SetRelativeOrder",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "SetRelativeOrder",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPowerConjugateCollector",
+                            "IsDeepThoughtCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetRelativeOrder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetRelativeOrderNC",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "SetRelativeOrderNC: for from-the-left collector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "SetRelativeOrderNC",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetRelativeOrderNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GetCommutatorNC: for from the left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetCommutatorNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GetConjugateNC: finite pow-conj single collector",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "GetConjugateNC: from the left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetConjugateNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GetPowerNC",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPowerConjugateCollector",
+                            "IsSingleCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "GetPowerNC: from-the-left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetPowerNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SingleCollector",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "SingleCollector",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "SingleCollector",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "SingleCollector",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SingleCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SingleCollectorByGenerators",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SingleCollectorByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CombinatorialCollector",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "CombinatorialCollector",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "CombinatorialCollector",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "CombinatorialCollector",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CombinatorialCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CombinatorialCollectorByGenerators",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CombinatorialCollectorByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DeepThoughtCollector",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "DeepThoughtCollector",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeepThoughtCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DeepThoughtCollectorByGenerators",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeepThoughtCollectorByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": [
+                {
+                    "comment": "EvaluateOverlapCBA: polyc. collector, 2 hom. lists, 3 pos. integers",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ]
+        },
+        "name": "EvaluateOverlapCBA",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": [
+                {
+                    "comment": "EvaluateOverlapBNA: polyc. collector, 2 hom. lists, 3 pos. integers",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ]
+        },
+        "name": "EvaluateOverlapBNA",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": [
+                {
+                    "comment": "EvaluateOverlapBAN: polyc. collector, 2 hom. lists, 3 pos. integers",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ]
+        },
+        "name": "EvaluateOverlapBAN",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "EvaluateOverlapANA: polyc. collector, 2 hom. lists, 3 pos. integers",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "6args": []
+        },
+        "name": "EvaluateOverlapANA",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MultiplicativeElementsWithInversesFamilyByRws: 32 bits family",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPolycyclicCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is32BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "MultiplicativeElementsWithInversesFamilyByRws: 16 bits family",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPolycyclicCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is16BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "MultiplicativeElementsWithInversesFamilyByRws: 8 bits family",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPolycyclicCollector",
+                            "IsUpToDatePolycyclicCollector",
+                            "Is8BitsSingleCollectorRep",
+                            "IsDefaultRhsTypeSingleCollector"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "MultiplicativeElementsWithInversesFamilyByRws: generic method",
+                    "filters": [
+                        [
+                            "IsPolycyclicCollector"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "MultiplicativeElementsWithInversesFamilyByRws",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MultiplicativeElementsWithInversesFamilyByRws",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementsFamilyByRws"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ElementByRws: using 32Bits_AssocWord",
+                    "filters": [
+                        [
+                            "IsElementsFamilyBy32BitsSingleCollector"
+                        ],
+                        [
+                            "Is32BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ElementByRws: using 16Bits_AssocWord",
+                    "filters": [
+                        [
+                            "IsElementsFamilyBy16BitsSingleCollector"
+                        ],
+                        [
+                            "Is16BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ElementByRws: using 8Bits_AssocWord",
+                    "filters": [
+                        [
+                            "IsElementsFamilyBy8BitsSingleCollector"
+                        ],
+                        [
+                            "Is8BitsAssocWord"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ElementByRws",
+                    "filters": [
+                        [
+                            "IsElementsFamilyByRws"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ElementByRws",
+                    "filters": [
+                        [
+                            "IsElementsFamilyByRws"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementByRws",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupByRws",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupByRws",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupByRwsNC: rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromGroup",
+                            "Tester(IsBuiltFromGroup)"
+                        ]
+                    ],
+                    "rank": 110
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupByRwsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefiningPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DefiningPcgs)"
+                        ]
+                    ],
+                    "rank": 20003
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefiningPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DefiningPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DefiningPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DefiningPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DefiningPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PolycyclicFactorGroup: for free group, empty list using ' PolycyclicFactorGroupByRelators'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "PolycyclicFactorGroup: for free group, list using ' PolycyclicFactorGroupByRelators'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PolycyclicFactorGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PolycyclicFactorGroupNC: for free group, list using ' PolycyclicFactorGroupByRelators'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PolycyclicFactorGroupNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PolycyclicFactorGroupByRelatorsNC: generic method for family, generators, relators",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PolycyclicFactorGroupByRelatorsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PolycyclicFactorGroupByRelators: generic method for family, generators, relators",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PolycyclicFactorGroupByRelators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MonomialComparisonFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MonomialComparisonFunction)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MonomialComparisonFunction: default: use extrep",
+                    "filters": [
+                        [
+                            "IsMonomialOrderingDefaultRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MonomialComparisonFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonomialOrdering"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MonomialComparisonFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MonomialComparisonFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MonomialComparisonFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MonomialComparisonFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MonomialExtrepComparisonFun: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MonomialExtrepComparisonFun)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "MonomialExtrepComparisonFun: functions are themselves -- for compatibility",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MonomialExtrepComparisonFun",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MonomialExtrepComparisonFun): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MonomialExtrepComparisonFun): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MonomialExtrepComparisonFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MonomialExtrepComparisonFun)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OccuringVariableIndices: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OccuringVariableIndices)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "OccuringVariableIndices: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OccuringVariableIndices",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonomialOrdering"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OccuringVariableIndices): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OccuringVariableIndices): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OccuringVariableIndices)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OccuringVariableIndices)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeadingMonomialOfPolynomial: with ordering",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingMonomialOfPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeadingCoefficientOfPolynomial: with ordering",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingCoefficientOfPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomialFunction"
+                ],
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeadingTermOfPolynomial: with ordering",
+                    "filters": [
+                        [
+                            "IsPolynomialFunction"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingTermOfPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList",
+                    "CategoryCollections(IsRationalFunction)"
+                ],
+                [
+                    "IsMonomialOrdering"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "Tester(LeftActingRingOfIdeal)",
+                    "Tester(RightActingRingOfIdeal)",
+                    "CategoryCollections(IsRationalFunction)"
+                ],
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GroebnerBasis: ideal with stored GB",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)",
+                            "CategoryCollections(IsRationalFunction)",
+                            "Tester(StoredGroebnerBasis)"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "GroebnerBasis: ideal",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)",
+                            "CategoryCollections(IsRationalFunction)"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GroebnerBasis: polynomials",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "CategoryCollections(IsRationalFunction)"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "GroebnerBasis: fix function",
+                    "filters": [
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroebnerBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList",
+                    "CategoryCollections(IsRationalFunction)"
+                ],
+                [
+                    "IsMonomialOrdering"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "Tester(LeftActingRingOfIdeal)",
+                    "Tester(RightActingRingOfIdeal)",
+                    "CategoryCollections(IsRationalFunction)"
+                ],
+                [
+                    "IsMonomialOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReducedGroebnerBasis: ideal",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)",
+                            "CategoryCollections(IsRationalFunction)"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "ReducedGroebnerBasis: polynomials",
+                    "filters": [
+                        [
+                            "IsHomogeneousList",
+                            "CategoryCollections(IsRationalFunction)"
+                        ],
+                        [
+                            "IsMonomialOrdering"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ReducedGroebnerBasis: fix function",
+                    "filters": [
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedGroebnerBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "Tester(LeftActingRingOfIdeal)",
+                    "Tester(RightActingRingOfIdeal)",
+                    "CategoryCollections(IsRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StoredGroebnerBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StoredGroebnerBasis)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "StoredGroebnerBasis: ideal",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "Tester(LeftActingRingOfIdeal)",
+                            "Tester(RightActingRingOfIdeal)",
+                            "CategoryCollections(IsRationalFunction)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "StoredGroebnerBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "CategoryCollections(IsRationalFunction)"
+                        ]
+                    ],
+                    "rank": -26
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StoredGroebnerBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "Tester(LeftActingRingOfIdeal)",
+                    "Tester(RightActingRingOfIdeal)",
+                    "CategoryCollections(IsRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StoredGroebnerBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StoredGroebnerBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StoredGroebnerBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "Tester(LeftActingRingOfIdeal)",
+                    "Tester(RightActingRingOfIdeal)",
+                    "CategoryCollections(IsRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StoredGroebnerBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PcgsByPcSequence",
+                    "filters": [
+                        [
+                            "IsElementsFamilyByRws"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PcgsByPcSequence",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PcgsByPcSequence",
+                    "filters": [
+                        [
+                            "IsElementsFamilyByRws"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PcgsByPcSequence",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcgsByPcSequence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PcgsByPcSequenceNC: elements family by rws, empty sequence",
+                    "filters": [
+                        [
+                            "IsElementsFamilyByRws"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "PcgsByPcSequenceNC: pc series, empty sequence",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "PcgsByPcSequenceNC: elements family by rws with defining pcgs",
+                    "filters": [
+                        [
+                            "IsElementsFamilyByRws",
+                            "Tester(DefiningPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "PcgsByPcSequenceNC: elements family by rws",
+                    "filters": [
+                        [
+                            "IsElementsFamilyByRws"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PcgsByPcSequenceNC: pc series",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcgsByPcSequenceNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [],
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "PcgsByPcSequenceCons: generic constructor",
+                    "filters": [
+                        [
+                            "IsPcgsDefaultRep"
+                        ],
+                        [],
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -3
+                }
+            ],
+            "6args": []
+        },
+        "name": "PcgsByPcSequenceCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcGroupWithPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcGroupWithPcgs)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "PcGroupWithPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "PcGroupWithPcgs: pcgs modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcGroupWithPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcGroupWithPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcGroupWithPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcGroupWithPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcGroupWithPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupOfPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GroupOfPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "GroupOfPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "GroupOfPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "GroupOfPcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupOfPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GroupOfPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GroupOfPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GroupOfPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GroupOfPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OneOfPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OneOfPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OneOfPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OneOfPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OneOfPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OneOfPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OneOfPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcSeries)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "PcSeries",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "PcSeries: construct subgroups",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPcgsElementaryAbelianSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPcgsElementaryAbelianSeries)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "IsPcgsElementaryAbelianSeries: test if elm. abelian",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPcgsElementaryAbelianSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPcgsElementaryAbelianSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPcgsElementaryAbelianSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPcgsElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPcgsElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcgsElementaryAbelianSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcgsElementaryAbelianSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: for pc group with parent group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: CRISP method for pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: for PCgroups via SpecialPcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: for group with parent group",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: generic group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: if special pcgs is known",
+                    "filters": [
+                        [
+                            "Tester(SpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: group list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "PcgsElementaryAbelianSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcgsElementaryAbelianSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcgsElementaryAbelianSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcgsElementaryAbelianSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcgsElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcgsElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndicesEANormalSteps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndicesEANormalSteps)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "IndicesEANormalSteps: special pcgs: LGFirst",
+                    "filters": [
+                        [
+                            "IsSpecialPcgs",
+                            "Tester(IsSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "IndicesEANormalSteps: inherit from parent",
+                    "filters": [
+                        [
+                            "IsInducedPcgs",
+                            "Tester(ParentPcgs)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IndicesEANormalSteps: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicesEANormalSteps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndicesEANormalSteps): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndicesEANormalSteps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndicesEANormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndicesEANormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EANormalSeriesByPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EANormalSeriesByPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "EANormalSeriesByPcgs: perm group modulo rep",
+                    "filters": [
+                        [
+                            "IsPcgsElementaryAbelianSeries",
+                            "Tester(IsPcgsElementaryAbelianSeries)",
+                            "IsModuloPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "EANormalSeriesByPcgs: perm group rep",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsElementaryAbelianSeries",
+                            "Tester(IsPcgsElementaryAbelianSeries)",
+                            "IsPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "EANormalSeriesByPcgs: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesEANormalSteps)",
+                            "IsPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "EANormalSeriesByPcgs: from PcSeries",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(PcSeries)",
+                            "Tester(IndicesEANormalSteps)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "EANormalSeriesByPcgs: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesEANormalSteps)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "EANormalSeriesByPcgs: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EANormalSeriesByPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EANormalSeriesByPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EANormalSeriesByPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EANormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EANormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPcgsCentralSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPcgsCentralSeries)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPcgsCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPcgsCentralSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPcgsCentralSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPcgsCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPcgsCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcgsCentralSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcgsCentralSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PcgsCentralSeries: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "PcgsCentralSeries: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "PcgsCentralSeries: for pc groups use SpecialPcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "PcgsCentralSeries: for pcgs computable use SpecialPcgs",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PcgsCentralSeries: if special pcgs is known",
+                    "filters": [
+                        [
+                            "Tester(SpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PcgsCentralSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcgsCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcgsCentralSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcgsCentralSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcgsCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcgsCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndicesCentralNormalSteps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndicesCentralNormalSteps)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "IndicesCentralNormalSteps: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicesCentralNormalSteps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndicesCentralNormalSteps): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndicesCentralNormalSteps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndicesCentralNormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndicesCentralNormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentralNormalSeriesByPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CentralNormalSeriesByPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "CentralNormalSeriesByPcgs: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesCentralNormalSteps)",
+                            "IsPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "CentralNormalSeriesByPcgs: from PcSeries",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(PcSeries)",
+                            "Tester(IndicesCentralNormalSteps)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "CentralNormalSeriesByPcgs: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesCentralNormalSteps)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "CentralNormalSeriesByPcgs: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralNormalSeriesByPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CentralNormalSeriesByPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CentralNormalSeriesByPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CentralNormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CentralNormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPcgsPCentralSeriesPGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPcgsPCentralSeriesPGroup)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPcgsPCentralSeriesPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPcgsPCentralSeriesPGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPcgsPCentralSeriesPGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPcgsPCentralSeriesPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPcgsPCentralSeriesPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcgsPCentralSeriesPGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcgsPCentralSeriesPGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PcgsPCentralSeriesPGroup: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "PcgsPCentralSeriesPGroup: for permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "PcgsPCentralSeriesPGroup: for pc groups use SpecialPcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "PcgsPCentralSeriesPGroup: for pcgs computable use SpecialPcgs",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "PcgsPCentralSeriesPGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcgsPCentralSeriesPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcgsPCentralSeriesPGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcgsPCentralSeriesPGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcgsPCentralSeriesPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcgsPCentralSeriesPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndicesPCentralNormalStepsPGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndicesPCentralNormalStepsPGroup)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "IndicesPCentralNormalStepsPGroup: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicesPCentralNormalStepsPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndicesPCentralNormalStepsPGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndicesPCentralNormalStepsPGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndicesPCentralNormalStepsPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndicesPCentralNormalStepsPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PCentralNormalSeriesByPcgsPGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PCentralNormalSeriesByPcgsPGroup)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "PCentralNormalSeriesByPcgsPGroup: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesPCentralNormalStepsPGroup)",
+                            "IsPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "PCentralNormalSeriesByPcgsPGroup: from PcSeries",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(PcSeries)",
+                            "Tester(IndicesPCentralNormalStepsPGroup)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PCentralNormalSeriesByPcgsPGroup: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesPCentralNormalStepsPGroup)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PCentralNormalSeriesByPcgsPGroup: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PCentralNormalSeriesByPcgsPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PCentralNormalSeriesByPcgsPGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PCentralNormalSeriesByPcgsPGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PCentralNormalSeriesByPcgsPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PCentralNormalSeriesByPcgsPGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPcgsChiefSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPcgsChiefSeries)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPcgsChiefSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPcgsChiefSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPcgsChiefSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPcgsChiefSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPcgsChiefSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcgsChiefSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcgsChiefSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PcgsChiefSeries: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "PcgsChiefSeries: compute chief series and pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PcgsChiefSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcgsChiefSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcgsChiefSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcgsChiefSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcgsChiefSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcgsChiefSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndicesChiefNormalSteps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndicesChiefNormalSteps)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "IndicesChiefNormalSteps: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicesChiefNormalSteps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndicesChiefNormalSteps): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndicesChiefNormalSteps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndicesChiefNormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndicesChiefNormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ChiefNormalSeriesByPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ChiefNormalSeriesByPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "ChiefNormalSeriesByPcgs: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesChiefNormalSteps)",
+                            "IsPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ChiefNormalSeriesByPcgs: from PcSeries",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(PcSeries)",
+                            "Tester(IndicesChiefNormalSteps)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ChiefNormalSeriesByPcgs: from indices",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesChiefNormalSteps)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ChiefNormalSeriesByPcgs: compatibility only",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ChiefNormalSeriesByPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ChiefNormalSeriesByPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ChiefNormalSeriesByPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ChiefNormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ChiefNormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndicesNormalSteps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndicesNormalSteps)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "IndicesNormalSteps: generic",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicesNormalSteps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndicesNormalSteps): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndicesNormalSteps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndicesNormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndicesNormalSteps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalSeriesByPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalSeriesByPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "NormalSeriesByPcgs: generic",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalSeriesByPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalSeriesByPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalSeriesByPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalSeriesByPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrimeOrdersPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "IsPrimeOrdersPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsPrimeOrdersPcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimeOrdersPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPrimeOrdersPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPrimeOrdersPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPrimeOrdersPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPrimeOrdersPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFiniteOrdersPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFiniteOrdersPcgs)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "IsFiniteOrdersPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsFiniteOrdersPcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFiniteOrdersPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFiniteOrdersPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFiniteOrdersPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFiniteOrdersPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFiniteOrdersPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RefinedPcGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RefinedPcGroup)"
+                        ]
+                    ],
+                    "rank": 20039
+                },
+                {
+                    "comment": "RefinedPcGroup: group with refined pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "RefinedPcGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RefinedPcGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RefinedPcGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RefinedPcGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RefinedPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RefinedPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismRefinedPcGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismRefinedPcGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsomorphismRefinedPcGroup: group with refined pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsomorphismRefinedPcGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismRefinedPcGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismRefinedPcGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismRefinedPcGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismRefinedPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismRefinedPcGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DepthOfPcElement: handled by nice monomorphism: attribute CollElm",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 360
+                },
+                {
+                    "comment": "DepthOfPcElement: family pcgs (32 bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 185
+                },
+                {
+                    "comment": "DepthOfPcElement: family pcgs (16 bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 185
+                },
+                {
+                    "comment": "DepthOfPcElement: family pcgs (8 bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 185
+                },
+                {
+                    "comment": "DepthOfPcElement: family pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "DepthOfPcElement: for pcgs of direct product",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDirectProductRep"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "DepthOfPcElement: permpcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "DepthOfPcElement: pcgs by pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsByPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "DepthOfPcElement: sorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsSortedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "DepthOfPcElement: induced pcgs",
+                    "filters": [
+                        [
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "DepthOfPcElement: unsorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsUnsortedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "DepthOfPcElement: pcgs modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "DepthOfPcElement: generic methods, ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "DepthOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "DepthOfPcElement: permpcgs,start",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "DepthOfPcElement: pcgs modulo pcgs, ignoring <min>",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "DepthOfPcElement: pcgs modulo pcgs, ignoring <min>",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DepthOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DifferenceOfPcElement: generic methods, PcElementByExponents/ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 21
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DifferenceOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExponentOfPcElement: via nicoemorphism",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "ExponentOfPcElement: family pcgs (32bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is32BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 204
+                },
+                {
+                    "comment": "ExponentOfPcElement: family pcgs (16bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is16BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 204
+                },
+                {
+                    "comment": "ExponentOfPcElement: family pcgs (8bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is8BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 204
+                },
+                {
+                    "comment": "ExponentOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "ExponentOfPcElement: induced pcgs",
+                    "filters": [
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "ExponentOfPcElement: sorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsSortedPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ExponentOfPcElement: unsorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsUnsortedPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExponentOfPcElement: pcgs modulo tail-pcgs, ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExponentOfPcElement: generic method, ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "ExponentOfPcElement: pcgs modulo pcgs, ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExponentsOfPcElement: handled by nice monomorphism: attribute CollElm",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 360
+                },
+                {
+                    "comment": "ExponentsOfPcElement: family pcgs/32 bit",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 179
+                },
+                {
+                    "comment": "ExponentsOfPcElement: family pcgs/16 bit",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 179
+                },
+                {
+                    "comment": "ExponentsOfPcElement: family pcgs/8 bit",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 179
+                },
+                {
+                    "comment": "ExponentsOfPcElement: family pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "ExponentsOfPcElement: for pcgs of direct product",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsDirectProductRep"
+                        ],
+                        [
+                            "IsDirectProductElement"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "ExponentsOfPcElement: perm group",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "ExponentsOfPcElement: subset of induced pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsSubsetInducedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ExponentsOfPcElement: induced pcgs",
+                    "filters": [
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "ExponentsOfPcElement: fp",
+                    "filters": [
+                        [
+                            "IsModuloPcgsFpGroupRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "ExponentsOfPcElement: pcgs by pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPcgsByPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExponentsOfPcElement: sorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsSortedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ExponentsOfPcElement: subset induced pcgs modulo tail-pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsRep",
+                            "IsNumeratorParentForExponentsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ExponentsOfPcElement: unsorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsUnsortedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ExponentsOfPcElement: pcgs modulo tail-pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ExponentsOfPcElement: modpcgs numerator parent layers",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloPcgsRep",
+                            "IsNumeratorParentLayersForExponentsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ExponentsOfPcElement: pcgs modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ExponentsOfPcElement: pc series",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 389
+                },
+                {
+                    "comment": "ExponentsOfPcElement: perm group with 0 positions",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 377
+                },
+                {
+                    "comment": "ExponentsOfPcElement: family pcgs/32 bit",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "Is32BitsPcWordRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 181
+                },
+                {
+                    "comment": "ExponentsOfPcElement: family pcgs/16 bit",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "Is16BitsPcWordRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 181
+                },
+                {
+                    "comment": "ExponentsOfPcElement: family pcgs/8 bit",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "Is8BitsPcWordRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 181
+                },
+                {
+                    "comment": "ExponentsOfPcElement: perm group with positions",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "ExponentsOfPcElement: perm group with 0 positions",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "ExponentsOfPcElement: subset of induced pcgs, subrange",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsSubsetInducedPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ExponentsOfPcElement: induced pcgs, subrange",
+                    "filters": [
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "ExponentsOfPcElement: sorted pcgs/range",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsSortedPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ExponentsOfPcElement: subset induced pcgs modulo tail-pcgs, subrange",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsRep",
+                            "IsNumeratorParentForExponentsRep"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ExponentsOfPcElement: unsorted pcgs/range",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsUnsortedPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExponentsOfPcElement: pcgs modulo tail-pcgs, subrange",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExponentsOfPcElement: pcgs modulo pcgs, subrange",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloPcgsRep"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ExponentsOfPcElement: with positions, falling back to ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ExponentsOfPcElement: pcgs mod. pcgs,range, falling back to Exp.OfPcElement",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentsOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExponentsOfConjugate: family pcgs: look up",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "ExponentsOfConjugate: subset induced pcgs modulo tail-pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsRep",
+                            "IsNumeratorParentForExponentsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "ExponentsOfConjugate: generic: compute conjugate",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 58
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentsOfConjugate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExponentsOfRelativePower: family pcgs: look up",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 95
+                },
+                {
+                    "comment": "ExponentsOfRelativePower: subset induced pcgs modulo tail-pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsRep",
+                            "IsNumeratorParentForExponentsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ExponentsOfRelativePower: generic: compute power",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentsOfRelativePower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExponentsOfCommutator: generic: compute commutator",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 58
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentsOfCommutator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeadingExponentOfPcElement: handled by nice monomorphism: attribute CollElm",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 360
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: family pcgs (32 bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 185
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: family pcgs (16 bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 185
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: family pcgs (8 bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 185
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: family pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: subset induced pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsSubsetInducedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: sorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsSortedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: unsorted pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsUnsortedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: generic methods, ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "LeadingExponentOfPcElement: pcgs modulo pcgs, use ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingExponentOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DepthAndLeadingExponentOfPcElement: permpcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "DepthAndLeadingExponentOfPcElement: generic methods, ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DepthAndLeadingExponentOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PcElementByExponentsNC: family pcgs, FFE",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "PcElementByExponentsNC: family pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "PcElementByExponentsNC: subset induced wrt family pcgs, FFE",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "PcElementByExponentsNC: subset induced wrt family pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "PcElementByExponentsNC: modulo subset induced wrt family pcgs, FFE",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsNumeratorParentPcgsFamilyPcgs",
+                            "Tester(IsNumeratorParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedNumeratorModuloTailPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "PcElementByExponentsNC: modulo subset induced wrt family pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsNumeratorParentPcgsFamilyPcgs",
+                            "Tester(IsNumeratorParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedNumeratorModuloTailPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method: modulo, FFE",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method: modulo",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method for empty lists",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method for empty lists",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method: call LinearCombinationPcgs",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PcElementByExponentsNC: generic method for empty list as basis or basisindex, modulo",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 10039
+                },
+                {
+                    "comment": "PcElementByExponentsNC: family pcgs, basisind, FFE",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 138
+                },
+                {
+                    "comment": "PcElementByExponentsNC: family pcgs, index",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 138
+                },
+                {
+                    "comment": "PcElementByExponentsNC: subset induced wrt family pcgs, FFE,index",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "PcElementByExponentsNC: subset induced wrt family pcgs, index",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "PcElementByExponentsNC: modulo subset induced wrt family pcgs, FFE, index",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsNumeratorParentPcgsFamilyPcgs",
+                            "Tester(IsNumeratorParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedNumeratorModuloTailPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 94
+                },
+                {
+                    "comment": "PcElementByExponentsNC: modulo subset induced wrt family pcgs,index",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsNumeratorParentPcgsFamilyPcgs",
+                            "Tester(IsNumeratorParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedNumeratorModuloTailPcgsRep"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 94
+                },
+                {
+                    "comment": "PcElementByExponentsNC: index: defer to basis,FFE",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "PcElementByExponentsNC: index: defer to basis",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method for empty lists",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "PcElementByExponentsNC: multiply base elts., FFE",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "PcElementByExponentsNC: multiply basis elements",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method: modulo, basis, FFE",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsFFE)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "PcElementByExponentsNC: generic method: modulo, basis",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 53
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcElementByExponentsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SumOfPcElement: generic methods, PcElementByExponents+ExponentsOfPcElement",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 21
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SumOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ReducedPcElement: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ReducedPcElement: pcgs modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 20
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RelativeOrderOfPcElement: fp",
+                    "filters": [
+                        [
+                            "IsModuloPcgsFpGroupRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "RelativeOrderOfPcElement: for IsPrimeOrdersPcgs using RelativeOrders",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        []
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "RelativeOrderOfPcElement: general method using RelativeOrders",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "RelativeOrderOfPcElement: pcgs modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        []
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelativeOrderOfPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "HeadPcElementByNumber: family pcgs (32bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is32BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 203
+                },
+                {
+                    "comment": "HeadPcElementByNumber: family pcgs (16bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is16BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 203
+                },
+                {
+                    "comment": "HeadPcElementByNumber: family pcgs (8bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is8BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 203
+                },
+                {
+                    "comment": "HeadPcElementByNumber: using 'ExponentsOfPcElement', 'PcElementByExponents'",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HeadPcElementByNumber",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CleanedTailPcElement: family pcgs (32bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is32BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 203
+                },
+                {
+                    "comment": "CleanedTailPcElement: family pcgs (16bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is16BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 203
+                },
+                {
+                    "comment": "CleanedTailPcElement: family pcgs (8bits)",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is8BitsPcWordRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 203
+                },
+                {
+                    "comment": "CleanedTailPcElement: family pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "CleanedTailPcElement: sorted pcgs - defer to sorting pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsSortedPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "CleanedTailPcElement: generic: do nothing",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CleanedTailPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ExtendedIntersectionSumPcgs: generic method for modulo pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 29
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtendedIntersectionSumPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IntersectionSumPcgs: prime orders pcgs, tail-pcgs, list",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsInducedPcgs",
+                            "IsTailInducedPcgsRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "IntersectionSumPcgs: using 'ExtendedIntersectionSumPcgs'",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntersectionSumPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NormalIntersectionPcgs: prime orders pcgs, tail-pcgs, induced-pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsInducedPcgs",
+                            "IsTailInducedPcgsRep"
+                        ],
+                        [
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ]
+                    ],
+                    "rank": 79
+                },
+                {
+                    "comment": "NormalIntersectionPcgs: prime orders pcgs, tail-pcgs, list",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsInducedPcgs",
+                            "IsTailInducedPcgsRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "NormalIntersectionPcgs: using 'ExtendedIntersectionSumPcgs'",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalIntersectionPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SumPcgs: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SumPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SumFactorizationFunctionPcgs: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 29
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SumFactorizationFunctionPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EnumeratorByPcgs: pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "EnumeratorByPcgs: pcgs, sublist",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EnumeratorByPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExtendedPcgs: perm pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "ExtendedPcgs: pcgs, empty list",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "ExtendedPcgs: induced pcgs",
+                    "filters": [
+                        [
+                            "IsInducedPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtendedPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedPcgsByPcSequence",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "InducedPcgsByPcSequence",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsByPcSequence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedPcgsByPcSequenceNC: tail of perm pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsPcgsPermGroupRep"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "InducedPcgsByPcSequenceNC: pcgs, empty list",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "InducedPcgsByPcSequenceNC: pcgs, homogeneous list",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "InducedPcgsByPcSequenceNC: pcgs, empty list,depths",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "InducedPcgsByPcSequenceNC: pcgs, homogeneous list, depths",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsCollection"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsByPcSequenceNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeadCoeffsIGS: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeadCoeffsIGS)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "LeadCoeffsIGS: generic",
+                    "filters": [
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadCoeffsIGS",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeadCoeffsIGS): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeadCoeffsIGS): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeadCoeffsIGS)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeadCoeffsIGS)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "InducedPcgsByPcSequenceAndGenerators",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsByPcSequenceAndGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedPcgsByGenerators",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "InducedPcgsByGenerators: pcgs, collection",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedPcgsByGeneratorsNC: pcgs, empty list",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "InducedPcgsByGeneratorsNC: prime order pcgs, collection",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "InducedPcgsByGeneratorsNC:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsByGeneratorsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "InducedPcgsByGeneratorsWithImages",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "InducedPcgsByGeneratorsWithImages",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsByGeneratorsWithImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CanonicalPcgsByGeneratorsWithImages",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "CanonicalPcgsByGeneratorsWithImages",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalPcgsByGeneratorsWithImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "AsInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsInducedPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ParentPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ParentPcgs)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ParentPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParentPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ParentPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ParentPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ParentPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ParentPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalPcgs)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "CanonicalPcgs: of an canonical pcgs",
+                    "filters": [
+                        [
+                            "IsCanonicalPcgs",
+                            "Tester(IsCanonicalPcgs)"
+                        ]
+                    ],
+                    "rank": 10024
+                },
+                {
+                    "comment": "CanonicalPcgs: induced prime orders pcgs",
+                    "filters": [
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsInducedPcgs"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "CanonicalPcgs:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsInducedPcgs"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCanonicalPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCanonicalPcgs)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCanonicalPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCanonicalPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCanonicalPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCanonicalPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCanonicalPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsParentPcgsFamilyPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsParentPcgsFamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsParentPcgsFamilyPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsParentPcgsFamilyPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsParentPcgsFamilyPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsParentPcgsFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsParentPcgsFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ElementaryAbelianSubseries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ElementaryAbelianSubseries)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "ElementaryAbelianSubseries: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementaryAbelianSubseries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ElementaryAbelianSubseries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ElementaryAbelianSubseries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ElementaryAbelianSubseries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ElementaryAbelianSubseries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CanonicalPcElement: tail induced pcgs, 32bits word",
+                    "filters": [
+                        [
+                            "IsInducedPcgs",
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsTailInducedPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is32BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 158
+                },
+                {
+                    "comment": "CanonicalPcElement: tail induced pcgs, 16bits word",
+                    "filters": [
+                        [
+                            "IsInducedPcgs",
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsTailInducedPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is16BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 158
+                },
+                {
+                    "comment": "CanonicalPcElement: tail induced pcgs, 8bits word",
+                    "filters": [
+                        [
+                            "IsInducedPcgs",
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsTailInducedPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverseByRws",
+                            "Is8BitsPcWordRep"
+                        ]
+                    ],
+                    "rank": 158
+                },
+                {
+                    "comment": "CanonicalPcElement: generic method",
+                    "filters": [
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInducedPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SiftedPcElement: family pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsFamilyPcgs",
+                            "Tester(IsFamilyPcgs)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "SiftedPcElement: for induced pcgs",
+                    "filters": [
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsInducedPcgs",
+                            "IsInducedPcgsRep"
+                        ],
+                        []
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SiftedPcElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HomomorphicCanonicalPcgs: pcgs, list",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "HomomorphicCanonicalPcgs: pcgs, list, object",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HomomorphicCanonicalPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HomomorphicInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "HomomorphicInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "HomomorphicInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "HomomorphicInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        []
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "HomomorphicInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "HomomorphicInducedPcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        []
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HomomorphicInducedPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFamilyPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFamilyPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFamilyPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFamilyPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ModuloPcgsByPcSequenceNC: generic method for pcgs mod pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ModuloPcgsByPcSequenceNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ModuloPcgsByPcSequence: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsInducedPcgs"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ModuloPcgsByPcSequence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ModuloPcgs: for permutation groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "ModuloPcgs: subgroups fp",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "ModuloPcgs: for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ModuloPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DenominatorOfModuloPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DenominatorOfModuloPcgs)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "DenominatorOfModuloPcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "DenominatorOfModuloPcgs: modolo-tail-pcgs-by-list-rep",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsByListRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "DenominatorOfModuloPcgs: fp",
+                    "filters": [
+                        [
+                            "IsModuloPcgsFpGroupRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "DenominatorOfModuloPcgs: for pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DenominatorOfModuloPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DenominatorOfModuloPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DenominatorOfModuloPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DenominatorOfModuloPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DenominatorOfModuloPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NumeratorOfModuloPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NumeratorOfModuloPcgs)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "NumeratorOfModuloPcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgsPermGroupRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "NumeratorOfModuloPcgs: modolo-tail-pcgs-by-list-rep",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsModuloTailPcgsByListRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "NumeratorOfModuloPcgs: fp",
+                    "filters": [
+                        [
+                            "IsModuloPcgsFpGroupRep"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "NumeratorOfModuloPcgs: for pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumeratorOfModuloPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NumeratorOfModuloPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NumeratorOfModuloPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NumeratorOfModuloPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NumeratorOfModuloPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNumeratorParentPcgsFamilyPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNumeratorParentPcgsFamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNumeratorParentPcgsFamilyPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNumeratorParentPcgsFamilyPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNumeratorParentPcgsFamilyPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNumeratorParentPcgsFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNumeratorParentPcgsFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsModuloPcgs"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExponentsConjugateLayer: subset induced pcgs",
+                    "filters": [
+                        [
+                            "IsParentPcgsFamilyPcgs",
+                            "Tester(IsParentPcgsFamilyPcgs)",
+                            "IsTailInducedPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "ExponentsConjugateLayer: subset induced modulo pcgs",
+                    "filters": [
+                        [
+                            "IsModuloPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsNumeratorParentPcgsFamilyPcgs",
+                            "Tester(IsNumeratorParentPcgsFamilyPcgs)",
+                            "IsSubsetInducedNumeratorModuloTailPcgsRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ExponentsConjugateLayer: default: compute brute force",
+                    "filters": [
+                        [
+                            "IsModuloPcgs"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentsConjugateLayer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSpecialPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSpecialPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSpecialPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSpecialPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpecialPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "SpecialPcgs: method for special pcgs",
+                    "filters": [
+                        [
+                            "IsSpecialPcgs",
+                            "Tester(IsSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "SpecialPcgs: last resort method which tests solvability",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SpecialPcgs: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SpecialPcgs: generic method for pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs",
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)",
+                            "IsFiniteOrdersPcgs",
+                            "Tester(IsFiniteOrdersPcgs)"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpecialPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SpecialPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SpecialPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LGHeads: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LGHeads)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "LGHeads: for special pcgs",
+                    "filters": [
+                        [
+                            "IsSpecialPcgs",
+                            "Tester(IsSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LGHeads",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LGHeads): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LGHeads): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LGHeads)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LGHeads)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LGTails: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LGTails)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "LGTails: for special pcgs",
+                    "filters": [
+                        [
+                            "IsSpecialPcgs",
+                            "Tester(IsSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LGTails",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LGTails): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LGTails): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LGTails)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LGTails)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LGWeights: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LGWeights)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "LGWeights: for induced wrt special",
+                    "filters": [
+                        [
+                            "IsInducedPcgsWrtSpecialPcgs",
+                            "Tester(IsInducedPcgsWrtSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LGWeights",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LGWeights): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LGWeights): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LGWeights)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LGWeights)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LGLayers: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LGLayers)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "LGLayers: for induced wrt special",
+                    "filters": [
+                        [
+                            "IsInducedPcgsWrtSpecialPcgs",
+                            "Tester(IsInducedPcgsWrtSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LGLayers",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LGLayers): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LGLayers): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LGLayers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LGLayers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LGFirst: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LGFirst)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "LGFirst: for induced wrt special",
+                    "filters": [
+                        [
+                            "IsInducedPcgsWrtSpecialPcgs",
+                            "Tester(IsInducedPcgsWrtSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LGFirst",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LGFirst): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LGFirst): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LGFirst)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LGFirst)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LGLength: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LGLength)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "LGLength: for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LGLength: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LGLength",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LGLength): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LGLength): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LGLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LGLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InducedPcgsWrtSpecialPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InducedPcgsWrtSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "InducedPcgsWrtSpecialPcgs: method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "InducedPcgsWrtSpecialPcgs: for groups that have already an induced pcgs wrt family pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(InducedPcgsWrtFamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "InducedPcgsWrtSpecialPcgs: for groups that have already an induced pcgs wrt home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(InducedPcgsWrtHomePcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "InducedPcgsWrtSpecialPcgs: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "InducedPcgsWrtSpecialPcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsWrtSpecialPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InducedPcgsWrtSpecialPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InducedPcgsWrtSpecialPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InducedPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InducedPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalPcgsWrtSpecialPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalPcgsWrtSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CanonicalPcgsWrtSpecialPcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalPcgsWrtSpecialPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalPcgsWrtSpecialPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalPcgsWrtSpecialPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsInducedPcgsWrtSpecialPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsInducedPcgsWrtSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInducedPcgsWrtSpecialPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsInducedPcgsWrtSpecialPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsInducedPcgsWrtSpecialPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsInducedPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsInducedPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCanonicalPcgsWrtSpecialPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCanonicalPcgsWrtSpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 20024
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCanonicalPcgsWrtSpecialPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCanonicalPcgsWrtSpecialPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCanonicalPcgsWrtSpecialPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCanonicalPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCanonicalPcgsWrtSpecialPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalPcgsWrtFamilyPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalPcgsWrtFamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CanonicalPcgsWrtFamilyPcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "CanonicalPcgsWrtFamilyPcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalPcgsWrtFamilyPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalPcgsWrtFamilyPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalPcgsWrtFamilyPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalPcgsWrtFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalPcgsWrtFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalPcgsWrtHomePcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalPcgsWrtHomePcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CanonicalPcgsWrtHomePcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "CanonicalPcgsWrtHomePcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalPcgsWrtHomePcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalPcgsWrtHomePcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalPcgsWrtHomePcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalPcgsWrtHomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalPcgsWrtHomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FamilyPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "FamilyPcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FamilyPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FamilyPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FamilyPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HomePcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "HomePcgs: use a perm pcgs if possible",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(Pcgs)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "HomePcgs: try to compute a perm pcgs",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "HomePcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "HomePcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HomePcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(HomePcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(HomePcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(HomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(HomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InducedPcgsWrtFamilyPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InducedPcgsWrtFamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "InducedPcgsWrtFamilyPcgs: whole family",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "InducedPcgsWrtFamilyPcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "InducedPcgsWrtFamilyPcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsWrtFamilyPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InducedPcgsWrtFamilyPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InducedPcgsWrtFamilyPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InducedPcgsWrtFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InducedPcgsWrtFamilyPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedPcgs: cache pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedPcgsOp: sift existing pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(Pcgs)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "InducedPcgsOp: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedInducedPcgses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedInducedPcgses)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedInducedPcgses: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedInducedPcgses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedInducedPcgses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedInducedPcgses): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedInducedPcgses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedInducedPcgses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedInducedPcgses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InducedPcgsWrtHomePcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InducedPcgsWrtHomePcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "InducedPcgsWrtHomePcgs: tail of perm pcgs",
+                    "filters": [
+                        [
+                            "Tester(HomePcgs)",
+                            "IsMemberPcSeriesPermGroup"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "InducedPcgsWrtHomePcgs: pc group: home=family",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "InducedPcgsWrtHomePcgs: from generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "InducedPcgsWrtHomePcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedPcgsWrtHomePcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InducedPcgsWrtHomePcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InducedPcgsWrtHomePcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InducedPcgsWrtHomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InducedPcgsWrtHomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Pcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Pcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Pcgs: take induced pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(InducedPcgsWrtHomePcgs)"
+                        ]
+                    ],
+                    "rank": 10034
+                },
+                {
+                    "comment": "Pcgs: fail if insolvable",
+                    "filters": [
+                        [
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 10034
+                },
+                {
+                    "comment": "Pcgs: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 367
+                },
+                {
+                    "comment": "Pcgs: tail of perm pcgs",
+                    "filters": [
+                        [
+                            "IsMemberPcSeriesPermGroup"
+                        ]
+                    ],
+                    "rank": 156
+                },
+                {
+                    "comment": "Pcgs: Sims's method",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 155
+                },
+                {
+                    "comment": "Pcgs: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "Pcgs: from independent generators of abelian group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CanEasilyComputeWithIndependentGensAbelianGroup"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Pcgs: from independent generators of abelian group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "Tester(IndependentGeneratorsOfAbelianGroup)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Pcgs: for a group containing the whole family and with known family pcgs",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Pcgs: for a group with known home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "Pcgs: for a group with known family pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FamilyPcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Pcgs: generic method using CompositionSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Pcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Pcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Pcgs)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Setter(Pcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Pcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Pcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Pcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneralizedPcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneralizedPcgs)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "GeneralizedPcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(Pcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "GeneralizedPcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneralizedPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneralizedPcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneralizedPcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneralizedPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneralizedPcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SubgroupByPcgs: subgroup with pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubgroupByPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AffineAction: group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "AffineAction: pcgs",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "AffineAction: generators",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "AffineAction: group2",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "6args": []
+        },
+        "name": "AffineAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "LinearAction",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "LinearAction",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "LinearAction",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "LinearAction",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LinearAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OmegaSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OmegaSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "OmegaSeries: for p-groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "OmegaSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OmegaSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OmegaSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OmegaSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OmegaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OmegaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "Tester(HomePcgs)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizerInHomePcgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizerInHomePcgs)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "NormalizerInHomePcgs: for group with home pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(HomePcgs)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "NormalizerInHomePcgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerInHomePcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "Tester(HomePcgs)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizerInHomePcgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizerInHomePcgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizerInHomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "Tester(HomePcgs)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizerInHomePcgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsMagma"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MultiplicationTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MultiplicationTable)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "MultiplicationTable: for a magma",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "MultiplicationTable: for a list of elements",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MultiplicationTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagma"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MultiplicationTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MultiplicationTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MultiplicationTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MultiplicationTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AllBlocks: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AllBlocks)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "AllBlocks: generic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "AllBlocks: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AllBlocks",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AllBlocks): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AllBlocks): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AllBlocks)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AllBlocks)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransitiveIdentification: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransitiveIdentification)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "TransitiveIdentification: generic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "TransitiveIdentification: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransitiveIdentification",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransitiveIdentification): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransitiveIdentification): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransitiveIdentification)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransitiveIdentification)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimitiveIdentification: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimitiveIdentification)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "PrimitiveIdentification: generic",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "PrimitiveIdentification: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimitiveIdentification",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimitiveIdentification): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimitiveIdentification): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimitiveIdentification)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimitiveIdentification)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ONanScottType: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ONanScottType)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "ONanScottType: primitive permgroups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "ONanScottType: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ONanScottType",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ONanScottType): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ONanScottType): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ONanScottType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ONanScottType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SocleTypePrimitiveGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SocleTypePrimitiveGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "SocleTypePrimitiveGroup: primitive permgroups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "SocleTypePrimitiveGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SocleTypePrimitiveGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SocleTypePrimitiveGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SocleTypePrimitiveGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SocleTypePrimitiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SocleTypePrimitiveGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TwoClosure: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TwoClosure)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "TwoClosure: permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "TwoClosure: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TwoClosure",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TwoClosure): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TwoClosure): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TwoClosure)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TwoClosure)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GroupGeneralMappingByImages: make onto",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "GroupGeneralMappingByImages: for group, group, list, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 70
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupGeneralMappingByImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GroupGeneralMappingByImagesNC: from a group handled by a niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 372
+                },
+                {
+                    "comment": "GroupGeneralMappingByImagesNC: make onto",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "GroupGeneralMappingByImagesNC: from a group handled by a niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 405
+                },
+                {
+                    "comment": "GroupGeneralMappingByImagesNC: for pcp group, pcp group, list, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "GroupGeneralMappingByImagesNC: for group, pcp group, list, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "GroupGeneralMappingByImagesNC: for pcp group, group, list, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "GroupGeneralMappingByImagesNC: for group, group, list, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 70
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupGeneralMappingByImagesNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GroupHomomorphismByImagesNC: for group, group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "GroupHomomorphismByImagesNC: for group, group, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 68
+                },
+                {
+                    "comment": "GroupHomomorphismByImagesNC: for group, list, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "GroupHomomorphismByImagesNC: for group, group, list, list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 70
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupHomomorphismByImagesNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsGroupGeneralMappingByImages: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsGroupGeneralMappingByImages)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "AsGroupGeneralMappingByImages: for GHBI",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 10017
+                },
+                {
+                    "comment": "AsGroupGeneralMappingByImages: for Niceomorphisms: avoid recursion",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsNiceMonomorphism"
+                        ]
+                    ],
+                    "rank": 347
+                },
+                {
+                    "comment": "AsGroupGeneralMappingByImages: for conjugator isomorphism",
+                    "filters": [
+                        [
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "AsGroupGeneralMappingByImages: for group homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "AsGroupGeneralMappingByImages: for group general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "AsGroupGeneralMappingByImages: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsGroupGeneralMappingByImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsGroupGeneralMappingByImages): assign MappingOfWhichItIsAsGGMBI",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "Setter(AsGroupGeneralMappingByImages): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsGroupGeneralMappingByImages): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsGroupGeneralMappingByImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsGroupGeneralMappingByImages)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MappingOfWhichItIsAsGGMBI: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MappingOfWhichItIsAsGGMBI)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "MappingOfWhichItIsAsGGMBI: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MappingOfWhichItIsAsGGMBI",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MappingOfWhichItIsAsGGMBI): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MappingOfWhichItIsAsGGMBI): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MappingOfWhichItIsAsGGMBI)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MappingOfWhichItIsAsGGMBI)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: for group, and trivial group (delegate to `IdentityMapping')",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 10102
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 401
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup, via pcp representation",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup, via pcp representation",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: test if known/try solvable factor for permutation groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: trivial image fp case",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: for subgroups of fp groups by quotient rep.",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: for subgroups of fp groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCOp: search for operation",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismByNormalSubgroupNCOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCInParent: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalHomomorphismByNormalSubgroupNCInParent)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCInParent: method that calls the two-argument operation NaturalHomomorphismByNormalSubgroupNCOp",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNCInParent: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismByNormalSubgroupNCInParent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalHomomorphismByNormalSubgroupNCInParent): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalHomomorphismByNormalSubgroupNCInParent): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalHomomorphismByNormalSubgroupNCInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalHomomorphismByNormalSubgroupNCInParent)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNC: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "NaturalHomomorphismByNormalSubgroupNC: try to exploit the in-parent attribute NaturalHomomorphismByNormalSubgroupNCInParent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismByNormalSubgroupNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugatorIsomorphism: for group and mult.-elm.-with-inverse",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugatorIsomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugatorAutomorphismNC: group and mult.-elm.-with-inverse",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugatorAutomorphismNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InnerAutomorphismNC: for group and mult.-elm.-with-inverse",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InnerAutomorphismNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsConjugatorIsomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsConjugatorIsomorphism: for a f.p. group general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsConjugatorIsomorphism: for a matrix group general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsConjugatorIsomorphism: perm group homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsConjugatorIsomorphism: for a pc group general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsConjugatorIsomorphism: for a group general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsConjugatorIsomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsConjugatorIsomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsConjugatorIsomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsConjugatorIsomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsConjugatorIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsConjugatorIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsInnerAutomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsInnerAutomorphism)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsInnerAutomorphism: for a group general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsInnerAutomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInnerAutomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsInnerAutomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsInnerAutomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsInnerAutomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsInnerAutomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsConjugatorIsomorphism",
+                    "Tester(IsConjugatorIsomorphism)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConjugatorOfConjugatorIsomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConjugatorOfConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "ConjugatorOfConjugatorIsomorphism: default -- try RepresentativeAction",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)",
+                            "IsConjugatorIsomorphism",
+                            "Tester(IsConjugatorIsomorphism)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ConjugatorOfConjugatorIsomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugatorOfConjugatorIsomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsConjugatorIsomorphism",
+                    "Tester(IsConjugatorIsomorphism)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConjugatorOfConjugatorIsomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConjugatorOfConjugatorIsomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConjugatorOfConjugatorIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsConjugatorIsomorphism",
+                    "Tester(IsConjugatorIsomorphism)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConjugatorOfConjugatorIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImagesSmallestGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImagesSmallestGenerators)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "ImagesSmallestGenerators: group homomorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ImagesSmallestGenerators: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImagesSmallestGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImagesSmallestGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImagesSmallestGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImagesSmallestGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImagesSmallestGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RegularActionHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RegularActionHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "RegularActionHomomorphism: generic",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "RegularActionHomomorphism:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "RegularActionHomomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RegularActionHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RegularActionHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RegularActionHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RegularActionHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RegularActionHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NaturalIsomorphismByPcgs: for group and pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalIsomorphismByPcgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DirectProductOp: for a list of permutation groups, and a permutation group",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(CategoryCollections(IsPerm))"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "DirectProductOp: for pcp groups",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "DirectProductOp: for a list (of pc groups), and a pc group",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "DirectProductOp: matrix groups",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "DirectProductOp: for a list of fp groups, and a fp group",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "DirectProductOp: for a list (of groups), and a group",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectProductOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SubdirectProductOp: permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 150
+                },
+                {
+                    "comment": "SubdirectProductOp: pcgroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 126
+                },
+                {
+                    "comment": "SubdirectProductOp: groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 100
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubdirectProductOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SemidirectProduct: generic method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "SemidirectProduct: generic method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "SemidirectProduct: automorphisms group with group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SemidirectProduct: Induced permutation automorphisms",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 133
+                },
+                {
+                    "comment": "SemidirectProduct: generic method for permutation groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 133
+                },
+                {
+                    "comment": "SemidirectProduct: group with vector space: affine",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsFullRowModule",
+                            "Tester(IsFullRowModule)"
+                        ]
+                    ],
+                    "rank": 101
+                },
+                {
+                    "comment": "SemidirectProduct: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 93
+                },
+                {
+                    "comment": "SemidirectProduct: group with fp",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "SemidirectProduct: fp with group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "SemidirectProduct: different representations",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 81
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemidirectProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "WreathProduct: permgroups: imprimitive",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "WreathProduct: imprimitive matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 101
+                },
+                {
+                    "comment": "WreathProduct: generic groups with perm",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 88
+                },
+                {
+                    "comment": "WreathProduct: generic groups, no perm",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "WreathProduct: permgroups and action",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSPGeneralMapping"
+                        ]
+                    ],
+                    "rank": 124
+                },
+                {
+                    "comment": "WreathProduct",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "WreathProduct: generic groups with permhom",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSPGeneralMapping"
+                        ]
+                    ],
+                    "rank": 74
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "WreathProduct",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 126
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WreathProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "StandardWreathProduct: generic groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StandardWreathProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FreeProductOp: for a list (of groups), and a group",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeProductOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectProductInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DirectProductInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectProductInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DirectProductInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DirectProductInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DirectProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DirectProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SubdirectProductInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SubdirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SubdirectProductInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubdirectProductInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SubdirectProductInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SubdirectProductInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SubdirectProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SubdirectProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemidirectProductInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemidirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SemidirectProductInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemidirectProductInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemidirectProductInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemidirectProductInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemidirectProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemidirectProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WreathProductInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WreathProductInfo)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "WreathProductInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WreathProductInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WreathProductInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WreathProductInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WreathProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WreathProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeProductInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeProductInfo)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "FreeProductInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeProductInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeProductInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeProductInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeProductInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNaturalSymmetricGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsNaturalSymmetricGroup: knows size",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsNaturalSymmetricGroup: comprehensive",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsNaturalSymmetricGroup: for non-permutation group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsNaturalSymmetricGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNaturalSymmetricGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNaturalSymmetricGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNaturalSymmetricGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNaturalSymmetricGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNaturalSymmetricGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNaturalAlternatingGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsNaturalAlternatingGroup: knows size",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsNaturalAlternatingGroup: comprehensive",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsNaturalAlternatingGroup: for non-permutation group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsNaturalAlternatingGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNaturalAlternatingGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNaturalAlternatingGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNaturalAlternatingGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNaturalAlternatingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNaturalAlternatingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAlternatingGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsAlternatingGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsAlternatingGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAlternatingGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAlternatingGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAlternatingGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAlternatingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAlternatingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSymmetricGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSymmetricGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSymmetricGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSymmetricGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSymmetricGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSymmetricGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSymmetricGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSymmetricGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SymmetricParentGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SymmetricParentGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "SymmetricParentGroup: natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "SymmetricParentGroup: symm(moved pts)",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "SymmetricParentGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymmetricParentGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SymmetricParentGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SymmetricParentGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SymmetricParentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SymmetricParentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AlternatingSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AlternatingSubgroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "AlternatingSubgroup: for perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "AlternatingSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlternatingSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AlternatingSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AlternatingSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AlternatingSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AlternatingSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrbitStabilizingParentGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrbitStabilizingParentGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "OrbitStabilizingParentGroup: direct product of S_n's",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "OrbitStabilizingParentGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrbitStabilizingParentGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrbitStabilizingParentGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrbitStabilizingParentGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrbitStabilizingParentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrbitStabilizingParentGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IsTrivialNormalIntersection: if minimal normal subgroups are computed",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MinimalNormalSubgroups)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 100
+                },
+                {
+                    "comment": "IsTrivialNormalIntersection: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 99
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTrivialNormalIntersection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalComplement: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalComplement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalComplementNC: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalComplementNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectFactorsOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DirectFactorsOfGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DirectFactorsOfGroup: for direct products if normal subgroups are computed",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(NormalSubgroups)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "DirectFactorsOfGroup: if normal subgroups are computed",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(NormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "DirectFactorsOfGroup: for direct products",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DirectProductInfo)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "DirectFactorsOfGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DirectFactorsOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectFactorsOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DirectFactorsOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DirectFactorsOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DirectFactorsOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DirectFactorsOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemidirectFactorsOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemidirectFactorsOfGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SemidirectFactorsOfGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SemidirectFactorsOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemidirectFactorsOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemidirectFactorsOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemidirectFactorsOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemidirectFactorsOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemidirectFactorsOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DecompositionTypesOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DecompositionTypesOfGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DecompositionTypesOfGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DecompositionTypesOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DecompositionTypesOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DecompositionTypesOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DecompositionTypesOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DecompositionTypesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DecompositionTypesOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsDihedralGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsDihedralGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsDihedralGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsDihedralGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsDihedralGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsDihedralGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsDihedralGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsDihedralGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsDihedralGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DihedralGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DihedralGenerators)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DihedralGenerators: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DihedralGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DihedralGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DihedralGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DihedralGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DihedralGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsQuaternionGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsQuaternionGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsQuaternionGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsQuaternionGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsQuaternionGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsQuaternionGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsQuaternionGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsQuaternionGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsQuaternionGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "QuaternionGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(QuaternionGenerators)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "QuaternionGenerators: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuaternionGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(QuaternionGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(QuaternionGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(QuaternionGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(QuaternionGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsQuasiDihedralGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsQuasiDihedralGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsQuasiDihedralGroup: generic method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsQuasiDihedralGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsQuasiDihedralGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsQuasiDihedralGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsQuasiDihedralGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsQuasiDihedralGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsQuasiDihedralGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "QuasiDihedralGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(QuasiDihedralGenerators)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "QuasiDihedralGenerators: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuasiDihedralGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(QuasiDihedralGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(QuasiDihedralGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(QuasiDihedralGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(QuasiDihedralGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPSL: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPSL)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsPSL: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsPSL: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPSL",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPSL): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPSL): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ParametersOfGroupViewedAsPSL: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ParametersOfGroupViewedAsPSL)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ParametersOfGroupViewedAsPSL: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParametersOfGroupViewedAsPSL",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ParametersOfGroupViewedAsPSL): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ParametersOfGroupViewedAsPSL): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ParametersOfGroupViewedAsPSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ParametersOfGroupViewedAsPSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ParametersOfGroupViewedAsSL: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ParametersOfGroupViewedAsSL)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ParametersOfGroupViewedAsSL: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParametersOfGroupViewedAsSL",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ParametersOfGroupViewedAsSL): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ParametersOfGroupViewedAsSL): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ParametersOfGroupViewedAsSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ParametersOfGroupViewedAsSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ParametersOfGroupViewedAsGL: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ParametersOfGroupViewedAsGL)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ParametersOfGroupViewedAsGL: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParametersOfGroupViewedAsGL",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ParametersOfGroupViewedAsGL): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ParametersOfGroupViewedAsGL): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ParametersOfGroupViewedAsGL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ParametersOfGroupViewedAsGL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AlternatingDegree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AlternatingDegree)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "AlternatingDegree: generic method, dispatch to `IsAlternatingGroup'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "AlternatingDegree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlternatingDegree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AlternatingDegree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AlternatingDegree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AlternatingDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AlternatingDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SymmetricDegree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SymmetricDegree)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SymmetricDegree: generic method, dispatch to `IsSymmetricGroup'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SymmetricDegree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymmetricDegree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SymmetricDegree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SymmetricDegree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SymmetricDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SymmetricDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PSLDegree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PSLDegree)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PSLDegree: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PSLDegree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PSLDegree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PSLDegree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PSLDegree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PSLDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PSLDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PSLUnderlyingField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PSLUnderlyingField)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PSLUnderlyingField: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PSLUnderlyingField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PSLUnderlyingField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PSLUnderlyingField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PSLUnderlyingField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PSLUnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PSLUnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SLDegree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SLDegree)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SLDegree: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SLDegree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SLDegree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SLDegree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SLDegree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SLDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SLDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SLUnderlyingField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SLUnderlyingField)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SLUnderlyingField: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SLUnderlyingField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SLUnderlyingField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SLUnderlyingField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SLUnderlyingField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SLUnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SLUnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GLDegree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GLDegree)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "GLDegree: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "GLDegree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GLDegree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GLDegree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GLDegree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GLDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GLDegree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GLUnderlyingField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GLUnderlyingField)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "GLUnderlyingField: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "GLUnderlyingField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GLUnderlyingField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GLUnderlyingField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GLUnderlyingField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GLUnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GLUnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StructureDescription: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StructureDescription)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "StructureDescription: for groups handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 367
+                },
+                {
+                    "comment": "StructureDescription: for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "StructureDescription: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StructureDescription",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StructureDescription): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StructureDescription): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StructureDescription)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StructureDescription)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPQuotientSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPQuotientSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPQuotientSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPQuotientSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPQuotientSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPQuotientSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpQuotientSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNilpQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpQuotientSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNilpQuotientSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNilpQuotientSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNilpQuotientSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNilpQuotientSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "QuotientSystem: pquotient",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuotientSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GetDefinitionNC",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetDefinitionNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetDefinitionNC",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetDefinitionNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClearDefinitionNC",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClearDefinitionNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefineNewGenerators: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefineNewGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SplitWordTail: p-quotient system, word",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SplitWordTail",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExtRepByTailVector: p-quotient system, vector",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtRepByTailVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorNumberOfQuotient: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorNumberOfQuotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TailsInverses: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TailsInverses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputeTails: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputeTails",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EvaluateConsistency: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EvaluateConsistency",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IncorporateCentralRelations: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IncorporateCentralRelations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RenumberHighestWeightGenerators: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RenumberHighestWeightGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EvaluateRelators: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EvaluateRelators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LiftEpimorphism: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LiftEpimorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GeneratorsOfLayer: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfLayer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LengthOfDescendingSeries: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LengthOfDescendingSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RanksOfDescendingSeries: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RanksOfDescendingSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CheckConsistencyOfDefinitions: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CheckConsistencyOfDefinitions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupByQuotientSystem: p-group from a p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupByQuotientSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TraceDefinition: p-quotient system",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TraceDefinition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EpimorphismPGroup: finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "EpimorphismPGroup: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "EpimorphismPGroup: for subgroups of finitely presented groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "EpimorphismPGroup: finite group, class bound",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "EpimorphismPGroup: for finitely presented groups, class bound",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 76
+                },
+                {
+                    "comment": "EpimorphismPGroup: for subgroups of finitely presented groups, class bound",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 73
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EpimorphismPGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EpimorphismQuotientSystem: for p-quotient systems",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EpimorphismQuotientSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EpimorphismNilpotentQuotientOp: full fp group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        []
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "EpimorphismNilpotentQuotientOp: subgroup fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EpimorphismNilpotentQuotientOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPQuotientSystem",
+                    "Tester(IsPQuotientSystem)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Nucleus: for a p-quotient system and a group",
+                    "filters": [
+                        [
+                            "IsPQuotientSystem",
+                            "Tester(IsPQuotientSystem)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Nucleus",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ActingDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ActingDomain)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ActingDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ActingDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ActingDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ActingDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HomeEnumerator: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(HomeEnumerator)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "HomeEnumerator",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "HomeEnumerator",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HomeEnumerator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(HomeEnumerator): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(HomeEnumerator): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(HomeEnumerator)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(HomeEnumerator)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ActionKernelExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ActionKernelExternalSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ActionKernelExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ActionKernelExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ActionKernelExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ActionKernelExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ActionKernelExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLinearActionHomomorphism"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LinearActionBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LinearActionBasis)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "LinearActionBasis: projective with extra vector",
+                    "filters": [
+                        [
+                            "IsProjectiveActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "LinearActionBasis: find basis in domain",
+                    "filters": [
+                        [
+                            "IsLinearActionHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LinearActionBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLinearActionHomomorphism"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LinearActionBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LinearActionBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LinearActionBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLinearActionHomomorphism"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LinearActionBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FunctionAction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FunctionAction)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "FunctionAction: ExternalSetByActorsRep",
+                    "filters": [
+                        [
+                            "IsExternalSetByActorsRep"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FunctionAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FunctionAction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FunctionAction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FunctionAction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FunctionAction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StabilizerOfExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StabilizerOfExternalSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "StabilizerOfExternalSet",
+                    "filters": [
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "StabilizerOfExternalSet",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "StabilizerOfExternalSet",
+                    "filters": [
+                        [
+                            "IsExternalOrbit",
+                            "IsExternalSetByPcgs"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "StabilizerOfExternalSet: stabilizer of the represenattive",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StabilizerOfExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StabilizerOfExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StabilizerOfExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StabilizerOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StabilizerOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalRepresentativeOfExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalRepresentativeOfExternalSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "CanonicalRepresentativeOfExternalSet: via `ActorOfExternalSet'",
+                    "filters": [
+                        [
+                            "IsExternalOrbit",
+                            "IsExternalSetByPcgs"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "CanonicalRepresentativeOfExternalSet: by CanonicalRepresentativeDeterminator",
+                    "filters": [
+                        [
+                            "IsExternalSet",
+                            "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "CanonicalRepresentativeOfExternalSet: smallest element",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalRepresentativeOfExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalRepresentativeOfExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalRepresentativeOfExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalRepresentativeOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalRepresentativeOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalRepresentativeDeterminatorOfExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalRepresentativeDeterminatorOfExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalRepresentativeDeterminatorOfExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalRepresentativeDeterminatorOfExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalRepresentativeDeterminatorOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalRepresentativeDeterminatorOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanEasilyDetermineCanonicalRepresentativeExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanEasilyDetermineCanonicalRepresentativeExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanEasilyDetermineCanonicalRepresentativeExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanEasilyDetermineCanonicalRepresentativeExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanEasilyDetermineCanonicalRepresentativeExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ActorOfExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ActorOfExternalSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "ActorOfExternalSet",
+                    "filters": [
+                        [
+                            "IsConjugacyClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ActorOfExternalSet",
+                    "filters": [
+                        [
+                            "IsExternalOrbit",
+                            "IsExternalSetByPcgs"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ActorOfExternalSet",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ActorOfExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ActorOfExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ActorOfExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ActorOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ActorOfExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PreOrbishProcessing",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreOrbishProcessing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ActionHomomorphismAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ActionHomomorphismAttr)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "ActionHomomorphismAttr: call OpHomConstructor",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ActionHomomorphismAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ActionHomomorphismAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ActionHomomorphismAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ActionHomomorphismAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ActionHomomorphismAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SurjectiveActionHomomorphismAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SurjectiveActionHomomorphismAttr)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "SurjectiveActionHomomorphismAttr: call Ac.Hom.Constructor",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SurjectiveActionHomomorphismAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SurjectiveActionHomomorphismAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SurjectiveActionHomomorphismAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SurjectiveActionHomomorphismAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SurjectiveActionHomomorphismAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsActionHomomorphism"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingExternalSet)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsActionHomomorphism"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsActionHomomorphism"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "SparseActionHomomorphismOp: no domain given",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "SparseActionHomomorphismOp: domain given",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ]
+        },
+        "name": "SparseActionHomomorphismOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "SortedSparseActionHomomorphismOp: no domain given",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "6args": []
+        },
+        "name": "SortedSparseActionHomomorphismOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExternalSet: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExternalSet)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "ExternalSet: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ExternalSet: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ExternalSet: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExternalSet: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ExternalSet: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ExternalSet: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "ExternalSet: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "ExternalSet: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ExternalSet: G, D, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "ExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExternalSet): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExternalSet): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExternalSet)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedExternalSet: restrict the acting domain",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedExternalSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "ExternalSubsetOp: G, start, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "ExternalSubsetOp: G, xset, start, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsExternalSet"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "ExternalSubsetOp: G, D, start, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ]
+        },
+        "name": "ExternalSubsetOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "ExternalOrbitOp: G, pnt, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "ExternalOrbitOp: G, xset, pnt, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsExternalSet"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExternalOrbitOp: G, D, pnt, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ]
+        },
+        "name": "ExternalOrbitOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "OrbitOp: G, H, gens, oprs, opr for AffineCrystGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 121
+                },
+                {
+                    "comment": "OrbitOp: G, H, gens, oprs, opr for AffineCrystGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 121
+                },
+                {
+                    "comment": "OrbitOp: G, int, gens, perms, act = `OnPoints'",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "OrbitOp: action via prime order pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "OrbitOp: G, pnt, [ 1gen ], [ 1act ], act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "OrbitOp: standard orbit algorithm:list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "OrbitOp: via prime order pcgs, with domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "OrbitOp: G, D, pnt, [ 1gen ], [ 1act ], act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "OrbitOp: with domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ]
+        },
+        "name": "OrbitOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Orbits: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Orbits)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "Orbits: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Orbits: group without domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Orbits: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Orbits: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Orbits: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Orbits: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Orbits: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "Orbits: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "Orbits: permgroup on points",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 126
+                },
+                {
+                    "comment": "Orbits: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Orbits: for arbitrary domains",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "Orbits",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Orbits): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Orbits): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Orbits)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Orbits)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrbitsDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrbitsDomain)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "OrbitsDomain: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "OrbitsDomain: group without domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "OrbitsDomain: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "OrbitsDomain: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "OrbitsDomain: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "OrbitsDomain: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "OrbitsDomain: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "OrbitsDomain: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "OrbitsDomain: permgroup on points",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 126
+                },
+                {
+                    "comment": "OrbitsDomain: empty domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "OrbitsDomain: empty domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "OrbitsDomain: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "OrbitsDomain: for quick position domains",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsQuickPositionList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "OrbitsDomain: for arbitrary domains",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "OrbitsDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrbitsDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrbitsDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrbitsDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrbitsDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "OrbitLengthOp: compute orbit",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "OrbitLengthOp: compute orbit",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ]
+        },
+        "name": "OrbitLengthOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrbitLengths: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrbitLengths)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "OrbitLengths: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "OrbitLengths: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "OrbitLengths: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "OrbitLengths: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "OrbitLengths: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "OrbitLengths: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "OrbitLengths: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "OrbitLengths: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "OrbitLengths: compute orbits",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "OrbitLengths",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrbitLengths): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrbitLengths): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrbitLengths)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrbitLengths)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrbitLengthsDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrbitLengthsDomain)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "OrbitLengthsDomain: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "OrbitLengthsDomain: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "OrbitLengthsDomain: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "OrbitLengthsDomain: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "OrbitLengthsDomain: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "OrbitLengthsDomain: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "OrbitLengthsDomain: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "OrbitLengthsDomain: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "OrbitLengthsDomain: compute orbits",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "OrbitLengthsDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrbitLengthsDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrbitLengthsDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrbitLengthsDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrbitLengthsDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "OrbitStabilizerOp: G, H, gens, oprs, opr for AffineCrystGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 111
+                },
+                {
+                    "comment": "OrbitStabilizerOp: G, H, gens, oprs, opr for AffineCrystGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 111
+                },
+                {
+                    "comment": "OrbitStabilizerOp: permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "OrbitStabilizerOp: G, pnt, pcgs, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "OrbitStabilizerOp: `OrbitStabilizerAlgorithm' without domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "OrbitStabilizerOp: G, D, pnt, pcgs, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "OrbitStabilizerOp: `OrbitStabilizerAlgorithm' with domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ]
+        },
+        "name": "OrbitStabilizerOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExternalOrbits: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExternalOrbits)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "ExternalOrbits: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ExternalOrbits: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ExternalOrbits: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExternalOrbits: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ExternalOrbits: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ExternalOrbits: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "ExternalOrbits: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "ExternalOrbits: G, xset, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsExternalSet"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExternalOrbits: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ExternalOrbits: G, D, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "ExternalOrbits",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExternalOrbits): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExternalOrbits): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExternalOrbits)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExternalOrbits)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExternalOrbitsStabilizers: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExternalOrbitsStabilizers)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "ExternalOrbitsStabilizers: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ExternalOrbitsStabilizers: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ExternalOrbitsStabilizers: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExternalOrbitsStabilizers: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ExternalOrbitsStabilizers: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "ExternalOrbitsStabilizers: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "ExternalOrbitsStabilizers: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "ExternalOrbitsStabilizers: external set",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsExternalSet"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ExternalOrbitsStabilizers: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "ExternalOrbitsStabilizers: arbitrary domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "ExternalOrbitsStabilizers",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExternalOrbitsStabilizers): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExternalOrbitsStabilizers): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExternalOrbitsStabilizers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExternalOrbitsStabilizers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Transitivity: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Transitivity)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "Transitivity: for a permutation group with known size",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Transitivity: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Transitivity: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Transitivity: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Transitivity: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Transitivity: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "Transitivity: for an ordinary table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Transitivity: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Transitivity: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "Transitivity: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "Transitivity: permgroup on numbers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "Transitivity: G, [  ], gens, perms, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "Transitivity: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Transitivity: of the image of an ophom",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "Transitivity",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Transitivity): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Transitivity): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Transitivity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Transitivity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BlocksAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BlocksAttr)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BlocksAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BlocksAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BlocksAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BlocksAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BlocksAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "BlocksOp: G, D, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "BlocksOp: integers, with seed",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 155
+                },
+                {
+                    "comment": "BlocksOp: permgroup on integers",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 143
+                },
+                {
+                    "comment": "BlocksOp: G, [  ], seed, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 77
+                },
+                {
+                    "comment": "BlocksOp: via action homomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ]
+        },
+        "name": "BlocksOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalBlocksAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalBlocksAttr)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalBlocksAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalBlocksAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalBlocksAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalBlocksAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalBlocksAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "MaximalBlocksOp: G, D, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "MaximalBlocksOp: G, D, seed, gens, acts, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ]
+        },
+        "name": "MaximalBlocksOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RepresentativesMinimalBlocksAttr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RepresentativesMinimalBlocksAttr)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativesMinimalBlocksAttr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RepresentativesMinimalBlocksAttr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RepresentativesMinimalBlocksAttr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RepresentativesMinimalBlocksAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RepresentativesMinimalBlocksAttr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "RepresentativesMinimalBlocksOp: permgrp on points",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 126
+                },
+                {
+                    "comment": "RepresentativesMinimalBlocksOp: general case: translate",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "RepresentativesMinimalBlocksOp: G, domain, noseed, gens, perms, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 129
+                }
+            ]
+        },
+        "name": "RepresentativesMinimalBlocksOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Earns: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Earns)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "Earns: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Earns: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Earns: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Earns: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Earns: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Earns: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "Earns: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "Earns: G, ints, gens, perms, act",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 65
+                },
+                {
+                    "comment": "Earns: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "6args": []
+        },
+        "name": "Earns",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Earns): never set fail",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "Setter(Earns): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Earns): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Earns)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Earns)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTransitive: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTransitive)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "IsTransitive: for a permutation group (use shortcuts)",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsTransitive: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsTransitive: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsTransitive: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsTransitive: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsTransitive: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "IsTransitive: for an ordinary table and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsTransitive: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsTransitive: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "IsTransitive: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "IsTransitive: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsTransitive: compare with orbit of element",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "IsTransitive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTransitive): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTransitive): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTransitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTransitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrimitive: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPrimitive)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "IsPrimitive: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsPrimitive: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsPrimitive: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsPrimitive: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsPrimitive: for matrix group over field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                },
+                {
+                    "comment": "IsPrimitive: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsPrimitive: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsPrimitive: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsPrimitive: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "IsPrimitive: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "IsPrimitive: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsPrimitive: transitive and no blocks",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "IsPrimitive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPrimitive): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPrimitive): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPrimitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPrimitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrimitiveAffine: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPrimitiveAffine)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "IsPrimitiveAffine: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsPrimitiveAffine: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsPrimitiveAffine: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsPrimitiveAffine: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsPrimitiveAffine: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsPrimitiveAffine: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "IsPrimitiveAffine: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "IsPrimitiveAffine: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsPrimitiveAffine: primitive and earns",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "IsPrimitiveAffine",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPrimitiveAffine): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPrimitiveAffine): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPrimitiveAffine)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPrimitiveAffine)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSemiRegular: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSemiRegular)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "IsSemiRegular: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsSemiRegular: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsSemiRegular: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsSemiRegular: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsSemiRegular: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsSemiRegular: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "IsSemiRegular: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "IsSemiRegular: permgroup on numbers",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 126
+                },
+                {
+                    "comment": "IsSemiRegular: G, D, gens, [  ], act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "IsSemiRegular: G, [  ], gens, perms, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "IsSemiRegular: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsSemiRegular: via ophom",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "IsSemiRegular",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSemiRegular): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSemiRegular): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSemiRegular)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSemiRegular)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRegular: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRegular)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "IsRegular: permgroup with known size",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsRegular: permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsRegular: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsRegular: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsRegular: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsRegular: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IsRegular: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsRegular: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "IsRegular: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "IsRegular: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsRegular: transitive and semiregular",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "IsRegular",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRegular): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRegular): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRegular)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRegular)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankAction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RankAction)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "RankAction: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "RankAction: for an external set",
+                    "filters": [
+                        [
+                            "IsExternalSet"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "RankAction: for a permutation group and a domain or list of integers",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "RankAction: for a group and a domain or list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "RankAction: for permutation group, domain or list of integers, and function",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "RankAction: for a group, a domain or list, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "RankAction: for a group, a domain or list, and two lists",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "RankAction: G, [  ], gens, perms, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "RankAction: G, ints, gens, perms, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "RankAction: for a group, a domain, two lists, and a function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "RankAction: via ophom",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "6args": []
+        },
+        "name": "RankAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RankAction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RankAction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RankAction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalSet"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RankAction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PermutationOp: object on list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermutationOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "PermutationCycleOp: of object in list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermutationCycleOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CycleOp: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 129
+                },
+                {
+                    "comment": "CycleOp: for a permutation with memory and an integer",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "CycleOp: perm, int",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CycleOp: perm, int, act",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "CycleOp",
+                    "filters": [
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "CycleOp: of object in list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CycleOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CyclesOp",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CyclesOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CycleLengthOp: straight line program perms",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsStraightLineProgElm"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 129
+                },
+                {
+                    "comment": "CycleLengthOp: for a permutation with memory and an integer",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsObjWithMemory"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 128
+                },
+                {
+                    "comment": "CycleLengthOp: perm, int",
+                    "filters": [
+                        [
+                            "IsPerm",
+                            "IsInternalRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CycleLengthOp: perm, int, act",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "CycleLengthOp",
+                    "filters": [
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "CycleLengthOp",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CycleLengthOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CycleLengthsOp",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CycleLengthsOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "CycleIndexOp: finite group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CycleIndexOp: element",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CycleIndexOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [],
+                [],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "RepresentativeActionOp: TF Method on elements",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingFreeLiftSetup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 440
+                },
+                {
+                    "comment": "RepresentativeActionOp: nice group on elements",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 389
+                },
+                {
+                    "comment": "RepresentativeActionOp: G, d, e, opr for AffineCrystGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 160
+                },
+                {
+                    "comment": "RepresentativeActionOp: G, d, e, opr for AffineCrystGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 160
+                },
+                {
+                    "comment": "RepresentativeActionOp: for subgroups of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 152
+                },
+                {
+                    "comment": "RepresentativeActionOp: pc group on subgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 130
+                },
+                {
+                    "comment": "RepresentativeActionOp: for natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "RepresentativeActionOp: natural alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "RepresentativeActionOp: cycle structure comparison for solvable perm groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "RepresentativeActionOp: permgrp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "RepresentativeActionOp: for conjugation of elements in a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "RepresentativeActionOp: element conjugacy in pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "RepresentativeActionOp: trivial general cases",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "RepresentativeActionOp: orbit algorithm: trace transversal",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "5args": [
+                {
+                    "comment": "RepresentativeActionOp: ignore domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "6args": []
+        },
+        "name": "RepresentativeActionOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "StabilizerFuncOp: use normalizer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 271
+                },
+                {
+                    "comment": "StabilizerFuncOp: alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "StabilizerFuncOp: symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "StabilizerFuncOp: permutation group with generators list",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "StabilizerFuncOp: G (solv.), pnt, gens, gens, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "StabilizerFuncOp: G, pnt, pcgs, acts, act, calling `Pcgs_MutableOrbitStabilizerOp'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "StabilizerFuncOp: G (solv.), pnt, gens, gens, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "StabilizerFuncOp: `OrbitStabilizerAlgorithm' without domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "6args": [
+                {
+                    "comment": "StabilizerFuncOp: with domain, use normalizer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 273
+                },
+                {
+                    "comment": "StabilizerFuncOp: alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 112
+                },
+                {
+                    "comment": "StabilizerFuncOp: symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 112
+                },
+                {
+                    "comment": "StabilizerFuncOp: permutation group with domain",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "StabilizerFuncOp: G (solv.), D,pnt, gens, gens, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "StabilizerFuncOp: G, D, pnt, pcgs, acts, act, calling `Pcgs_MutableOrbitStabilizerOp'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [],
+                        [
+                            "IsPrimeOrdersPcgs",
+                            "Tester(IsPrimeOrdersPcgs)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "StabilizerFuncOp: G (solv.), D,pnt, gens, gens, act",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "StabilizerFuncOp: `OrbitStabilizerAlgorithm' with domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ]
+        },
+        "name": "StabilizerFuncOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [],
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": [
+                {
+                    "comment": "OrbitStabilizerAlgorithm: for pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "OrbitStabilizerAlgorithm: use stabilizer size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanComputeSizeAnySubgroup"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "OrbitStabilizerAlgorithm: collect stabilizer generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ]
+        },
+        "name": "OrbitStabilizerAlgorithm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "AbelianSubfactorAction: generic:use modulo pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 99
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbelianSubfactorAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DomainForAction: matrix/matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "DomainForAction: FFE vector/matrix",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "CategoryCollections(IsFFE)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "DomainForAction: vector/permgrp",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "DomainForAction: default: fail",
+                    "filters": [
+                        [],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DomainForAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "StabChainOp: trivial group",
+                    "filters": [
+                        [
+                            "IsTrivial",
+                            "Tester(IsTrivial)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "StabChainOp: with base",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 87
+                },
+                {
+                    "comment": "StabChainOp: empty base",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "StabChainOp: alternating group",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "StabChainOp: symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "StabChainOp: group and option",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 59
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StabChainOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StabChainMutable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StabChainMutable)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "StabChainMutable: call StabChainOp",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "StabChainMutable: for blocks homomorphism",
+                    "filters": [
+                        [
+                            "IsBlocksHomomorphism"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "StabChainMutable: perm to perm mapping by images",
+                    "filters": [
+                        [
+                            "IsPermGroupGeneralMappingByImages",
+                            "IsToPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "StabChainMutable: perm mapping by images",
+                    "filters": [
+                        [
+                            "IsPermGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StabChainMutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StabChainMutable): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StabChainMutable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StabChainMutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StabChainMutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StabChainImmutable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StabChainImmutable)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "StabChainImmutable: use StabChainMutable",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StabChainImmutable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StabChainImmutable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StabChainImmutable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StabChainImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StabChainImmutable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StabChainOptions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StabChainOptions)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "StabChainOptions",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "StabChainOptions: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StabChainOptions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StabChainOptions): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StabChainOptions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StabChainOptions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StabChainOptions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaseOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BaseOfGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "BaseOfGroup: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "BaseOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaseOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BaseOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BaseOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BaseOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BaseOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalStabChain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimalStabChain)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "MinimalStabChain: matrix group via niceo",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 388
+                },
+                {
+                    "comment": "MinimalStabChain: Perm",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "MinimalStabChain: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalStabChain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimalStabChain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimalStabChain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimalStabChain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimalStabChain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "MembershipTestKnownBase",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "MembershipTestKnownBase: stabchain, base, word",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MembershipTestKnownBase",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermOnEnumerator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugacyClass: class of element",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ConjugacyClass: class of element and centralizer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugacyClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RationalClass",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RationalClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalClassGroupRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DecomposedRationalClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DecomposedRationalClass)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "DecomposedRationalClass: generic",
+                    "filters": [
+                        [
+                            "IsRationalClassGroupRep"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DecomposedRationalClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalClassGroupRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DecomposedRationalClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DecomposedRationalClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DecomposedRationalClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalClassGroupRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DecomposedRationalClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StoredPermliftSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StoredPermliftSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "StoredPermliftSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "StoredPermliftSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StoredPermliftSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StoredPermliftSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StoredPermliftSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StoredPermliftSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StoredPermliftSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AscendingChainOp: PermGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "AscendingChainOp: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AscendingChainOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedAscendingChains: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedAscendingChains)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ComputedAscendingChains: init",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedAscendingChains: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedAscendingChains",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedAscendingChains): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedAscendingChains): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedAscendingChains)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedAscendingChains)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CanonicalRightCosetElement: finite matric group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 418
+                },
+                {
+                    "comment": "CanonicalRightCosetElement: Perm",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "CanonicalRightCosetElement: for AffineCrystGroupOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        []
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "CanonicalRightCosetElement: for AffineCrystGroupOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        []
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "CanonicalRightCosetElement: Pc",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        []
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "CanonicalRightCosetElement: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalRightCosetElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeftActingGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeftActingGroup)"
+                        ]
+                    ],
+                    "rank": 20011
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftActingGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeftActingGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeftActingGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeftActingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeftActingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RightActingGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RightActingGroup)"
+                        ]
+                    ],
+                    "rank": 20011
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightActingGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RightActingGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RightActingGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RightActingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RightActingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DoubleCoset: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "DoubleCoset: with size",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 85
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DoubleCoset",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DoubleCosetsNC: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 99
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DoubleCosetsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "DoubleCosetRepsAndSizes: Pc",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 138
+                },
+                {
+                    "comment": "DoubleCosetRepsAndSizes: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 99
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DoubleCosetRepsAndSizes",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RepresentativesContainedRightCosets: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RepresentativesContainedRightCosets)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "RepresentativesContainedRightCosets: generic",
+                    "filters": [
+                        [
+                            "IsDoubleCoset"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativesContainedRightCosets",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RepresentativesContainedRightCosets): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RepresentativesContainedRightCosets): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RepresentativesContainedRightCosets)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDoubleCoset"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RepresentativesContainedRightCosets)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightCoset: use subgroup size",
+                    "filters": [
+                        [
+                            "Tester(Size)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "RightCoset: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightCoset",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightCosetsNC: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 401
+                },
+                {
+                    "comment": "RightCosetsNC: perm groups, use RightTransversal",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "RightCosetsNC: AffineCrystGroupOnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "RightCosetsNC: AffineCrystGroupOnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 106
+                },
+                {
+                    "comment": "RightCosetsNC: pc groups, use RightTransversal",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "RightCosetsNC: generic: orbit",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightCosetsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DoCheapActionImages: permutation",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "DoCheapActionImages: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DoCheapActionImages",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FindActionKernel: Niceo",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 400
+                },
+                {
+                    "comment": "FindActionKernel: perm",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 116
+                },
+                {
+                    "comment": "FindActionKernel: generic for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 75
+                },
+                {
+                    "comment": "FindActionKernel: general case: can't do",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FindActionKernel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalHomomorphismsPool: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalHomomorphismsPool)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NaturalHomomorphismsPool",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NaturalHomomorphismsPool: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismsPool",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalHomomorphismsPool): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalHomomorphismsPool): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalHomomorphismsPool)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalHomomorphismsPool)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FactorCosetAction: by right transversal operation, Niceo",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 400
+                },
+                {
+                    "comment": "FactorCosetAction: for full fp group on subgroup",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 76
+                },
+                {
+                    "comment": "FactorCosetAction: subgrp in quotient Rep",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup",
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "FactorCosetAction: for subgroups of an fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "FactorCosetAction: by right transversal operation",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "FactorCosetAction: by right transversal operation, given kernel, Niceo",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 433
+                },
+                {
+                    "comment": "FactorCosetAction: by right transversal operation, given kernel",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 99
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorCosetAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "AbsolutIrreducibleModules: generic method for groups with pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "AbsolutIrreducibleModules: generic method for groups and finite field",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 107
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbsolutIrreducibleModules",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IrreducibleModules: generic method for groups with pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 114
+                },
+                {
+                    "comment": "IrreducibleModules: generic method for groups and finite field",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 107
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IrreducibleModules",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RegularModule: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 85
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RegularModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OCAddToFunctions2: pc group",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "OCAddToFunctions2: generic",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OCAddToFunctions2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OCAddRelations: pc group",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "OCAddRelations: perm group",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OCAddRelations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "OCNormalRelations: pc group",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OCNormalRelations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OCAddSumMatrices: pc group",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsPcgs"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "OCAddSumMatrices: perm group",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OCAddSumMatrices",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OCAddBigMatrices: general",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OCAddBigMatrices",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OCCoprimeComplement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "OCAddComplement: pc group",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "OCAddComplement: generic",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OCAddComplement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ComplementClassesRepresentativesSolvableNC: pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 76
+                },
+                {
+                    "comment": "ComplementClassesRepresentativesSolvableNC: using cohomology",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComplementClassesRepresentativesSolvableNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ComplementClassesRepresentatives: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 96
+                },
+                {
+                    "comment": "ComplementClassesRepresentatives: solvable normal subgroup or factor group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "ComplementClassesRepresentatives: tell that the normal subgroup must be solvable",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComplementClassesRepresentatives",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TwoCocycles: generic method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        []
+                    ],
+                    "rank": 46
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TwoCocycles",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TwoCoboundaries: generic method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        []
+                    ],
+                    "rank": 46
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TwoCoboundaries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TwoCohomology: generic method for pc groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        []
+                    ],
+                    "rank": 46
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TwoCohomology",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CanEasilyComputePcgs"
+                ],
+                [],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "Extension: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Extension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CanEasilyComputePcgs"
+                ],
+                [],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExtensionNC: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtensionNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CanEasilyComputePcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Extensions: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Extensions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CanEasilyComputePcgs"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExtensionRepresentatives: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 72
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtensionRepresentatives",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CanEasilyComputePcgs"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SplitExtension: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        []
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SplitExtension: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [],
+                        [
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SplitExtension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CanEasilyComputePcgs"
+                ],
+                [],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "TopExtensionsByAutomorphism: generic method for groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 56
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TopExtensionsByAutomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CanEasilyComputePcgs"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CyclicTopExtensions: generic method for pc groups",
+                    "filters": [
+                        [
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 56
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CyclicTopExtensions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SocleComplement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SocleComplement)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SocleComplement: for primitive solvable group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsPrimitiveSolvableGroup",
+                            "Tester(IsPrimitiveSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "SocleComplement: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SocleComplement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SocleComplement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SocleComplement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SocleComplement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SocleComplement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SocleDimensions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SocleDimensions)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SocleDimensions: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SocleDimensions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SocleDimensions): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SocleDimensions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SocleDimensions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SocleDimensions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ModuleOfExtension: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ModuleOfExtension)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ModuleOfExtension: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ModuleOfExtension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ModuleOfExtension): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ModuleOfExtension): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ModuleOfExtension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ModuleOfExtension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OmegaAndLowerPCentralSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OmegaAndLowerPCentralSeries)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "OmegaAndLowerPCentralSeries: omega and lower central",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "OmegaAndLowerPCentralSeries: general case: warn that no method available",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "OmegaAndLowerPCentralSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OmegaAndLowerPCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OmegaAndLowerPCentralSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OmegaAndLowerPCentralSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OmegaAndLowerPCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OmegaAndLowerPCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SchurCover: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SchurCover)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SchurCover: of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "SchurCover: general: Holt's algorithm",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SchurCover: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SchurCover",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SchurCover): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SchurCover): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SchurCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SchurCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EpimorphismSchurCover: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EpimorphismSchurCover)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "EpimorphismSchurCover: Use copy of AtlasRep's 6-fold cover",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "EpimorphismSchurCover: Use library copy of double cover",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "EpimorphismSchurCover: Use library copy of double cover",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "EpimorphismSchurCover: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "EpimorphismSchurCover: generic, via fp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "EpimorphismSchurCover: Holt's algorithm",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "EpimorphismSchurCover: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "EpimorphismSchurCover: Holt's algorithm, primes",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EpimorphismSchurCover",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EpimorphismSchurCover): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EpimorphismSchurCover): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EpimorphismSchurCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EpimorphismSchurCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AbelianInvariantsMultiplier: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AbelianInvariantsMultiplier)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "AbelianInvariantsMultiplier: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "AbelianInvariantsMultiplier: naive",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "AbelianInvariantsMultiplier: via Sylow Subgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "AbelianInvariantsMultiplier: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbelianInvariantsMultiplier",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AbelianInvariantsMultiplier): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AbelianInvariantsMultiplier): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AbelianInvariantsMultiplier)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AbelianInvariantsMultiplier)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Epicentre: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Epicentre)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Epicentre: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Epicentre: Naive Method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Epicentre: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Epicentre: Naive method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Epicentre",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Epicentre): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Epicentre): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Epicentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Epicentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NonabelianExteriorSquare: Naive method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NonabelianExteriorSquare",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EpimorphismNonabelianExteriorSquare: Naive method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EpimorphismNonabelianExteriorSquare",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCentralFactor: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCentralFactor)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsCentralFactor: Naive method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsCentralFactor: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCentralFactor",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCentralFactor): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCentralFactor): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCentralFactor)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCentralFactor)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SchurCoverOfSymmetricGroup: P=3, Sign=+1 by default",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SchurCoverOfSymmetricGroup: Sign=+1 by default",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SchurCoverOfSymmetricGroup: Use explicit matrix reps for degrees 1,2,3",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "SchurCoverOfSymmetricGroup: Use Lukas Maas's inductive construction of a basic spin rep",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 55
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SchurCoverOfSymmetricGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DoubleCoverOfAlternatingGroup: P=3 by default",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DoubleCoverOfAlternatingGroup: Use Lukas Maas's inductive construction of a basic spin rep",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DoubleCoverOfAlternatingGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugacyClassSubgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 86
+                },
+                {
+                    "comment": "ConjugacyClassSubgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugacyClassSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExternalOrbit"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClassElementLattice: for classes of subgroups",
+                    "filters": [
+                        [
+                            "IsConjugacyClassSubgroupsRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassElementLattice",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Zuppos: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Zuppos)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Zuppos: group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Zuppos: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Zuppos: group with condition",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Zuppos",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Zuppos): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Zuppos): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Zuppos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Zuppos)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLatticeSubgroupsRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalSubgroupsLattice: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalSubgroupsLattice)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MaximalSubgroupsLattice: cyclic extension",
+                    "filters": [
+                        [
+                            "IsLatticeSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalSubgroupsLattice",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLatticeSubgroupsRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalSubgroupsLattice): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalSubgroupsLattice): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalSubgroupsLattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLatticeSubgroupsRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalSubgroupsLattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLatticeSubgroupsRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalSupergroupsLattice: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimalSupergroupsLattice)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MinimalSupergroupsLattice: cyclic extension",
+                    "filters": [
+                        [
+                            "IsLatticeSubgroupsRep"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalSupergroupsLattice",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLatticeSubgroupsRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimalSupergroupsLattice): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimalSupergroupsLattice): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimalSupergroupsLattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLatticeSubgroupsRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimalSupergroupsLattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TomDataAlmostSimpleRecognition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TomDataAlmostSimpleRecognition)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "TomDataAlmostSimpleRecognition: alt",
+                    "filters": [
+                        [
+                            "IsNaturalAlternatingGroup",
+                            "Tester(IsNaturalAlternatingGroup)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "TomDataAlmostSimpleRecognition: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TomDataAlmostSimpleRecognition: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TomDataAlmostSimpleRecognition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TomDataAlmostSimpleRecognition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TomDataAlmostSimpleRecognition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TomDataAlmostSimpleRecognition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TomDataAlmostSimpleRecognition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SubgroupsOrbitsAndNormalizers: perm group on list",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 61
+                },
+                {
+                    "comment": "SubgroupsOrbitsAndNormalizers: pc group on list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "SubgroupsOrbitsAndNormalizers: generic on list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "SubgroupsOrbitsAndNormalizers: generic on record with list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubgroupsOrbitsAndNormalizers",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFrattiniFree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFrattiniFree)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsFrattiniFree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFrattiniFree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFrattiniFree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFrattiniFree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFrattiniFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFrattiniFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LinesOfStraightLineProgram: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LinesOfStraightLineProgram)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LinesOfStraightLineProgram",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LinesOfStraightLineProgram): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LinesOfStraightLineProgram): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LinesOfStraightLineProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LinesOfStraightLineProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrInputsOfStraightLineProgram: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrInputsOfStraightLineProgram)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "NrInputsOfStraightLineProgram: for a straight line program",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrInputsOfStraightLineProgram",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrInputsOfStraightLineProgram): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrInputsOfStraightLineProgram): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrInputsOfStraightLineProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrInputsOfStraightLineProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ResultOfStraightLineProgram: for a straight line program with slot usage pattern, a list",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram",
+                            "Tester(SlotUsagePattern)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "ResultOfStraightLineProgram: for a straight line program, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ResultOfStraightLineProgram",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StraightLineProgElmType: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StraightLineProgElmType)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "StraightLineProgElmType: generic",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StraightLineProgElmType",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StraightLineProgElmType): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StraightLineProgElmType): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StraightLineProgElmType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StraightLineProgElmType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StretchImportantSLPElement: straight line program elements",
+                    "filters": [
+                        [
+                            "IsStraightLineProgElm"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "StretchImportantSLPElement: arbitrary elements: do nothing",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StretchImportantSLPElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SlotUsagePattern: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SlotUsagePattern)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "SlotUsagePattern: for an slp",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SlotUsagePattern",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SlotUsagePattern): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SlotUsagePattern): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SlotUsagePattern)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SlotUsagePattern)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LargestNrSlots: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LargestNrSlots)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "LargestNrSlots: for a straight line program",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LargestNrSlots",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LargestNrSlots): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LargestNrSlots): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LargestNrSlots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LargestNrSlots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TypeOfObjWithMemory: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TypeOfObjWithMemory)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "TypeOfObjWithMemory: generic",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TypeOfObjWithMemory",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TypeOfObjWithMemory): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TypeOfObjWithMemory): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TypeOfObjWithMemory)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TypeOfObjWithMemory)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StripMemory: for an object with memory",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "StripMemory: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "StripMemory: fallback for all objects",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StripMemory",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ForgetMemory: nice error message for memory objects",
+                    "filters": [
+                        [
+                            "IsObjWithMemory"
+                        ]
+                    ],
+                    "rank": 107
+                },
+                {
+                    "comment": "ForgetMemory: for a mutable list",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ForgetMemory: nice error message for all objects",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ForgetMemory",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FpElmEqualityMethod: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FpElmEqualityMethod)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FpElmEqualityMethod: generic dispatcher",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FpElmEqualityMethod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FpElmEqualityMethod): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FpElmEqualityMethod): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FpElmEqualityMethod)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FpElmEqualityMethod)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FpElmComparisonMethod: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FpElmComparisonMethod)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FpElmComparisonMethod: generic dispatcher",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FpElmComparisonMethod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FpElmComparisonMethod): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FpElmComparisonMethod): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FpElmComparisonMethod)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FpElmComparisonMethod)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FpElementNFFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FpElementNFFunction)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FpElementNFFunction",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FpElementNFFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FpElementNFFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FpElementNFFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FpElementNFFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FpElementNFFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpGroup)"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse",
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ElementOfFpGroup: for a family of free group elements, and an assoc. word",
+                    "filters": [
+                        [
+                            "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "ElementOfFpGroup: for a family of f.p. group elements, and an assoc. word",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpGroup)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementOfFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CosetTableInWholeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CosetTableInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CosetTableInWholeGroup: ByQuoSubRep",
+                    "filters": [
+                        [
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "CosetTableInWholeGroup: from augmented table Mtc",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "Tester(AugmentedCosetTableMtcInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "CosetTableInWholeGroup: from augmented table Rrs",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "Tester(AugmentedCosetTableRrsInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "CosetTableInWholeGroup: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "CosetTableInWholeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetTableInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CosetTableInWholeGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CosetTableInWholeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CosetTableInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CosetTableInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TryCosetTableInWholeGroup: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TryCosetTableInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CosetTableNormalClosureInWholeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CosetTableNormalClosureInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CosetTableNormalClosureInWholeGroup: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "CosetTableNormalClosureInWholeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetTableNormalClosureInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CosetTableNormalClosureInWholeGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CosetTableNormalClosureInWholeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CosetTableNormalClosureInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CosetTableNormalClosureInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsSubgroupOfWholeGroupByQuotient: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsSubgroupOfWholeGroupByQuotient)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "AsSubgroupOfWholeGroupByQuotient: is already",
+                    "filters": [
+                        [
+                            "IsSubgroupOfWholeGroupByQuotientRep"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "AsSubgroupOfWholeGroupByQuotient: create",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsSubgroupOfWholeGroupByQuotient",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsSubgroupOfWholeGroupByQuotient): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsSubgroupOfWholeGroupByQuotient): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsSubgroupOfWholeGroupByQuotient)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsSubgroupOfWholeGroupByQuotient)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LowIndexSubgroupsFpGroupIterator: supply trivial subgroup",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "LowIndexSubgroupsFpGroupIterator: full f.p. group, subgroup of it",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "LowIndexSubgroupsFpGroupIterator: full f.p. group, subgroup of it -- still the old code",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 91
+                },
+                {
+                    "comment": "LowIndexSubgroupsFpGroupIterator: subgroups of f.p. group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 89
+                },
+                {
+                    "comment": "LowIndexSubgroupsFpGroupIterator: supply trivial subgroup, with exclusion list",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 59
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "LowIndexSubgroupsFpGroupIterator: full f.p. group, subgroup of it, with exclusion list",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 94
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowIndexSubgroupsFpGroupIterator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LowIndexSubgroupsFpGroup: supply trivial subgroup",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "LowIndexSubgroupsFpGroup: subgroups of full fp group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 92
+                },
+                {
+                    "comment": "LowIndexSubgroupsFpGroup: subgroups of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 89
+                },
+                {
+                    "comment": "LowIndexSubgroupsFpGroup: with exclusion list, supply trivial subgroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 59
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "LowIndexSubgroupsFpGroup: subgroups of full fp group, with exclusion list",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 94
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowIndexSubgroupsFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGeneratorsOfFpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGeneratorsOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpGroup: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpGroup: for a finitely presented group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGeneratorsOfFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGeneratorsOfFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGeneratorsOfFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGeneratorsOfWholeGroup: for a finitely presented group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGeneratorsOfWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelatorsOfFpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelatorsOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "RelatorsOfFpGroup: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "RelatorsOfFpGroup: for finitely presented group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelatorsOfFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelatorsOfFpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelatorsOfFpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelatorsOfFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelatorsOfFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGroupOfFpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGroupOfFpGroup)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "FreeGroupOfFpGroup: for a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsGroupOfFamily",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "FreeGroupOfFpGroup: for a finitely presented group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGroupOfFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGroupOfFpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGroupOfFpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGroupOfFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGroupOfFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndicesInvolutaryGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndicesInvolutaryGenerators)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "IndicesInvolutaryGenerators: for finitely presented group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicesInvolutaryGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndicesInvolutaryGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndicesInvolutaryGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndicesInvolutaryGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfFamily",
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndicesInvolutaryGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StoredExcludedOrders: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StoredExcludedOrders)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "StoredExcludedOrders: fp group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StoredExcludedOrders",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StoredExcludedOrders): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StoredExcludedOrders): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StoredExcludedOrders)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StoredExcludedOrders)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FPFaithHom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FPFaithHom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "FPFaithHom: try perm or pc hom",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FPFaithHom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FPFaithHom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FPFaithHom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FPFaithHom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FPFaithHom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentedCosetTableMtcInWholeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentedCosetTableMtcInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "AugmentedCosetTableMtcInWholeGroup: subgroup of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "AugmentedCosetTableMtcInWholeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentedCosetTableMtcInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentedCosetTableMtcInWholeGroup): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentedCosetTableMtcInWholeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentedCosetTableMtcInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentedCosetTableMtcInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentedCosetTableRrsInWholeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentedCosetTableRrsInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "AugmentedCosetTableRrsInWholeGroup: use Mtc table",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup",
+                            "Tester(AugmentedCosetTableMtcInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "AugmentedCosetTableRrsInWholeGroup: subgroup of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "AugmentedCosetTableRrsInWholeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentedCosetTableRrsInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentedCosetTableRrsInWholeGroup): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentedCosetTableRrsInWholeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentedCosetTableRrsInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentedCosetTableRrsInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentedCosetTableNormalClosureInWholeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentedCosetTableNormalClosureInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "AugmentedCosetTableNormalClosureInWholeGroup: subgroup of fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "AugmentedCosetTableNormalClosureInWholeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentedCosetTableNormalClosureInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentedCosetTableNormalClosureInWholeGroup): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentedCosetTableNormalClosureInWholeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentedCosetTableNormalClosureInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentedCosetTableNormalClosureInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AugmentedCosetTableNormalClosure: for finitely presented groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentedCosetTableNormalClosure",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CosetTableBySubgroup: use `CosetTableInWholeGroup",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "CosetTableBySubgroup: coset action",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetTableBySubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPresentation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimaryGeneratorWords: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimaryGeneratorWords)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimaryGeneratorWords",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPresentation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimaryGeneratorWords): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimaryGeneratorWords): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimaryGeneratorWords)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPresentation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimaryGeneratorWords)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TietzeOrigin: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TietzeOrigin)"
+                        ]
+                    ],
+                    "rank": 20037
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TietzeOrigin",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TietzeOrigin): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TietzeOrigin): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TietzeOrigin)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TietzeOrigin)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPresentation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TzOptions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TzOptions)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "TzOptions: set default values",
+                    "filters": [
+                        [
+                            "IsPresentation"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TzOptions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPresentation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TzOptions): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TzOptions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TzOptions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPresentation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TzOptions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsWordDecompHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsWordDecompHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20018
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsWordDecompHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsWordDecompHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsWordDecompHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsWordDecompHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsWordDecompHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CosetTableFpHom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CosetTableFpHom)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "CosetTableFpHom: for fp homomorphisms",
+                    "filters": [
+                        [
+                            "IsGroupGeneralMappingByImages",
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetTableFpHom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CosetTableFpHom): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CosetTableFpHom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CosetTableFpHom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CosetTableFpHom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismSimplifiedFpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismSimplifiedFpGroup)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "IsomorphismSimplifiedFpGroup: using tietze transformations",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismSimplifiedFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismSimplifiedFpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismSimplifiedFpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismSimplifiedFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsSubgroupFpGroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismSimplifiedFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EpimorphismFromFreeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EpimorphismFromFreeGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "EpimorphismFromFreeGroup: general",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "EpimorphismFromFreeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EpimorphismFromFreeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EpimorphismFromFreeGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EpimorphismFromFreeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EpimorphismFromFreeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EpimorphismFromFreeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceMonomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "NiceMonomorphism: SeedFaithfulAction supersedes",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)",
+                            "Tester(SeedFaithfulAction)"
+                        ]
+                    ],
+                    "rank": 1369
+                },
+                {
+                    "comment": "NiceMonomorphism: for subgroups that get the nice monomorphism by their parent",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 755
+                },
+                {
+                    "comment": "NiceMonomorphism: falling back on GL",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 391
+                },
+                {
+                    "comment": "NiceMonomorphism: use NicomorphismOfGeneralMatrixGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 388
+                },
+                {
+                    "comment": "NiceMonomorphism: for automorphism groups",
+                    "filters": [
+                        [
+                            "IsGroupOfAutomorphismsFiniteGroup",
+                            "Tester(IsGroupOfAutomorphismsFiniteGroup)"
+                        ]
+                    ],
+                    "rank": 381
+                },
+                {
+                    "comment": "NiceMonomorphism: via IsomorphismAbelianGroupViaIndependentGenerators",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputeWithIndependentGensAbelianGroup",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "NiceMonomorphism: regular action",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 367
+                },
+                {
+                    "comment": "NiceMonomorphism: if a canonical nice monomorphism is already known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(CanonicalNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "NiceMonomorphism: for a (nonrational) cyclotomic matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceMonomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceMonomorphism): set `IsNiceomorphism' property",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 10056
+                },
+                {
+                    "comment": "Setter(NiceMonomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceMonomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCanonicalNiceMonomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCanonicalNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsCanonicalNiceMonomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCanonicalNiceMonomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCanonicalNiceMonomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCanonicalNiceMonomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCanonicalNiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCanonicalNiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalNiceMonomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "CanonicalNiceMonomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 388
+                },
+                {
+                    "comment": "CanonicalNiceMonomorphism: test canonicity of existing niceo",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(NiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalNiceMonomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalNiceMonomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalNiceMonomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalNiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalNiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceObject: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceObject)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "NiceObject",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 367
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceObject",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceObject): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceObject): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceObject)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceObject)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsHandledByNiceMonomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "IsHandledByNiceMonomorphism: for a cyclotomic matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsHandledByNiceMonomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsHandledByNiceMonomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsHandledByNiceMonomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsHandledByNiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsHandledByNiceMonomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GroupByNiceMonomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 50
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupByNiceMonomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SeedFaithfulAction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SeedFaithfulAction)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "SeedFaithfulAction: default: fail",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SeedFaithfulAction: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SeedFaithfulAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SeedFaithfulAction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SeedFaithfulAction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SeedFaithfulAction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SeedFaithfulAction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AutomorphismGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AutomorphismGroup)"
+                        ]
+                    ],
+                    "rank": 20008
+                },
+                {
+                    "comment": "AutomorphismGroup: for finite p-groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsPGroup",
+                            "Tester(IsPGroup)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "AutomorphismGroup: for free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "AutomorphismGroup: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "AutomorphismGroup: finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "AutomorphismGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AutomorphismGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AutomorphismGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AutomorphismGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AutomorphismGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AutomorphismGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupOfAutomorphisms: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupOfAutomorphisms)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsGroupOfAutomorphisms: test generators and one",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsGroupOfAutomorphisms: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupOfAutomorphisms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupOfAutomorphisms): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupOfAutomorphisms): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupOfAutomorphisms)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupOfAutomorphisms)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupOfAutomorphismsFiniteGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupOfAutomorphismsFiniteGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsGroupOfAutomorphismsFiniteGroup: default",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsGroupOfAutomorphismsFiniteGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupOfAutomorphismsFiniteGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupOfAutomorphismsFiniteGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupOfAutomorphismsFiniteGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupOfAutomorphismsFiniteGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupOfAutomorphismsFiniteGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfAutomorphisms",
+                    "Tester(IsGroupOfAutomorphisms)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AutomorphismDomain: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AutomorphismDomain)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "AutomorphismDomain: use source of one",
+                    "filters": [
+                        [
+                            "IsGroupOfAutomorphisms",
+                            "Tester(IsGroupOfAutomorphisms)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "AutomorphismDomain: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AutomorphismDomain",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfAutomorphisms",
+                    "Tester(IsGroupOfAutomorphisms)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AutomorphismDomain): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AutomorphismDomain): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AutomorphismDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfAutomorphisms",
+                    "Tester(IsGroupOfAutomorphisms)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AutomorphismDomain)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfAutomorphisms",
+                    "Tester(IsGroupOfAutomorphisms)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAutomorphismGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAutomorphismGroup)"
+                        ]
+                    ],
+                    "rank": 20037
+                },
+                {
+                    "comment": "IsAutomorphismGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAutomorphismGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfAutomorphisms",
+                    "Tester(IsGroupOfAutomorphisms)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAutomorphismGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAutomorphismGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAutomorphismGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfAutomorphisms",
+                    "Tester(IsGroupOfAutomorphisms)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAutomorphismGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InnerAutomorphismsAutomorphismGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InnerAutomorphismsAutomorphismGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "InnerAutomorphismsAutomorphismGroup: for automorphism groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsAutomorphismGroup",
+                            "Tester(IsAutomorphismGroup)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "InnerAutomorphismsAutomorphismGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InnerAutomorphismsAutomorphismGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InnerAutomorphismsAutomorphismGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InnerAutomorphismsAutomorphismGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InnerAutomorphismsAutomorphismGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InnerAutomorphismsAutomorphismGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GQuotients: whole fp group to finite group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "GQuotients: subgroup of an fp group",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 78
+                },
+                {
+                    "comment": "GQuotients: for groups which can compute element orders",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GQuotients",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsomorphicSubgroups: for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 85
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphicSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DefaultFieldOfMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DefaultFieldOfMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "DefaultFieldOfMatrixGroup: alg elms",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "DefaultFieldOfMatrixGroup: for a matrix group over an s.c. algebra",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "DefaultFieldOfMatrixGroup: for matrix group over the cyclotomics",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "DefaultFieldOfMatrixGroup: for a matrix group over a ring Z/nZ",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "DefaultFieldOfMatrixGroup: for a matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "DefaultFieldOfMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DefaultFieldOfMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DefaultFieldOfMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DefaultFieldOfMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DefaultFieldOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DefaultFieldOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DimensionOfMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DimensionOfMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "DimensionOfMatrixGroup: for matrix group with dimension",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(Dimension)"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "DimensionOfMatrixGroup: from one",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "Tester(OneImmutable)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "DimensionOfMatrixGroup: for matrix group with dimension",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(DimensionOfMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "DimensionOfMatrixGroup: from generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "DimensionOfMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DimensionOfMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DimensionOfMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DimensionOfMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DimensionOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DimensionOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FieldOfMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FieldOfMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "FieldOfMatrixGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "FieldOfMatrixGroup: for a matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "FieldOfMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FieldOfMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FieldOfMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FieldOfMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FieldOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FieldOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransposedMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransposedMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "TransposedMatrixGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "TransposedMatrixGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "TransposedMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransposedMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransposedMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransposedMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransposedMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransposedMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGeneralLinearGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGeneralLinearGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsGeneralLinearGroup: try natural",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsGeneralLinearGroup: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsGeneralLinearGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGeneralLinearGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGeneralLinearGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGeneralLinearGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGeneralLinearGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGeneralLinearGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNaturalGL: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNaturalGL)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsNaturalGL: size comparison",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 391
+                },
+                {
+                    "comment": "IsNaturalGL: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNaturalGL",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNaturalGL): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNaturalGL): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNaturalGL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNaturalGL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSpecialLinearGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSpecialLinearGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSpecialLinearGroup: generic method for finite groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSpecialLinearGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSpecialLinearGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSpecialLinearGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSpecialLinearGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSpecialLinearGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSpecialLinearGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNaturalSL: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNaturalSL)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsNaturalSL: size comparison",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 391
+                },
+                {
+                    "comment": "IsNaturalSL: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNaturalSL",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNaturalSL): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNaturalSL): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNaturalSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNaturalSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSubgroupSL: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSubgroupSL)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsSubgroupSL: determinant test for generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsSubgroupSL: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubgroupSL",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSubgroupSL): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSubgroupSL): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSubgroupSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSubgroupSL)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InvariantBilinearForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InvariantBilinearForm)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "InvariantBilinearForm: for a matrix group with known `InvariantQuadraticForm'",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(InvariantQuadraticForm)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "InvariantBilinearForm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InvariantBilinearForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InvariantBilinearForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InvariantBilinearForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InvariantBilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InvariantBilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullSubgroupGLorSLRespectingBilinearForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsFullSubgroupGLorSLRespectingBilinearForm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullSubgroupGLorSLRespectingBilinearForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullSubgroupGLorSLRespectingBilinearForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullSubgroupGLorSLRespectingBilinearForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullSubgroupGLorSLRespectingBilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullSubgroupGLorSLRespectingBilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InvariantSesquilinearForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InvariantSesquilinearForm)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "InvariantSesquilinearForm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InvariantSesquilinearForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InvariantSesquilinearForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InvariantSesquilinearForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InvariantSesquilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InvariantSesquilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullSubgroupGLorSLRespectingSesquilinearForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsFullSubgroupGLorSLRespectingSesquilinearForm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullSubgroupGLorSLRespectingSesquilinearForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullSubgroupGLorSLRespectingSesquilinearForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullSubgroupGLorSLRespectingSesquilinearForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullSubgroupGLorSLRespectingSesquilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InvariantQuadraticForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InvariantQuadraticForm)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "InvariantQuadraticForm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InvariantQuadraticForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InvariantQuadraticForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InvariantQuadraticForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InvariantQuadraticForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InvariantQuadraticForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullSubgroupGLorSLRespectingQuadraticForm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsFullSubgroupGLorSLRespectingQuadraticForm: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullSubgroupGLorSLRespectingQuadraticForm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullSubgroupGLorSLRespectingQuadraticForm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullSubgroupGLorSLRespectingQuadraticForm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullSubgroupGLorSLRespectingQuadraticForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FittingFreeLiftSetup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FittingFreeLiftSetup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "FittingFreeLiftSetup: permutation",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "FittingFreeLiftSetup: pc group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "FittingFreeLiftSetup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FittingFreeLiftSetup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FittingFreeLiftSetup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FittingFreeLiftSetup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FittingFreeLiftSetup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FittingFreeLiftSetup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RecogDecompinfoHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RecogDecompinfoHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "RecogDecompinfoHomomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RecogDecompinfoHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RecogDecompinfoHomomorphism): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RecogDecompinfoHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RecogDecompinfoHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RecogDecompinfoHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DirectFactorsFittingFreeSocle: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DirectFactorsFittingFreeSocle)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DirectFactorsFittingFreeSocle: generic",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "DirectFactorsFittingFreeSocle: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DirectFactorsFittingFreeSocle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DirectFactorsFittingFreeSocle): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DirectFactorsFittingFreeSocle): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DirectFactorsFittingFreeSocle)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DirectFactorsFittingFreeSocle)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ChiefSeriesTF: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ChiefSeriesTF)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ChiefSeriesTF: fitting free",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanComputeFittingFree"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ChiefSeriesTF: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ChiefSeriesTF",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ChiefSeriesTF): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ChiefSeriesTF): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ChiefSeriesTF)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ChiefSeriesTF)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRationalMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRationalMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "IsRationalMatrixGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsRationalMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRationalMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRationalMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRationalMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRationalMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRationalMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIntegerMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIntegerMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "IsIntegerMatrixGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsIntegerMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIntegerMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIntegerMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIntegerMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIntegerMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIntegerMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ZClassRepsQClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ZClassRepsQClass)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "ZClassRepsQClass: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ZClassRepsQClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ZClassRepsQClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ZClassRepsQClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ZClassRepsQClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ZClassRepsQClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizerInGLnZ: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizerInGLnZ)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "NormalizerInGLnZ: for PointGroups of space groups from the cryst. groups catalogue",
+                    "filters": [
+                        [
+                            "IsPointGroup",
+                            "Tester(IsPointGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NormalizerInGLnZ: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerInGLnZ",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizerInGLnZ): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizerInGLnZ): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizerInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizerInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentralizerInGLnZ: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CentralizerInGLnZ)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "CentralizerInGLnZ: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralizerInGLnZ",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CentralizerInGLnZ): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CentralizerInGLnZ): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CentralizerInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CentralizerInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBravaisGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBravaisGroup)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "IsBravaisGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsBravaisGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBravaisGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBravaisGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBravaisGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBravaisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBravaisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BravaisGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BravaisGroup)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "BravaisGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BravaisGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BravaisGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BravaisGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BravaisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BravaisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BravaisSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BravaisSubgroups)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "BravaisSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BravaisSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BravaisSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BravaisSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BravaisSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BravaisSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BravaisSupergroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BravaisSupergroups)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "BravaisSupergroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BravaisSupergroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BravaisSupergroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BravaisSupergroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BravaisSupergroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BravaisSupergroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizerInGLnZBravaisGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizerInGLnZBravaisGroup)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "NormalizerInGLnZBravaisGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerInGLnZBravaisGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizerInGLnZBravaisGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizerInGLnZBravaisGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizerInGLnZBravaisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizerInGLnZBravaisGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InvariantLattice: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InvariantLattice)"
+                        ]
+                    ],
+                    "rank": 20048
+                },
+                {
+                    "comment": "InvariantLattice: for rational matrix groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "InvariantLattice: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InvariantLattice",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InvariantLattice): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InvariantLattice): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InvariantLattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InvariantLattice)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TrivialGroupCons: perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "TrivialGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "TrivialGroupCons: pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": -62
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TrivialGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AbelianGroupCons: fp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -45
+                },
+                {
+                    "comment": "AbelianGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -48
+                },
+                {
+                    "comment": "AbelianGroupCons: perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "AbelianGroupCons: pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -62
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbelianGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AlternatingGroupCons: perm group with domain",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "AlternatingGroupCons: perm group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "AlternatingGroupCons: pcp group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "AlternatingGroupCons: pc group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -62
+                },
+                {
+                    "comment": "AlternatingGroupCons: regular perm group with domain",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsRegular",
+                            "Tester(IsRegular)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": -65
+                },
+                {
+                    "comment": "AlternatingGroupCons: regular perm group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsRegular",
+                            "Tester(IsRegular)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -65
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlternatingGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CyclicGroupCons: fp group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        []
+                    ],
+                    "rank": -36
+                },
+                {
+                    "comment": "CyclicGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": -48
+                },
+                {
+                    "comment": "CyclicGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "CyclicGroupCons: pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -62
+                },
+                {
+                    "comment": "CyclicGroupCons: regular perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsRegular",
+                            "Tester(IsRegular)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -65
+                },
+                {
+                    "comment": "CyclicGroupCons: matrix group for default field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CyclicGroupCons: matrix group for given field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CyclicGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DihedralGroupCons: fp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -45
+                },
+                {
+                    "comment": "DihedralGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInfinity"
+                        ]
+                    ],
+                    "rank": -48
+                },
+                {
+                    "comment": "DihedralGroupCons: perm. group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "DihedralGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "DihedralGroupCons: pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -62
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DihedralGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "QuaternionGroupCons: fp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -45
+                },
+                {
+                    "comment": "QuaternionGroupCons: perm. group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "QuaternionGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "QuaternionGroupCons: pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -62
+                },
+                {
+                    "comment": "QuaternionGroupCons: matrix group for default field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "QuaternionGroupCons: matrix group for given field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuaternionGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ElementaryAbelianGroupCons: fp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -45
+                },
+                {
+                    "comment": "ElementaryAbelianGroupCons: perm group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "ElementaryAbelianGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "ElementaryAbelianGroupCons: pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -62
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementaryAbelianGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FreeAbelianGroupCons: fp group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -36
+                },
+                {
+                    "comment": "FreeAbelianGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -48
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeAbelianGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ExtraspecialGroupCons: pcp group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "ExtraspecialGroupCons: pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -62
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtraspecialGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MathieuGroupCons: perm group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -58
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MathieuGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SymmetricGroupCons: perm group with domain",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "SymmetricGroupCons: perm group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "SymmetricGroupCons: pcp group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -60
+                },
+                {
+                    "comment": "SymmetricGroupCons: pc group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -62
+                },
+                {
+                    "comment": "SymmetricGroupCons: regular perm group with domain",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsRegular",
+                            "Tester(IsRegular)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": -65
+                },
+                {
+                    "comment": "SymmetricGroupCons: regular perm group with degree",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsRegular",
+                            "Tester(IsRegular)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": -65
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymmetricGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GeneralLinearGroupCons: some generators for GL_n(Z)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": -43
+                },
+                {
+                    "comment": "GeneralLinearGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -134
+                },
+                {
+                    "comment": "GeneralLinearGroupCons: natural GL for dimension and residue class ring",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "GeneralLinearGroupCons: matrix group for dimension and finite field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneralLinearGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "GeneralOrthogonalGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -152
+                },
+                {
+                    "comment": "GeneralOrthogonalGroupCons: GO for dimension and residue class ring for prime powers",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "GeneralOrthogonalGroupCons: matrix group for dimension and finite field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "GeneralOrthogonalGroupCons: matrix group for <e>, dimension, and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneralOrthogonalGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GeneralUnitaryGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -134
+                },
+                {
+                    "comment": "GeneralUnitaryGroupCons: matrix group for dimension and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneralUnitaryGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SpecialLinearGroupCons: some generators for SL_n(Z)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsIntegers"
+                        ]
+                    ],
+                    "rank": -43
+                },
+                {
+                    "comment": "SpecialLinearGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -134
+                },
+                {
+                    "comment": "SpecialLinearGroupCons: natural SL for dimension and residue class ring",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "SpecialLinearGroupCons: matrix group for dimension and finite field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpecialLinearGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SpecialOrthogonalGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -152
+                },
+                {
+                    "comment": "SpecialOrthogonalGroupCons: GO for dimension and residue class ring for prime powers",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "SpecialOrthogonalGroupCons: matrix group for dimension and finite field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "SpecialOrthogonalGroupCons: matrix group for <e>, dimension, and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpecialOrthogonalGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SpecialUnitaryGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -134
+                },
+                {
+                    "comment": "SpecialUnitaryGroupCons: matrix group for dimension and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpecialUnitaryGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SymplecticGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -134
+                },
+                {
+                    "comment": "SymplecticGroupCons: symplectic group for dimension and residue class ring for prime powers",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "CategoryCollections(IsZmodnZObjNonprime)"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "SymplecticGroupCons: matrix group for dimension and finite field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": -388
+                },
+                {
+                    "comment": "SymplecticGroupCons: matrix group for dimension and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymplecticGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "OmegaCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        []
+                    ],
+                    "rank": -134
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "OmegaCons: matrix group for <e>, dimension, and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OmegaCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GeneralSemilinearGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -154
+                },
+                {
+                    "comment": "GeneralSemilinearGroupCons: matrix group for dimension and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneralSemilinearGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SpecialSemilinearGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -154
+                },
+                {
+                    "comment": "SpecialSemilinearGroupCons: matrix group for dimension and finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpecialSemilinearGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ProjectiveGeneralLinearGroupCons: action on lines",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -54
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectiveGeneralLinearGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ProjectiveSpecialLinearGroupCons: action on lines",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -54
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectiveSpecialLinearGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ProjectiveGeneralUnitaryGroupCons: action on lines",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -54
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectiveGeneralUnitaryGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ProjectiveSpecialUnitaryGroupCons: action on lines",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -54
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectiveSpecialUnitaryGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ProjectiveSymplecticGroupCons: action on lines",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -54
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectiveSymplecticGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ProjectiveOmegaCons: action on lines",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -54
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectiveOmegaCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PerfGrpConst: fp grp",
+                    "filters": [
+                        [
+                            "IsSubgroupFpGroup"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -35
+                },
+                {
+                    "comment": "PerfGrpConst: perm grp",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -58
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PerfGrpConst",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PerfectIdentification: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PerfectIdentification)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "PerfectIdentification: id. for perfect groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PerfectIdentification: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PerfectIdentification",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PerfectIdentification): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PerfectIdentification): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PerfectIdentification)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PerfectIdentification)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SuzukiGroupCons: permutation group for finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -58
+                },
+                {
+                    "comment": "SuzukiGroupCons: matrix group for finite field size",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -388
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SuzukiGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReeGroupCons: matrix",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": -43
+                },
+                {
+                    "comment": "ReeGroupCons: convert to permgroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": -116
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReeGroupCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DataAboutSimpleGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DataAboutSimpleGroup)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DataAboutSimpleGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DataAboutSimpleGroup",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "DataAboutSimpleGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DataAboutSimpleGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DataAboutSimpleGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DataAboutSimpleGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DataAboutSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DataAboutSimpleGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImfRecord: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImfRecord)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "ImfRecord: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImfRecord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImfRecord): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImfRecord): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImfRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImfRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrderingsFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrderingsFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "OrderingsFamily: for a family",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrderingsFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrderingsFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrderingsFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrderingsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrderingsFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsWellFoundedOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsWellFoundedOrdering)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsWellFoundedOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsWellFoundedOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsWellFoundedOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsWellFoundedOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsWellFoundedOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTotalOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTotalOrdering)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTotalOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTotalOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTotalOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTotalOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTotalOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FamilyForOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FamilyForOrdering)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FamilyForOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FamilyForOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FamilyForOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FamilyForOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FamilyForOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LessThanFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LessThanFunction)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "LessThanFunction: for an ordering which has a a LessThanOrEqualFunction",
+                    "filters": [
+                        [
+                            "IsOrdering",
+                            "Tester(LessThanOrEqualFunction)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LessThanFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LessThanFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LessThanFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LessThanFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LessThanFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LessThanOrEqualFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LessThanOrEqualFunction)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "LessThanOrEqualFunction: for an ordering which has a a LessThanFunction",
+                    "filters": [
+                        [
+                            "IsOrdering",
+                            "Tester(LessThanFunction)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LessThanOrEqualFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LessThanOrEqualFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LessThanOrEqualFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LessThanOrEqualFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LessThanOrEqualFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IsLessThanUnder: for an ordering ",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 1
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLessThanUnder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IsLessThanOrEqualUnder: for an ordering and two objects ",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 1
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLessThanOrEqualUnder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IsIncomparableUnder: for an ordering",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 1
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIncomparableUnder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OrderingByLessThanFunctionNC: for a family and a function",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "OrderingByLessThanFunctionNC: for a family, a function, and a list of properties",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrderingByLessThanFunctionNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OrderingByLessThanOrEqualFunctionNC: for a family and a function",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "OrderingByLessThanOrEqualFunctionNC: for a family, a function, and a list of properties",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrderingByLessThanOrEqualFunctionNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsOrderingOnFamilyOfAssocWords: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsOrderingOnFamilyOfAssocWords)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsOrderingOnFamilyOfAssocWords",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsOrderingOnFamilyOfAssocWords): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsOrderingOnFamilyOfAssocWords): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsOrderingOnFamilyOfAssocWords)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsOrderingOnFamilyOfAssocWords)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LetterRepWordsLessFunc: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LetterRepWordsLessFunc)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "LetterRepWordsLessFunc: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LetterRepWordsLessFunc",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LetterRepWordsLessFunc): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LetterRepWordsLessFunc): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LetterRepWordsLessFunc)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LetterRepWordsLessFunc)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTranslationInvariantOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTranslationInvariantOrdering)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "IsTranslationInvariantOrdering: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTranslationInvariantOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTranslationInvariantOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTranslationInvariantOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTranslationInvariantOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTranslationInvariantOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrderingOnGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrderingOnGenerators)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "OrderingOnGenerators: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrderingOnGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrderingOnGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrderingOnGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrderingOnGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrderingOnGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily",
+                    "CategoryFamily((IsWord and IsAssociativeElement))"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections((IsWord and IsAssociativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LexicographicOrdering: for a free monoid",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "LexicographicOrdering: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "LexicographicOrdering: for a family of words of a free semigroup or free monoid",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "LexicographicOrdering: for a free monoid and a list of generators",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "LexicographicOrdering: for a free semigroup and a list of generators",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "LexicographicOrdering: for a free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "LexicographicOrdering: for a free semigroup and a list",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "LexicographicOrdering: for a family of words of a free semigroup or free monoid and a list of generators",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "LexicographicOrdering: for a family of words of a free semigroup or free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LexicographicOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily",
+                    "CategoryFamily((IsWord and IsAssociativeElement))"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections((IsWord and IsAssociativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ShortLexOrdering: for a free monoid",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ShortLexOrdering: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ShortLexOrdering: for a family of words of a free semigroup or free  monoid",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ShortLexOrdering: for a free monoid and a list of generators in the required order ",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "ShortLexOrdering: for a free semigroup and a list of generators in the required order",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ShortLexOrdering: for a free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ShortLexOrdering: for a free semigroup and a list",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ShortLexOrdering: for a family of words of a free semigroup or free monoid and a list of generators",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "ShortLexOrdering: for a family of free words of a free semigroup or free  monoid and a list",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ShortLexOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsShortLexOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsShortLexOrdering)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "IsShortLexOrdering: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsShortLexOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsShortLexOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsShortLexOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsShortLexOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsShortLexOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily",
+                    "CategoryFamily((IsWord and IsAssociativeElement))"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections((IsWord and IsAssociativeElement))"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "WeightLexOrdering: for a free monoid, a list of generators and a list of weights",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "WeightLexOrdering: for a free semigroup, a list of generators and a list of weights",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "WeightLexOrdering: for a free monoid, a list giving ordering on generators and a list of weights",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "WeightLexOrdering: for a free semigroup, a list giving ordering on generators and a list of weights",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "WeightLexOrdering: for a family of words of a free semigroup or free monoid, a list of generators and a list of weights",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "WeightLexOrdering: for a family of words of a free semigroup or free monoid, and two lists",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeightLexOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WeightOfGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WeightOfGenerators)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "WeightOfGenerators: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeightOfGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WeightOfGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WeightOfGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WeightOfGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WeightOfGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsWeightLexOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsWeightLexOrdering)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "IsWeightLexOrdering: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsWeightLexOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsWeightLexOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsWeightLexOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsWeightLexOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsOrderingOnFamilyOfAssocWords",
+                    "Tester(IsOrderingOnFamilyOfAssocWords)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsWeightLexOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily((IsWord and IsAssociativeElement))"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BasicWreathProductOrdering: for a free monoid",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "BasicWreathProductOrdering: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "BasicWreathProductOrdering: for a family of words of a free semigroup or free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "BasicWreathProductOrdering: for a free monoid and a list of generators",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "BasicWreathProductOrdering: for a free semigroup and a list of generators",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "BasicWreathProductOrdering: for a free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "BasicWreathProductOrdering: for a free semigroup and a list",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "BasicWreathProductOrdering: for a family of words of a free semigroup or free monoid and a list of generators",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "BasicWreathProductOrdering: for a family of words of a free semigroup or free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BasicWreathProductOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBasicWreathProductOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBasicWreathProductOrdering)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBasicWreathProductOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBasicWreathProductOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBasicWreathProductOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBasicWreathProductOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBasicWreathProductOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "WreathProductOrdering: for a free monoid",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "WreathProductOrdering: for a free semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "WreathProductOrdering: for a family of words of a free semigroup or free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "WreathProductOrdering: for a free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "WreathProductOrdering: for a free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "WreathProductOrdering: for a free semigroup and a list",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "WreathProductOrdering: for a family of associative words, a list of generators and a list with the levels of the generators",
+                    "filters": [
+                        [
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "WreathProductOrdering: for a family of words of a free semigroup or free monoid and a list",
+                    "filters": [
+                        [
+                            "IsFamily",
+                            "CategoryFamily((IsWord and IsAssociativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WreathProductOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsWreathProductOrdering: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsWreathProductOrdering)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsWreathProductOrdering",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsWreathProductOrdering): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsWreathProductOrdering): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsWreathProductOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsWreathProductOrdering)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsWreathProductOrdering",
+                    "Tester(IsWreathProductOrdering)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LevelsOfGenerators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LevelsOfGenerators)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "LevelsOfGenerators: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LevelsOfGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsWreathProductOrdering",
+                    "Tester(IsWreathProductOrdering)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LevelsOfGenerators): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LevelsOfGenerators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LevelsOfGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdering",
+                    "IsWreathProductOrdering",
+                    "Tester(IsWreathProductOrdering)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LevelsOfGenerators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Transformation: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Transformation: for a list and list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Transformation: for a list and function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Transformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TransformationListList: for a list and list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformationListList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransformationList: for a list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformationList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsDenseList",
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                [
+                    "IsDenseList",
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TransformationByImageAndKernel: for a list of positive integers and a list of positive integers",
+                    "filters": [
+                        [
+                            "IsDenseList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "IsDenseList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 58
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformationByImageAndKernel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsZeroCyc"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NumberTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "NumberTransformation: for a transformation and zero",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "NumberTransformation: for a transformation and positive integer",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumberTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TransformationNumber: for a positive integer and positive integer",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformationNumber",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LargestImageOfMovedPoint: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LargestImageOfMovedPoint)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "LargestImageOfMovedPoint: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "LargestImageOfMovedPoint: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "LargestImageOfMovedPoint: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "LargestImageOfMovedPoint: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "LargestImageOfMovedPoint: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "LargestImageOfMovedPoint: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LargestImageOfMovedPoint",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LargestImageOfMovedPoint): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LargestImageOfMovedPoint): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LargestImageOfMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LargestImageOfMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SmallestImageOfMovedPoint: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SmallestImageOfMovedPoint)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "SmallestImageOfMovedPoint: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "SmallestImageOfMovedPoint: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "SmallestImageOfMovedPoint: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "SmallestImageOfMovedPoint: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "SmallestImageOfMovedPoint: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "SmallestImageOfMovedPoint: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SmallestImageOfMovedPoint",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SmallestImageOfMovedPoint): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SmallestImageOfMovedPoint): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SmallestImageOfMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SmallestImageOfMovedPoint)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsZeroCyc"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RankOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "RankOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "RankOfTransformation: for a transformation and zero",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "RankOfTransformation: for a transformation and pos int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "RankOfTransformation: for a transformation and dense list",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RankOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RankOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RankOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RankOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RankOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsBinaryRelation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsBinaryRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsPermutation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsPermutation)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "AsPermutation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "AsPermutation: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AsPermutation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsPermutation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsPermutation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsPermutation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsPermutation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsPermutation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsTransformation)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "AsTransformation: for binary relations on points",
+                    "filters": [
+                        [
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsBinaryRelationOnPointsRep"
+                        ]
+                    ],
+                    "rank": 12
+                },
+                {
+                    "comment": "AsTransformation: for a permutation",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AsTransformation: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AsTransformation: for relation over [1..n]",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AsTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "AsTransformation: for a partial perm and positive integer",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "AsTransformation: for a permutation and positive integer",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "AsTransformation: for a transformation and degree",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PermutationOfImage: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PermutationOfImage)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "PermutationOfImage: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermutationOfImage",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PermutationOfImage): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PermutationOfImage): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PermutationOfImage)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PermutationOfImage)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConstantTransformation: for a pos int and pos int",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConstantTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOfTransformationCollection: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOfTransformationCollection)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "DegreeOfTransformationCollection: for a transformation collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOfTransformationCollection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOfTransformationCollection): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOfTransformationCollection): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOfTransformationCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsTransformation)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOfTransformationCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsZeroCyc"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FlatKernelOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FlatKernelOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "FlatKernelOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "FlatKernelOfTransformation: for a transformation and zero",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "FlatKernelOfTransformation: for a transformation and pos int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FlatKernelOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FlatKernelOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FlatKernelOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FlatKernelOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FlatKernelOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsZeroCyc"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImageListOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ImageListOfTransformation: for a transformation and zero",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImageListOfTransformation: for a transformation and pos int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImageListOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsZeroCyc"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImageSetOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImageSetOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ImageSetOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ImageSetOfTransformation: for a transformation and zero",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "ImageSetOfTransformation: for a transformation and pos int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImageSetOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImageSetOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImageSetOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImageSetOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImageSetOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndexPeriodOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndexPeriodOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IndexPeriodOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndexPeriodOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndexPeriodOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndexPeriodOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndexPeriodOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndexPeriodOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsInjectiveListTrans: for a list and trans",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsInjectiveListTrans: for a list and list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInjectiveListTrans",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsBool"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsZeroCyc"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KernelOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KernelOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "KernelOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "KernelOfTransformation: for a transformation and pos int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "KernelOfTransformation: for a transformation and pos int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "KernelOfTransformation: for a transformation, positive integer and boolean",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KernelOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KernelOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KernelOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KernelOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KernelOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PermLeftQuoTransformationNC: for a transformation and transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermLeftQuoTransformationNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PermLeftQuoTransformation: for a transformation and transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermLeftQuoTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PreImagesOfTransformation: for a transformation and positive integer",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImagesOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RandomTransformation: for a pos. int.",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "RandomTransformation: for pos int and pos int",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RandomTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedTransformationNC: for a transformation and list",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedTransformationNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedTransformation: for transformation and list",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SmallestIdempotentPower: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SmallestIdempotentPower)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "SmallestIdempotentPower: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "SmallestIdempotentPower: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SmallestIdempotentPower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SmallestIdempotentPower): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SmallestIdempotentPower): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SmallestIdempotentPower)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SmallestIdempotentPower)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TrimTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "TrimTransformation: for a transformation and pos int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TrimTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                [
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Idempotent: for a list of pos ints and list of pos ints",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ],
+                        [
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Idempotent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TransformationOp: for an obj and domain",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "TransformationOp: for an obj and list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "TransformationOp: for an obj, domain, and function",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "TransformationOp: for object, list, function",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformationOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TransformationOpNC: for object and domain",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "TransformationOpNC: for object and list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "TransformationOpNC: for object, domain, function",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "TransformationOpNC: for object, list, function",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformationOpNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComponentRepsOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComponentRepsOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ComponentRepsOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComponentRepsOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComponentRepsOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComponentRepsOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComponentRepsOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComponentRepsOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrComponentsOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrComponentsOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "NrComponentsOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrComponentsOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrComponentsOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrComponentsOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrComponentsOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrComponentsOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComponentsOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComponentsOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ComponentsOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComponentsOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComponentsOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComponentsOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComponentsOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComponentsOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ComponentTransformationInt: for a transformation and positive integer",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComponentTransformationInt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CycleTransformationInt: for a transformation and positive integer",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CycleTransformationInt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ],
+            [
+                [
+                    "IsTransformation"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CyclesOfTransformation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CyclesOfTransformation)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "CyclesOfTransformation: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CyclesOfTransformation: for a transformation and list",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CyclesOfTransformation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CyclesOfTransformation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CyclesOfTransformation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CyclesOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CyclesOfTransformation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeftOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LeftOne)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "LeftOne: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "LeftOne: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LeftOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LeftOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LeftOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LeftOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RightOne: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RightOne)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "RightOne: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "RightOne: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightOne",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RightOne): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RightOne): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RightOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RightOne)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsTransformation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "OnKernelAntiAction: for a list and transformation",
+                    "filters": [
+                        [
+                            "IsDenseList",
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OnKernelAntiAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DomainOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DomainOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "DomainOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DomainOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DomainOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DomainOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DomainOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DomainOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImageListOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImageListOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ImageListOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImageListOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImageListOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImageListOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImageListOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImageListOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImageSetOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImageSetOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ImageSetOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImageSetOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImageSetOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImageSetOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImageSetOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImageSetOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IndexPeriodOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IndexPeriodOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IndexPeriodOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndexPeriodOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IndexPeriodOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IndexPeriodOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IndexPeriodOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IndexPeriodOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComponentRepsOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComponentRepsOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ComponentRepsOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComponentRepsOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComponentRepsOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComponentRepsOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComponentRepsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComponentRepsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrComponentsOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrComponentsOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "NrComponentsOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrComponentsOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrComponentsOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrComponentsOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrComponentsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrComponentsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComponentsOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComponentsOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "ComponentsOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComponentsOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComponentsOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComponentsOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComponentsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComponentsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FixedPointsOfPartialPerm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FixedPointsOfPartialPerm)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "FixedPointsOfPartialPerm: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "FixedPointsOfPartialPerm: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "FixedPointsOfPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FixedPointsOfPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FixedPointsOfPartialPerm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FixedPointsOfPartialPerm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FixedPointsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FixedPointsOfPartialPerm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrFixedPoints: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrFixedPoints)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "NrFixedPoints: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "NrFixedPoints: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "NrFixedPoints: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrFixedPoints",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrFixedPoints): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrFixedPoints): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrFixedPoints)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrFixedPoints)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PreImagePartialPerm: for a partial perm and positive integer",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImagePartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ComponentPartialPermInt: for a partial perm and positive integer",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComponentPartialPermInt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsAssociativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsAssociativeElement"
+                ],
+                [
+                    "IsZeroCyc"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsPartialPerm: for a perm",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "AsPartialPerm: for a transformation",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "AsPartialPerm: for a perm and zero",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 29
+                },
+                {
+                    "comment": "AsPartialPerm: for a perm and pos int",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "AsPartialPerm: for a transformation and positive int",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "AsPartialPerm: for a perm and a list",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 10
+                },
+                {
+                    "comment": "AsPartialPerm: for a transformation and list",
+                    "filters": [
+                        [
+                            "IsTransformation"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PermLeftQuoPartialPermNC: for a partial perm and partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ],
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermLeftQuoPartialPermNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ],
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PermLeftQuoPartialPerm: for a partial perm and partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ],
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermLeftQuoPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPartialPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TrimPartialPerm: for a partial perm",
+                    "filters": [
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TrimPartialPerm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PartialPermOp: for an obj and domain",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PartialPermOp: for an obj and list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PartialPermOp: for an obj, domain, and function",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PartialPermOp: for object, list, function",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PartialPermOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ]
+            ],
+            [
+                [],
+                [
+                    "IsCollection",
+                    "IsGeneralizedDomain"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PartialPermOpNC: for an obj and domain",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "PartialPermOpNC: for an obj and list",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PartialPermOpNC: for an obj, domain, and function",
+                    "filters": [
+                        [],
+                        [
+                            "IsCollection",
+                            "IsGeneralizedDomain"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "PartialPermOpNC: for object, list, function",
+                    "filters": [
+                        [],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PartialPermOpNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOfPartialPermCollection: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOfPartialPermCollection)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "DegreeOfPartialPermCollection: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "DegreeOfPartialPermCollection: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOfPartialPermCollection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOfPartialPermCollection): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOfPartialPermCollection): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CodegreeOfPartialPermCollection: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CodegreeOfPartialPermCollection)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "CodegreeOfPartialPermCollection: for a partial perm semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "CodegreeOfPartialPermCollection: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CodegreeOfPartialPermCollection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CodegreeOfPartialPermCollection): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CodegreeOfPartialPermCollection): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CodegreeOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CodegreeOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankOfPartialPermCollection: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RankOfPartialPermCollection)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "RankOfPartialPermCollection: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "RankOfPartialPermCollection: for a partial perm collection",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RankOfPartialPermCollection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RankOfPartialPermCollection): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RankOfPartialPermCollection): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RankOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RankOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DomainOfPartialPermCollection: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DomainOfPartialPermCollection)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "DomainOfPartialPermCollection: for a partal perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "DomainOfPartialPermCollection: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DomainOfPartialPermCollection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DomainOfPartialPermCollection): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DomainOfPartialPermCollection): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DomainOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DomainOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImageOfPartialPermCollection: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImageOfPartialPermCollection)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "ImageOfPartialPermCollection: for a partal perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ImageOfPartialPermCollection: for a partial perm coll",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImageOfPartialPermCollection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImageOfPartialPermCollection): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImageOfPartialPermCollection): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImageOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImageOfPartialPermCollection)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransformationRepresentation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransformationRepresentation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "TransformationRepresentation: for an endo general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsTransformationRepOfEndo"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "TransformationRepresentation: for an endo general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsEndoGeneralMapping",
+                            "Tester(IsEndoGeneralMapping)",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "TransformationRepresentation: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformationRepresentation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransformationRepresentation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransformationRepresentation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransformationRepresentation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsEndoGeneralMapping",
+                    "Tester(IsEndoGeneralMapping)",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransformationRepresentation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FpSemigroupOfElementOfFpSemigroup: for an element of an fp semigroup",
+                    "filters": [
+                        [
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FpSemigroupOfElementOfFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpSemigroup)"
+                ],
+                [
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ElementOfFpSemigroup: for a family of f.p. semigroup elements, and an assoc. word",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementOfFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGeneratorsOfFpSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGeneratorsOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpSemigroup: for a finitely presented semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGeneratorsOfFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGeneratorsOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGeneratorsOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeSemigroupOfFpSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeSemigroupOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "FreeSemigroupOfFpSemigroup: for a finitely presented semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "FreeSemigroupOfFpSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeSemigroupOfFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeSemigroupOfFpSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeSemigroupOfFpSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeSemigroupOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeSemigroupOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelationsOfFpSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelationsOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "RelationsOfFpSemigroup: method for a free semigroup",
+                    "filters": [
+                        [
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "RelationsOfFpSemigroup: for finitely presented semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "RelationsOfFpSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelationsOfFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelationsOfFpSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelationsOfFpSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelationsOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelationsOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismFpSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismFpSemigroup: for fp groups",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsomorphismFpSemigroup: for an fp monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsomorphismFpSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismFpSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismFpSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FpGrpMonSmgOfFpGrpMonSmgElement: for an element of an fp group",
+                    "filters": [
+                        [
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "FpGrpMonSmgOfFpGrpMonSmgElement: for an element of an fp monoid",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "FpGrpMonSmgOfFpGrpMonSmgElement: for an element of an fp semigroup",
+                    "filters": [
+                        [
+                            "IsElementOfFpSemigroup"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FpGrpMonSmgOfFpGrpMonSmgElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryFamily(IsElementOfFpMonoid)"
+                ],
+                [
+                    "IsMultiplicativeElementWithOne",
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ElementOfFpMonoid: for a family of f.p. monoid elements, and an assoc. word",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpMonoid)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithOne",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ElementOfFpMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpMonoid"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FpMonoidOfElementOfFpMonoid: for an fp monoid element",
+                    "filters": [
+                        [
+                            "IsElementOfFpMonoid"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FpMonoidOfElementOfFpMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGeneratorsOfFpMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGeneratorsOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpMonoid: for a finitely presented monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "FreeGeneratorsOfFpMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": -4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGeneratorsOfFpMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGeneratorsOfFpMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGeneratorsOfFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGeneratorsOfFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeMonoidOfFpMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeMonoidOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "FreeMonoidOfFpMonoid: for a finitely presented monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "FreeMonoidOfFpMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": -4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeMonoidOfFpMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeMonoidOfFpMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeMonoidOfFpMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeMonoidOfFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeMonoidOfFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelationsOfFpMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelationsOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 20026
+                },
+                {
+                    "comment": "RelationsOfFpMonoid: method for a free monoid",
+                    "filters": [
+                        [
+                            "IsFreeMonoid",
+                            "Tester(IsFreeMonoid)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "RelationsOfFpMonoid: for finitely presented monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "RelationsOfFpMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": -4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelationsOfFpMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelationsOfFpMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelationsOfFpMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelationsOfFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpMonoid)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelationsOfFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismFpMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismFpMonoid)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "IsomorphismFpMonoid: for an fp group",
+                    "filters": [
+                        [
+                            "IsGroupOfFamily",
+                            "IsSubgroupFpGroup"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsomorphismFpMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismFpMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismFpMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismFpMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismFpMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReducedConfluentRewritingSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ReducedConfluentRewritingSystem)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "ReducedConfluentRewritingSystem: for an fp monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "ReducedConfluentRewritingSystem: for an fp semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "ReducedConfluentRewritingSystem: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ReducedConfluentRewritingSystem: for an fp monoid and an ordering on the underlying free monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ],
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "ReducedConfluentRewritingSystem: for an fp semigroup and an order on the underlying free semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "ReducedConfluentRewritingSystem: for an fp semigroup and an ordering on the underlying free semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedConfluentRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ReducedConfluentRewritingSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ReducedConfluentRewritingSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ReducedConfluentRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ReducedConfluentRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeMonoidOfRewritingSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeMonoidOfRewritingSystem)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FreeMonoidOfRewritingSystem: for a monoid rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromMonoid",
+                            "Tester(IsBuiltFromMonoid)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeMonoidOfRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeMonoidOfRewritingSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeMonoidOfRewritingSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeMonoidOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeMonoidOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FamilyForRewritingSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FamilyForRewritingSystem)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FamilyForRewritingSystem: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FamilyForRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FamilyForRewritingSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FamilyForRewritingSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FamilyForRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FamilyForRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeSemigroupOfRewritingSystem: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeSemigroupOfRewritingSystem)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FreeSemigroupOfRewritingSystem: for a semigroup rewriting system",
+                    "filters": [
+                        [
+                            "IsRewritingSystem",
+                            "IsBuiltFromSemigroup",
+                            "Tester(IsBuiltFromSemigroup)"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeSemigroupOfRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeSemigroupOfRewritingSystem): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeSemigroupOfRewritingSystem): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeSemigroupOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeSemigroupOfRewritingSystem)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                [
+                    "IsOrdering"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KnuthBendixRewritingSystem: for an fp monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "KnuthBendixRewritingSystem: for an fp semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "KnuthBendixRewritingSystem: for an fp monoid and a function",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "KnuthBendixRewritingSystem: for an fp monoid and an order on the family of words of the underlying free monoid",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpMonoid)"
+                        ],
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "KnuthBendixRewritingSystem: for an fp semigroup and a function",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "KnuthBendixRewritingSystem: for an fp semigroup and an order on the family of words of the underlying free semigroup",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "KnuthBendixRewritingSystem: for a family of words of an fp monoid and on ordering on that family",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpMonoid)"
+                        ],
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "KnuthBendixRewritingSystem: for a family of words of an fp semigroup and on ordering on that family",
+                    "filters": [
+                        [
+                            "CategoryFamily(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsOrdering"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnuthBendixRewritingSystem",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsKnuthBendixRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TzRules: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TzRules)"
+                        ]
+                    ],
+                    "rank": 20006
+                },
+                {
+                    "comment": "TzRules: for a Knuth Bendix rewriting system",
+                    "filters": [
+                        [
+                            "IsKnuthBendixRewritingSystem",
+                            "IsKnuthBendixRewritingSystemRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TzRules",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsKnuthBendixRewritingSystem"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TzRules): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TzRules): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TzRules)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsKnuthBendixRewritingSystem"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TzRules)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CosetTableOfFpSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CosetTableOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "CosetTableOfFpSemigroup: for a right congruence on an fp semigroup",
+                    "filters": [
+                        [
+                            "IsRightMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CosetTableOfFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CosetTableOfFpSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CosetTableOfFpSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CosetTableOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CosetTableOfFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdjoinedIdentityFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdjoinedIdentityFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AdjoinedIdentityFamily",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdjoinedIdentityFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdjoinedIdentityFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdjoinedIdentityFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdjoinedIdentityFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdjoinedIdentityFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingSemigroupFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingSemigroupFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingSemigroupFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingSemigroupFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingSemigroupFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingSemigroupFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingSemigroupFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AdjoinedIdentityDefaultType: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AdjoinedIdentityDefaultType)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AdjoinedIdentityDefaultType",
+                    "filters": [
+                        [
+                            "IsFamily"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AdjoinedIdentityDefaultType",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AdjoinedIdentityDefaultType): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AdjoinedIdentityDefaultType): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AdjoinedIdentityDefaultType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AdjoinedIdentityDefaultType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MonoidByAdjoiningIdentity: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MonoidByAdjoiningIdentity)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "MonoidByAdjoiningIdentity",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MonoidByAdjoiningIdentity",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "MonoidByAdjoiningIdentity",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "MonoidByAdjoiningIdentity: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MonoidByAdjoiningIdentity",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MonoidByAdjoiningIdentity): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MonoidByAdjoiningIdentity): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MonoidByAdjoiningIdentity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MonoidByAdjoiningIdentity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonoidByAdjoiningIdentity"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingSemigroupOfMonoidByAdjoiningIdentity: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)"
+                        ]
+                    ],
+                    "rank": 20021
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingSemigroupOfMonoidByAdjoiningIdentity",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonoidByAdjoiningIdentity"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingSemigroupOfMonoidByAdjoiningIdentity): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingSemigroupOfMonoidByAdjoiningIdentity): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonoidByAdjoiningIdentity"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement",
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MonoidByAdjoiningIdentityElt: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MonoidByAdjoiningIdentityElt)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "MonoidByAdjoiningIdentityElt",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement",
+                            "IsAssociativeElement"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MonoidByAdjoiningIdentityElt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement",
+                    "IsAssociativeElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MonoidByAdjoiningIdentityElt): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MonoidByAdjoiningIdentityElt): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MonoidByAdjoiningIdentityElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement",
+                    "IsAssociativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MonoidByAdjoiningIdentityElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonoidByAdjoiningIdentityElt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt",
+                    "filters": [
+                        [
+                            "IsMonoidByAdjoiningIdentityElt"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonoidByAdjoiningIdentityElt"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMonoidByAdjoiningIdentityElt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRelation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFiniteSemigroupGreensRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFiniteSemigroupGreensRelation)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFiniteSemigroupGreensRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRelation"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFiniteSemigroupGreensRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFiniteSemigroupGreensRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFiniteSemigroupGreensRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRelation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFiniteSemigroupGreensRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensRRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensRRelation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensRRelation: for free semigroups",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "GreensRRelation: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensRRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensRRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensRRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensRRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensRRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensRRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensLRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensLRelation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensLRelation: for free semigroups",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "GreensLRelation: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensLRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensLRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensLRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensLRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensLRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensLRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensJRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensJRelation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensJRelation: for free semigroups",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "GreensJRelation: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensJRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensJRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensJRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensJRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensJRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensJRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensDRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensDRelation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensDRelation: for free semigroups",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "GreensDRelation: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensDRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensDRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensDRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensDRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensDRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensDRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensHRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensHRelation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensHRelation: for free semigroups",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFreeSemigroup",
+                            "Tester(IsFreeSemigroup)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "GreensHRelation: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensHRelation: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensHRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensHRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensHRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensHRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensHRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GreensRClassOfElement: for a semigroup and object",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensRClassOfElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GreensLClassOfElement: for a semigroup and object",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensLClassOfElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GreensDClassOfElement: for a semigroup and object",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensDClassOfElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GreensJClassOfElement: for a semigroup and object",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensJClassOfElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GreensHClassOfElement: for a semigroup and object",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensHClassOfElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithOne",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FroidurePinSimpleAlg: for a finite monoid",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FroidurePinSimpleAlg",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FroidurePinExtendedAlg: for a finite semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FroidurePinExtendedAlg",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AssociatedConcreteSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AssociatedConcreteSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "AssociatedConcreteSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AssociatedConcreteSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AssociatedConcreteSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AssociatedConcreteSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AssociatedConcreteSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWholeFamily",
+                    "Tester(IsWholeFamily)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsElementOfFpSemigroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AssociatedConcreteSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AssociatedFpSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AssociatedFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "AssociatedFpSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AssociatedFpSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AssociatedFpSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AssociatedFpSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AssociatedFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AssociatedFpSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensRClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensRClasses)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensRClasses: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensRClasses: for a Green's D-class",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "GreensRClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensRClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGreensDClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensRClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensRClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensRClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensRClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensLClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensLClasses)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensLClasses: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensLClasses: for a Green's D-class",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "GreensLClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensLClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGreensDClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensLClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensLClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensLClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensLClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensJClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensJClasses)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensJClasses: for a semigroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "GreensJClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensJClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensJClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensJClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensJClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensJClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensDClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensDClasses)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensDClasses: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensDClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensDClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensDClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensDClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensDClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensDClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsGreensClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GreensHClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GreensHClasses)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GreensHClasses: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "GreensHClasses: for a Green's Class",
+                    "filters": [
+                        [
+                            "IsGreensLClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "GreensHClasses: for a Green's Class",
+                    "filters": [
+                        [
+                            "IsGreensRClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "GreensHClasses: for a Green's Class",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "GreensHClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GreensHClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGreensClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GreensHClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GreensHClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GreensHClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GreensHClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensClass"
+                ],
+                [
+                    "IsGreensClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsGreensLessThanOrEqual: for two Green's classes",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ],
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGreensLessThanOrEqual",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RClassOfHClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RClassOfHClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "RClassOfHClass: for a Green's H-class",
+                    "filters": [
+                        [
+                            "IsGreensHClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RClassOfHClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RClassOfHClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RClassOfHClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RClassOfHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RClassOfHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LClassOfHClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LClassOfHClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "LClassOfHClass: for a Green's H-class",
+                    "filters": [
+                        [
+                            "IsGreensHClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LClassOfHClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LClassOfHClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LClassOfHClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LClassOfHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LClassOfHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DClassOfHClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DClassOfHClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "DClassOfHClass: for a Green's H-class",
+                    "filters": [
+                        [
+                            "IsGreensHClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DClassOfHClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DClassOfHClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DClassOfHClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DClassOfHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DClassOfHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensLClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DClassOfLClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DClassOfLClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "DClassOfLClass: for a Green's L-class",
+                    "filters": [
+                        [
+                            "IsGreensLClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DClassOfLClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensLClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DClassOfLClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DClassOfLClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DClassOfLClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensLClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DClassOfLClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DClassOfRClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DClassOfRClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "DClassOfRClass: for a Green's R-class",
+                    "filters": [
+                        [
+                            "IsGreensRClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DClassOfRClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DClassOfRClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DClassOfRClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DClassOfRClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DClassOfRClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupHClassOfGreensDClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GroupHClassOfGreensDClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "GroupHClassOfGreensDClass: for a Green's H-class",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupHClassOfGreensDClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GroupHClassOfGreensDClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GroupHClassOfGreensDClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GroupHClassOfGreensDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GroupHClassOfGreensDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRegularDClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRegularDClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "IsRegularDClass: for a Green's D class",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRegularDClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRegularDClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRegularDClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRegularDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRegularDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupHClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupHClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "IsGroupHClass: for Green's H-class",
+                    "filters": [
+                        [
+                            "IsGreensHClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupHClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupHClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupHClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensHClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupHClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EggBoxOfDClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EggBoxOfDClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "EggBoxOfDClass: for a Green's D class",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EggBoxOfDClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EggBoxOfDClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EggBoxOfDClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EggBoxOfDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EggBoxOfDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRelation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InternalRepGreensRelation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InternalRepGreensRelation)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InternalRepGreensRelation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRelation"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InternalRepGreensRelation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InternalRepGreensRelation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InternalRepGreensRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensRelation"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InternalRepGreensRelation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CanonicalGreensClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CanonicalGreensClass)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "CanonicalGreensClass: for a Green's class",
+                    "filters": [
+                        [
+                            "IsGreensClass"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CanonicalGreensClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CanonicalGreensClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CanonicalGreensClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CanonicalGreensClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CanonicalGreensClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DisplayEggBoxesOfSemigroup: for finite semigroups",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DisplayEggBoxesOfSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SemigroupHomomorphismByImagesNC: for a semigroup, semigroup, list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemigroupHomomorphismByImagesNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFpSemigpReducedElt: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFpSemigpReducedElt)"
+                        ]
+                    ],
+                    "rank": 20008
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFpSemigpReducedElt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpSemigroup"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFpSemigpReducedElt): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFpSemigpReducedElt): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFpSemigpReducedElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFpSemigpReducedElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpMonoid"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFpMonoidReducedElt: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFpMonoidReducedElt)"
+                        ]
+                    ],
+                    "rank": 20009
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFpMonoidReducedElt",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpMonoid"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFpMonoidReducedElt): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFpMonoidReducedElt): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFpMonoidReducedElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfFpMonoid"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFpMonoidReducedElt)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFullTransformationSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFullTransformationSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsFullTransformationSemigroup: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsFullTransformationSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsFullTransformationSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFullTransformationSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFullTransformationSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFullTransformationSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFullTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFullTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsTransformation)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOfTransformationSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOfTransformationSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "DegreeOfTransformationSemigroup: for a transformation group with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "DegreeOfTransformationSemigroup: for a transformation semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "DegreeOfTransformationSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOfTransformationSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsTransformation)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOfTransformationSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOfTransformationSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOfTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsTransformation)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOfTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismTransformationSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismTransformationSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for a perm group with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for a semigroup of general mappings",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsGeneralMapping)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: <fp-semigroup>",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for a semigroup with multiplicative neutral element and generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MultiplicativeNeutralElement)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for a semigroup with multiplicative neutral element",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MultiplicativeNeutralElement)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for a semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsomorphismTransformationSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismTransformationSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismTransformationSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismTransformationSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismTransformationMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismTransformationMonoid)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismTransformationMonoid: for a perm group with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IsomorphismTransformationMonoid: for partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsomorphismTransformationMonoid: for a semigroup with multiplicative neutral element and generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MultiplicativeNeutralElement)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsomorphismTransformationMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismTransformationMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismTransformationMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismTransformationMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismTransformationMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismTransformationMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsRightMagmaCongruence"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HomomorphismTransformationSemigroup: for an f.p. semigroup, and a right congruence",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsElementOfFpSemigroup)"
+                        ],
+                        [
+                            "IsRightMagmaCongruence"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HomomorphismTransformationSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AntiIsomorphismTransformationSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AntiIsomorphismTransformationSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "AntiIsomorphismTransformationSemigroup: for a semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "AntiIsomorphismTransformationSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AntiIsomorphismTransformationSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AntiIsomorphismTransformationSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AntiIsomorphismTransformationSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AntiIsomorphismTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AntiIsomorphismTransformationSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsReesMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RowOfReesMatrixSemigroupElement: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RowOfReesMatrixSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsReesZeroMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RowOfReesZeroMatrixSemigroupElement: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RowOfReesZeroMatrixSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsReesMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ColumnOfReesMatrixSemigroupElement: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ColumnOfReesMatrixSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsReesZeroMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ColumnOfReesZeroMatrixSemigroupElement: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ColumnOfReesZeroMatrixSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsReesMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingElementOfReesMatrixSemigroupElement: for a Rees matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingElementOfReesMatrixSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsReesZeroMatrixSemigroupElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingElementOfReesZeroMatrixSemigroupElement: for a Rees 0-matrix semigroup element",
+                    "filters": [
+                        [
+                            "IsReesZeroMatrixSemigroupElement"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingElementOfReesZeroMatrixSemigroupElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsReesMatrixSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsReesMatrixSemigroup: for a Rees matrix subsemigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsReesMatrixSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsReesMatrixSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsReesMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsReesMatrixSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsReesMatrixSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsReesMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsReesMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsReesZeroMatrixSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsReesZeroMatrixSemigroup: for a Rees 0-matrix subsemigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IsReesZeroMatrixSemigroup: for a semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsReesZeroMatrixSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsReesZeroMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsReesZeroMatrixSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsReesZeroMatrixSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsReesZeroMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsReesZeroMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsRectangularTable",
+                    "Tester(IsRectangularTable)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReesMatrixSemigroup: for a semigroup and a rectangular table",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRectangularTable",
+                            "Tester(IsRectangularTable)"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReesMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReesZeroMatrixSemigroup: for a semigroup and a dense list",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReesZeroMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "GeneratorsOfReesMatrixSemigroup: for a Rees matrix subsemigroup, rows, semigroup, columns",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfReesMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ReesMatrixSubsemigroup: for a Rees matrix semigroup, rows, semigroup, columns",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReesMatrixSubsemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "GeneratorsOfReesZeroMatrixSemigroup: for a Rees 0-matrix semigroup, rows, semigroup, columns",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsOfReesZeroMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ReesZeroMatrixSubsemigroup: for a Rees 0-matrix semigroup, rows, semigroup, columns",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReesZeroMatrixSubsemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Matrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Matrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Matrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Matrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Rows: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Rows)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "Rows: for a Rees 0-matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Rows: for a Rees matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Rows: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Rows",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Rows): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Rows): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Rows)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Rows)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Columns: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Columns)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "Columns: for a Rees 0-matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Columns: for a Rees matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Columns: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Columns",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Columns): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Columns): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Columns)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Columns)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingSemigroup)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "UnderlyingSemigroup: for a Rees 0-matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "UnderlyingSemigroup: for a Rees matrix semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "UnderlyingSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AssociatedReesMatrixSemigroupOfDClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AssociatedReesMatrixSemigroupOfDClass)"
+                        ]
+                    ],
+                    "rank": 20011
+                },
+                {
+                    "comment": "AssociatedReesMatrixSemigroupOfDClass: for a Green's D-class of a semigroup",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AssociatedReesMatrixSemigroupOfDClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AssociatedReesMatrixSemigroupOfDClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AssociatedReesMatrixSemigroupOfDClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AssociatedReesMatrixSemigroupOfDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AssociatedReesMatrixSemigroupOfDClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsGreensDClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismReesMatrixSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismReesMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismReesMatrixSemigroup: for a Rees matrix subsemigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsomorphismReesMatrixSemigroup: for a finite simple",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsomorphismReesMatrixSemigroup: for a D-class",
+                    "filters": [
+                        [
+                            "IsGreensDClass"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IsomorphismReesMatrixSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismReesMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGreensDClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismReesMatrixSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismReesMatrixSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismReesMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismReesMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismReesZeroMatrixSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismReesZeroMatrixSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismReesZeroMatrixSemigroup: for a Rees 0-matrix subsemigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IsomorphismReesZeroMatrixSemigroup: for a finite 0-simple",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsomorphismReesZeroMatrixSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismReesZeroMatrixSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismReesZeroMatrixSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismReesZeroMatrixSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismReesZeroMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismReesZeroMatrixSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReesMatrixSemigroupOfFamily: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ReesMatrixSemigroupOfFamily)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReesMatrixSemigroupOfFamily",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ReesMatrixSemigroupOfFamily): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ReesMatrixSemigroupOfFamily): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ReesMatrixSemigroupOfFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ReesMatrixSemigroupOfFamily)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TypeReesMatrixSemigroupElements: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TypeReesMatrixSemigroupElements)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "TypeReesMatrixSemigroupElements: for a subsemigroup of Rees 0-matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "TypeReesMatrixSemigroupElements: for a subsemigroup of Rees matrix semigroup",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "TypeReesMatrixSemigroupElements: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "CategoryCollections(IsReesMatrixSemigroupElement)"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TypeReesMatrixSemigroupElements",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TypeReesMatrixSemigroupElements): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TypeReesMatrixSemigroupElements): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TypeReesMatrixSemigroupElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsReesMatrixSemigroupElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TypeReesMatrixSemigroupElements)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "QuotientSemigroupPreimage: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(QuotientSemigroupPreimage)"
+                        ]
+                    ],
+                    "rank": 20017
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuotientSemigroupPreimage",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(QuotientSemigroupPreimage): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(QuotientSemigroupPreimage): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(QuotientSemigroupPreimage)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(QuotientSemigroupPreimage)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "QuotientSemigroupCongruence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(QuotientSemigroupCongruence)"
+                        ]
+                    ],
+                    "rank": 20017
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuotientSemigroupCongruence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(QuotientSemigroupCongruence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(QuotientSemigroupCongruence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(QuotientSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(QuotientSemigroupCongruence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "QuotientSemigroupHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(QuotientSemigroupHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20017
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "QuotientSemigroupHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(QuotientSemigroupHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(QuotientSemigroupHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(QuotientSemigroupHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsQuotientSemigroup"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(QuotientSemigroupHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOfPartialPermSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOfPartialPermSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "DegreeOfPartialPermSemigroup: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "DegreeOfPartialPermSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOfPartialPermSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOfPartialPermSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOfPartialPermSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOfPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOfPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CodegreeOfPartialPermSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CodegreeOfPartialPermSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "CodegreeOfPartialPermSemigroup: for an inverse partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsInverseSemigroup",
+                            "Tester(IsInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "CodegreeOfPartialPermSemigroup: for a partial perm semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "CodegreeOfPartialPermSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CodegreeOfPartialPermSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CodegreeOfPartialPermSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CodegreeOfPartialPermSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CodegreeOfPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CodegreeOfPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankOfPartialPermSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RankOfPartialPermSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "RankOfPartialPermSemigroup: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "RankOfPartialPermSemigroup: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "RankOfPartialPermSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RankOfPartialPermSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RankOfPartialPermSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RankOfPartialPermSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RankOfPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RankOfPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSymmetricInverseSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSymmetricInverseSemigroup)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "IsSymmetricInverseSemigroup: for a partial perm semigroup with generators",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "IsSymmetricInverseSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": -5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSymmetricInverseSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSymmetricInverseSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSymmetricInverseSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSymmetricInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPartialPerm)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSymmetricInverseSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SymmetricInverseSemigroup: for a integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SymmetricInverseSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismPartialPermSemigroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismPartialPermSemigroup)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismPartialPermSemigroup: for a perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsomorphismPartialPermSemigroup: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsomorphismPartialPermSemigroup: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsomorphismPartialPermSemigroup: for a semigroup with generators",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IsomorphismPartialPermSemigroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismPartialPermSemigroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismPartialPermSemigroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismPartialPermSemigroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismPartialPermSemigroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismPartialPermMonoid: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismPartialPermMonoid)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsomorphismPartialPermMonoid: for a perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsomorphismPartialPermMonoid: for a partial perm monoid",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagmaWithOne",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "IsomorphismPartialPermMonoid: for a partial perm semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPartialPerm)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "IsomorphismPartialPermMonoid: for a transformation semigroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsTransformation)",
+                            "IsMagma",
+                            "Tester(GeneratorsOfMagma)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsomorphismPartialPermMonoid: for a monoid with generators",
+                    "filters": [
+                        [
+                            "IsMagmaWithOne",
+                            "Tester(GeneratorsOfMagmaWithOne)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsomorphismPartialPermMonoid: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismPartialPermMonoid",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismPartialPermMonoid): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismPartialPermMonoid): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismPartialPermMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismPartialPermMonoid)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ],
+            [
+                [
+                    "IsLieAlgebraOfGroupRing",
+                    "Tester(IsLieAlgebraOfGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingGroup)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "UnderlyingGroup: LAGUNA: for a Lie algebra of a group ring",
+                    "filters": [
+                        [
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "UnderlyingGroup",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "UnderlyingGroup: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsLieAlgebraOfGroupRing",
+                    "Tester(IsLieAlgebraOfGroupRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdentificationOfConjugacyClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdentificationOfConjugacyClasses)"
+                        ]
+                    ],
+                    "rank": 20025
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdentificationOfConjugacyClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdentificationOfConjugacyClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdentificationOfConjugacyClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdentificationOfConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdentificationOfConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsOrdinaryTable"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CompatibleConjugacyClasses: one argument version, call `CompatibleConjugacyClassesDefault'",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CompatibleConjugacyClasses: two argument version, call `CompatibleConjugacyClassesDefault'",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CompatibleConjugacyClasses: three argument version, call `CompatibleConjugacyClassesDefault'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "CompatibleConjugacyClasses: four argument version, call `CompatibleConjugacyClassesDefault'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 58
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CompatibleConjugacyClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacterDegrees: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CharacterDegrees)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "CharacterDegrees: handled by nice monomorphism: Attribute",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 368
+                },
+                {
+                    "comment": "CharacterDegrees: for a group (call the two-argument version)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "CharacterDegrees: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "CharacterDegrees: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CharacterDegrees: for an abelian group, and an integer p (just strip off the p-part)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 80
+                },
+                {
+                    "comment": "CharacterDegrees: for a solvable group and an integer (Conlon's algorithm)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "CharacterDegrees: for a group, and zero",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "CharacterDegrees: for a group, and positive integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterDegrees",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CharacterDegrees): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CharacterDegrees): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CharacterDegrees)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CharacterDegrees)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Irr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Irr)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Irr: for a group (call the two-argument version)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Irr: for an ord. char. table with known group (delegate to the group)",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "Tester(UnderlyingGroup)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "Irr: for a <p>-solvable Brauer table (use the Fong-Swan Theorem)",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Irr: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Irr: partial method for a group, and zero",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 10054
+                },
+                {
+                    "comment": "Irr: via niceomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 389
+                },
+                {
+                    "comment": "Irr: ordinary characters for natural symmetric group",
+                    "filters": [
+                        [
+                            "IsNaturalSymmetricGroup",
+                            "Tester(IsNaturalSymmetricGroup)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 83
+                },
+                {
+                    "comment": "Irr: for a supersolvable group with known `IrrBaumClausen'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSupersolvableGroup",
+                            "Tester(IsSupersolvableGroup)",
+                            "Tester(IrrBaumClausen)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Irr: for a supersolvable group with known `IrrConlon'",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSupersolvableGroup",
+                            "Tester(IsSupersolvableGroup)",
+                            "Tester(IrrConlon)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "Irr: for a supersolvable group (Baum-Clausen algorithm)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSupersolvableGroup",
+                            "Tester(IsSupersolvableGroup)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Irr: for a supersolvable group (Conlon's algorithm)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSupersolvableGroup",
+                            "Tester(IsSupersolvableGroup)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Irr: Dixon/Schneider",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "Irr: for a group, and a prime",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Irr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Irr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Irr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Irr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Irr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LinearCharacters: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LinearCharacters)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "LinearCharacters: for a group (call the two-argument version)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LinearCharacters: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "LinearCharacters: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "LinearCharacters: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "LinearCharacters: for a group, and zero",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "LinearCharacters: for a group, and positive integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LinearCharacters",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LinearCharacters): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LinearCharacters): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LinearCharacters)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LinearCharacters)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBrauerTable"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IBr: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IBr)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "IBr: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IBr: for a group, and a prime integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IBr",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBrauerTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IBr): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IBr): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IBr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBrauerTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IBr)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrdinaryCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrdinaryCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "OrdinaryCharacterTable: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "OrdinaryCharacterTable: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrdinaryCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrdinaryCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrdinaryCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrdinaryCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrdinaryCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAlmostSimpleCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAlmostSimpleCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsAlmostSimpleCharacterTable: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAlmostSimpleCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAlmostSimpleCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAlmostSimpleCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAlmostSimpleCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAlmostSimpleCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonomialCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMonomialCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsMonomialCharacterTable: for an ordinary character table with underlying group",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "Tester(UnderlyingGroup)"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonomialCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMonomialCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMonomialCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMonomialCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMonomialCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpotentCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNilpotentCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsNilpotentCharacterTable: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotentCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNilpotentCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNilpotentCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNilpotentCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNilpotentCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPerfectCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPerfectCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsPerfectCharacterTable: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPerfectCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPerfectCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPerfectCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPerfectCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPerfectCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSimpleCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSimpleCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsSimpleCharacterTable: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSimpleCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSimpleCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSimpleCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSimpleCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSimpleCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSolvableCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSolvableCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsSolvableCharacterTable: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSolvableCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSolvableCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSolvableCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSolvableCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSolvableCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSporadicSimpleCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSporadicSimpleCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsSporadicSimpleCharacterTable: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSporadicSimpleCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSporadicSimpleCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSporadicSimpleCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSporadicSimpleCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSporadicSimpleCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSupersolvableCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSupersolvableCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsSupersolvableCharacterTable: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSupersolvableCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSupersolvableCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSupersolvableCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSupersolvableCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSupersolvableCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrdersClassRepresentatives: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrdersClassRepresentatives)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "OrdersClassRepresentatives: for a character table with known group",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable",
+                            "Tester(UnderlyingGroup)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "OrdersClassRepresentatives: for a Brauer character table (delegate to the ordinary table)",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "OrdersClassRepresentatives: for a character table, use known power maps",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrdersClassRepresentatives",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrdersClassRepresentatives): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrdersClassRepresentatives): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrdersClassRepresentatives)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrdersClassRepresentatives)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SizesCentralizers: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SizesCentralizers)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "SizesCentralizers: for a Brauer character table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "SizesCentralizers: for a character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SizesCentralizers",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SizesCentralizers): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SizesCentralizers): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SizesCentralizers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SizesCentralizers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SizesConjugacyClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SizesConjugacyClasses)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "SizesConjugacyClasses: for a Brauer character table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "SizesConjugacyClasses: for a character table ",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SizesConjugacyClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SizesConjugacyClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SizesConjugacyClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SizesConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SizesConjugacyClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AutomorphismsOfTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AutomorphismsOfTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "AutomorphismsOfTable: for a Brauer table in the case of good reduction",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "AutomorphismsOfTable: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AutomorphismsOfTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AutomorphismsOfTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AutomorphismsOfTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AutomorphismsOfTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AutomorphismsOfTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingCharacteristic: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingCharacteristic)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingCharacteristic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingCharacteristic): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingCharacteristic): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingCharacteristic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingCharacteristic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassNames: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassNames)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "ClassNames",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ClassNames",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassNames",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassNames): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassNames): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacterNames: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CharacterNames)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "CharacterNames",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterNames",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CharacterNames): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CharacterNames): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CharacterNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CharacterNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassParameters: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassParameters)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassParameters",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassParameters): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassParameters): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassParameters)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassParameters)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacterParameters: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CharacterParameters)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterParameters",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CharacterParameters): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CharacterParameters): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CharacterParameters)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CharacterParameters)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Identifier: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Identifier)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "Identifier: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "Identifier: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Identifier",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Identifier): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Identifier): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Identifier)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Identifier)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InverseClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InverseClasses)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "InverseClasses: for a character table with known irreducibles",
+                    "filters": [
+                        [
+                            "IsCharacterTable",
+                            "Tester(Irr)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "InverseClasses: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InverseClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InverseClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InverseClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InverseClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InverseClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RealClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RealClasses)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "RealClasses: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RealClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RealClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RealClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RealClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RealClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClassOrbit: for a character table, and a positive integer",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassOrbit",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassRoots: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassRoots)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "ClassRoots: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassRoots",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassRoots): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassRoots): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfNormalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfNormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfNormalSubgroups: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfNormalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfNormalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfMaximalNormalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfMaximalNormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfMaximalNormalSubgroups: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfMaximalNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfMaximalNormalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfMaximalNormalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfMaximalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfMaximalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfMinimalNormalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfMinimalNormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfMinimalNormalSubgroups: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfMinimalNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfMinimalNormalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfMinimalNormalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfMinimalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfMinimalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClassPositionsOfAgemo: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfAgemo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ],
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfCentre: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfCentre)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfCentre: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "ClassPositionsOfCentre: for a homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfCentre",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfCentre): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfCentre): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfCentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfCentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfDirectProductDecompositions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfDirectProductDecompositions)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfDirectProductDecompositions: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ClassPositionsOfDirectProductDecompositions: for an ordinary table, and a list of positive integers",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfDirectProductDecompositions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfDirectProductDecompositions): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfDirectProductDecompositions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfDirectProductDecompositions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfDirectProductDecompositions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfDerivedSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfDerivedSubgroup)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfDerivedSubgroup: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfDerivedSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfDerivedSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfDerivedSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfDerivedSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfDerivedSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfElementaryAbelianSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfElementaryAbelianSeries)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfElementaryAbelianSeries: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfElementaryAbelianSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfElementaryAbelianSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfElementaryAbelianSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfElementaryAbelianSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfFittingSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfFittingSubgroup)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfFittingSubgroup: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfFittingSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfFittingSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfFittingSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfFittingSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfFittingSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfSolvableRadical: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfSolvableRadical)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfSolvableRadical: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfSolvableRadical",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfSolvableRadical): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfSolvableRadical): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfSolvableRadical)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfSolvableRadical)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfLowerCentralSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfLowerCentralSeries)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfLowerCentralSeries: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfLowerCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfLowerCentralSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfLowerCentralSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfLowerCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfLowerCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfUpperCentralSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfUpperCentralSeries)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfUpperCentralSeries: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfUpperCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfUpperCentralSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfUpperCentralSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfUpperCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfUpperCentralSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfSolvableResiduum: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfSolvableResiduum)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfSolvableResiduum: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfSolvableResiduum",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfSolvableResiduum): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfSolvableResiduum): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfSolvableResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfSolvableResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfSupersolvableResiduum: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfSupersolvableResiduum)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ClassPositionsOfSupersolvableResiduum: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfSupersolvableResiduum",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfSupersolvableResiduum): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfSupersolvableResiduum): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfSupersolvableResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfSupersolvableResiduum)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClassPositionsOfPCore: for an ordinary table and a pos. integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfPCore",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList",
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClassPositionsOfNormalClosure: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfNormalClosure",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PrimeBlocks: for an ordinary table, and a positive integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimeBlocks",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PrimeBlocksOp: for an ordinary table, and a positive integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimeBlocksOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedPrimeBlockss: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedPrimeBlockss)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ComputedPrimeBlockss: for an ordinary table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedPrimeBlockss",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedPrimeBlockss): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedPrimeBlockss): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedPrimeBlockss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedPrimeBlockss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BlocksInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BlocksInfo)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "BlocksInfo: generic method for a Brauer character table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BlocksInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BlocksInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BlocksInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BlocksInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BlocksInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBrauerTable"
+                ]
+            ],
+            [
+                [
+                    "IsBrauerTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DecompositionMatrix: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DecompositionMatrix)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "DecompositionMatrix: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DecompositionMatrix: for a Brauer table, and a positive integer",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DecompositionMatrix",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBrauerTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DecompositionMatrix): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DecompositionMatrix): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DecompositionMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBrauerTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DecompositionMatrix)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPSolvableCharacterTable: for ord. char. table knowing `IsSolvableCharacterTable', and zero",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "Tester(IsSolvableCharacterTable)"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsPSolvableCharacterTable: for ord. char. table, and zero (call `IsPSolvableCharacterTableOp')",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsPSolvableCharacterTable: for ord.char.table, and pos.int. (call `IsPSolvableCharacterTableOp')",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPSolvableCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPSolvableCharacterTableOp: for an ordinary character table, an an integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPSolvableCharacterTableOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedIsPSolvableCharacterTables: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedIsPSolvableCharacterTables)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ComputedIsPSolvableCharacterTables: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedIsPSolvableCharacterTables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedIsPSolvableCharacterTables): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedIsPSolvableCharacterTables): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedIsPSolvableCharacterTables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedIsPSolvableCharacterTables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Indicator: for a character table, and a positive integer",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Indicator: for a character table, a homogeneous list, and a positive integer",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Indicator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IndicatorOp: for a Brauer character table and <n> = 2",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IndicatorOp: for an ord. character table, a hom. list, and a pos. integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IndicatorOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedIndicators: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedIndicators)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "ComputedIndicators: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedIndicators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedIndicators): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedIndicators): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedIndicators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedIndicators)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacterTable: [ IsGroup and HasTableOfMarks ]",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(TableOfMarks)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "CharacterTable: for a group (delegate to `OrdinaryCharacterTable')",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "CharacterTable: for a string",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "CharacterTable: [ IsTableOfMarks ]",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CharacterTable: for a group, and a prime integer",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "CharacterTable: for an ordinary table, and a prime integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "CharacterTable: for a string and an object",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        []
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CharacterTable: for a string and two objects",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BrauerTable: for a group, and a prime (delegate to the ord. table of the group)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "BrauerTable: for an ordinary table, and a prime",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BrauerTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsSpinSymTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BrauerTableOp: [ IsOrdinaryTable and IsLibraryCharacterTableRep, IsPosInt ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "IsLibraryCharacterTableRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 10044
+                },
+                {
+                    "comment": "BrauerTableOp: for an ordinary character table created by SpinSymCharacterTableOfMaximalYoungSubgroup() and a positive rational prime",
+                    "filters": [
+                        [
+                            "IsSpinSymTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "BrauerTableOp: for ordinary character table, and positive integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BrauerTableOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedBrauerTables: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedBrauerTables)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "ComputedBrauerTables: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedBrauerTables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedBrauerTables): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedBrauerTables): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedBrauerTables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedBrauerTables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DisplayOptions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DisplayOptions)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DisplayOptions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DisplayOptions): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DisplayOptions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DisplayOptions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DisplayOptions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CharacterTableDirectProduct: for two Brauer character tables",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CharacterTableDirectProduct: for one ordinary and one Brauer character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CharacterTableDirectProduct: for one Brauer table, and one ordinary character table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CharacterTableDirectProduct: for two ordinary character tables",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterTableDirectProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FactorsOfDirectProduct: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FactorsOfDirectProduct)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorsOfDirectProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FactorsOfDirectProduct): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FactorsOfDirectProduct): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FactorsOfDirectProduct)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FactorsOfDirectProduct)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CharacterTableFactorGroup: for a Brauer table, and a list of class positions",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "CharacterTableFactorGroup: for an ordinary table, and a list of class positions",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterTableFactorGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections(IsCyclotomic)"
+                ],
+                [
+                    "IsList",
+                    "CategoryCollections(IsCyclotomic)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacterTableIsoclinic: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CharacterTableIsoclinic)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "CharacterTableIsoclinic: for a Brauer table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "CharacterTableIsoclinic: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CharacterTableIsoclinic: for a Brauer table and a list of classes",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "CharacterTableIsoclinic: for an ordinary character table and a list of classes",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "CharacterTableIsoclinic: for a Brauer table and an ordinary table",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "CharacterTableIsoclinic: for a Brauer table and a class pos.",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "CharacterTableIsoclinic: for an ordinary character table and a class pos.",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CharacterTableIsoclinic: for a Brauer table and two lists of class positions",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "CharacterTableIsoclinic: for an ordinary character table and two lists of class positions",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 22
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterTableIsoclinic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CharacterTableIsoclinic): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CharacterTableIsoclinic): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CharacterTableIsoclinic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CharacterTableIsoclinic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SourceOfIsoclinicTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SourceOfIsoclinicTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SourceOfIsoclinicTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SourceOfIsoclinicTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SourceOfIsoclinicTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SourceOfIsoclinicTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SourceOfIsoclinicTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacterTableWithSortedCharacters: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CharacterTableWithSortedCharacters: for an ordinary character table, and a permutation",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterTableWithSortedCharacters",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SortedCharacters: for a character table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SortedCharacters: for a character table, a homogeneous list, and a string",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SortedCharacters",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsString"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacterTableWithSortedClasses: for a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CharacterTableWithSortedClasses: for an ordinary character table, and a permutation",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "CharacterTableWithSortedClasses: for a character table, and string",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacterTableWithSortedClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPermutation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPermutation)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPermutation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPermutation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPermutation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPermutation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPermutation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalSubgroupClassesInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalSubgroupClassesInfo)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "NormalSubgroupClassesInfo: default method, initialization",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalSubgroupClassesInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalSubgroupClassesInfo): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalSubgroupClassesInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalSubgroupClassesInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalSubgroupClassesInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20034
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ValuesOfClassFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ValuesOfClassFunction)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "ValuesOfClassFunction: for a dense list",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ValuesOfClassFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ValuesOfClassFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ValuesOfClassFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ValuesOfClassFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ValuesOfClassFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GlobalPartitionOfClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GlobalPartitionOfClasses)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "GlobalPartitionOfClasses: for an ordinary character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GlobalPartitionOfClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GlobalPartitionOfClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GlobalPartitionOfClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GlobalPartitionOfClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GlobalPartitionOfClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CorrespondingPermutations: for character table and list of group elements",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CorrespondingPermutations: for a char. table, a hom. list, and a list of group elements",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CorrespondingPermutations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsDenseList"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ClassFunction: for a group, and a dense list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "ClassFunction: for nearly character table, and dense list",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsDenseList"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "VirtualCharacter: for a group, and a dense list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "VirtualCharacter: for nearly character table, and dense list",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "VirtualCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsDenseList"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsDenseList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Character: for a group, and a dense list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "Character: for nearly character table, and dense list",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Character",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TrivialCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TrivialCharacter)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "TrivialCharacter: for a group (delegate to the table)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TrivialCharacter: for a character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TrivialCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TrivialCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TrivialCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TrivialCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TrivialCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalCharacter)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "NaturalCharacter: for a permutation group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "NaturalCharacter: for a matrix group in characteristic zero",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "NaturalCharacter: for a group general mapping",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "NaturalCharacter: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsCollection"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PermutationCharacter: for two groups (use double cosets)",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PermutationCharacter: group action on domain",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsCollection"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 36
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermutationCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsCharacter: for a virtual character",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsVirtualCharacter",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsCharacter: for a Brauer table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IsCharacter: for an ordinary character table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsVirtualCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsVirtualCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsVirtualCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsVirtualCharacter: for an ordinary character table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsVirtualCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsVirtualCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsVirtualCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsVirtualCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsVirtualCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIrreducibleCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIrreducibleCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsIrreducibleCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsIrreducibleCharacter: for a Brauer table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IsIrreducibleCharacter: for an ordinary character table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIrreducibleCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIrreducibleCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIrreducibleCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIrreducibleCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIrreducibleCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MatScalarProducts: for a homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MatScalarProducts: for an ordinary table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "MatScalarProducts: for two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "MatScalarProducts: for an ordinary table, and two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MatScalarProducts",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentreOfCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CentreOfCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "CentreOfCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CentreOfCharacter: for an ordinary table, and a homogeneous list ",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentreOfCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CentreOfCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CentreOfCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CentreOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CentreOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConstituentsOfCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConstituentsOfCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "ConstituentsOfCharacter: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction",
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ConstituentsOfCharacter",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ConstituentsOfCharacter: for a Brauer table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ConstituentsOfCharacter: for an ordinary table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConstituentsOfCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConstituentsOfCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConstituentsOfCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConstituentsOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConstituentsOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DegreeOfCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DegreeOfCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "DegreeOfCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DegreeOfCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DegreeOfCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DegreeOfCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DegreeOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DegreeOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InertiaSubgroup: for a group, and a class function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "InertiaSubgroup: for an ordinary table, a group, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 59
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InertiaSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KernelOfCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KernelOfCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "KernelOfCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "KernelOfCharacter: for an ordinary table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KernelOfCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KernelOfCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KernelOfCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KernelOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KernelOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassPositionsOfKernel: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassPositionsOfKernel)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "ClassPositionsOfKernel: for a homogeneous list",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassPositionsOfKernel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassPositionsOfKernel): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassPositionsOfKernel): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassPositionsOfKernel)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassPositionsOfKernel)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CycleStructureClass: for a class function, and a class position",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "CycleStructureClass: for an ordinary table, a list, and a class position",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CycleStructureClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentralCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CentralCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "CentralCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CentralCharacter: for an ordinary table, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CentralCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CentralCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CentralCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CentralCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DeterminantOfCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DeterminantOfCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "DeterminantOfCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DeterminantOfCharacter: for a nearly character table, and a class function",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 25
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeterminantOfCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DeterminantOfCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DeterminantOfCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DeterminantOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DeterminantOfCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EigenvaluesChar: for a class function and a positive integer",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 50
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "EigenvaluesChar: for a character table and a hom. list, and a pos.",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EigenvaluesChar",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Tensored: method for two homogeneous lists",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tensored",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedClassFunction: for a class function, and a group",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "RestrictedClassFunction: for class function and nearly character table",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "RestrictedClassFunction: for a class function and a group homomorphism",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "RestrictedClassFunction: for a character table, a homogeneous list, and a group",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "RestrictedClassFunction: for a character table, a homogeneous list, and a character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "RestrictedClassFunction: for a character table, a homogeneous list, and a group homomorphism",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedClassFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RestrictedClassFunctions: for list and group",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "RestrictedClassFunctions: for list and character table",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "RestrictedClassFunctions: for list and group homomorphism",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "RestrictedClassFunctions: for a character table, a list, and a group",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "RestrictedClassFunctions: for a character table, a list, and a character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "RestrictedClassFunctions: for a character table, a list, and a group homomorphism",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RestrictedClassFunctions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ],
+            [
+                [],
+                [],
+                []
+            ],
+            [
+                [],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 24
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 72
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "Restricted",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        []
+                    ],
+                    "rank": 70
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Restricted",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedClassFunction: for a class function and a group",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "InducedClassFunction: for class function and nearly character table",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "InducedClassFunction: for a class function and a group homomorphism",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "InducedClassFunction: for a character table, a homogeneous list, and a group",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "InducedClassFunction: for character table, homogeneous list, and nearly character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "InducedClassFunction: for a character table, a homogeneous list, and a group homomorphism",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedClassFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InducedClassFunctions: for list, and group",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "InducedClassFunctions: for list, and group homomorphism",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "InducedClassFunctions: for list, and group homomorphism",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "InducedClassFunctions: for a character table, a homogeneous list, and a group",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "InducedClassFunctions: for character table, homogeneous list, and nearly character table",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "InducedClassFunctions: for a character table, a homogeneous list, and a group homomorphism",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedClassFunctions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ],
+            [
+                [],
+                [],
+                []
+            ],
+            [
+                [],
+                [],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 37
+                },
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "Induced: for two nearly character tables, and homog list",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Induced",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [
+                {
+                    "comment": "Induced: for two nearly character tables and two homog. lists",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "CategoryCollections(IsCyclotomic)"
+                        ]
+                    ],
+                    "rank": 73
+                },
+                {
+                    "comment": "Induced: for two nearly character tables, homog list, and string",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Induced",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InducedCyclic: for a character table",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "InducedCyclic: for a character table and a string",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "InducedCyclic: for a character table and a hom. list",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "InducedCyclic: for a character table, a hom. list, and a string",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InducedCyclic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ReducedClassFunctions: for a list (of class functions)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ReducedClassFunctions: for ordinary character table, and list of class functions",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ReducedClassFunctions: for two lists (of class functions)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ReducedClassFunctions: for ordinary character table, and two lists (of class functions)",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedClassFunctions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ReducedCharacters: for two lists (of characters)",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ReducedCharacters: for ordinary character table, and two lists of characters",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ReducedCharacters",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Symmetrizations: for homogeneous list (of class functions) and character table",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Symmetrizations: for homogeneous list (of class functions) and positive integer",
+                    "filters": [
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Symmetrizations: for char. table, homog. list (of class functions), and table of Sn",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "Symmetrizations: for char. table, homog. list (of class functions), and pos. integer",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "Symmetrizations: for char. table, homog. list (of class functions), and record",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Symmetrizations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BrauerCharacterValue: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BrauerCharacterValue)"
+                        ]
+                    ],
+                    "rank": 20033
+                },
+                {
+                    "comment": "BrauerCharacterValue: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BrauerCharacterValue",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BrauerCharacterValue): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BrauerCharacterValue): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BrauerCharacterValue)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BrauerCharacterValue)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PowerMap: for a character table, and an integer",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PowerMap: for a character table, and two integers",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 56
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PowerMap",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PowerMapOp: for character table and zero",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsZeroCyc"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "PowerMapOp: for ordinary table with group, and positive integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "Tester(UnderlyingGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "PowerMapOp: for ordinary table, and positive integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "PowerMapOp: for Brauer table and integer",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "PowerMapOp: for character table and negative integer",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsNegRat"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PowerMapOp: for Brauer table, integer, positive integer",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "PowerMapOp: for ordinary table, integer, positive integer",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 59
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PowerMapOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedPowerMaps: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedPowerMaps)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "ComputedPowerMaps: for a nearly character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedPowerMaps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedPowerMaps): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedPowerMaps): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedPowerMaps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedPowerMaps)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsInt"
+                ]
+            ],
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PossiblePowerMaps: for a Brauer character table and a prime",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "PossiblePowerMaps: for an ordinary character table and a prime (add empty options record)",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PossiblePowerMaps: for a Brauer character table, a prime, and a record",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "PossiblePowerMaps: for an ordinary character table, a prime, and a record",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PossiblePowerMaps",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FusionConjugacyClasses: for a group homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "FusionConjugacyClasses: for two groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "FusionConjugacyClasses: for two nearly character tables",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "FusionConjugacyClasses: for a group homomorphism, and two nearly character tables",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FusionConjugacyClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FusionConjugacyClassesOp: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FusionConjugacyClassesOp)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "FusionConjugacyClassesOp: for a group homomorphism",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "FusionConjugacyClassesOp: for two ordinary tables with groups",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "Tester(UnderlyingGroup)"
+                        ],
+                        [
+                            "IsOrdinaryTable",
+                            "Tester(UnderlyingGroup)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "FusionConjugacyClassesOp: for two Brauer tables",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "FusionConjugacyClassesOp: for two ordinary tables",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "FusionConjugacyClassesOp: for a group homomorphism, and two character tables",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FusionConjugacyClassesOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FusionConjugacyClassesOp): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FusionConjugacyClassesOp): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FusionConjugacyClassesOp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FusionConjugacyClassesOp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedClassFusions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedClassFusions)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "ComputedClassFusions: for a nearly character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedClassFusions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedClassFusions): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedClassFusions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedClassFusions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedClassFusions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NamesOfFusionSources: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NamesOfFusionSources)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "NamesOfFusionSources: for a nearly character table",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NamesOfFusionSources",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NamesOfFusionSources): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NamesOfFusionSources): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NamesOfFusionSources)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NamesOfFusionSources)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PossibleClassFusions: for two Brauer tables",
+                    "filters": [
+                        [
+                            "IsBrauerTable"
+                        ],
+                        [
+                            "IsBrauerTable"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "PossibleClassFusions: for two ordinary character tables",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PossibleClassFusions: for two ordinary character tables, and a parameters record",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PossibleClassFusions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ],
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MatrixAutomorphisms: for a matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "MatrixAutomorphisms: for matrix, list of maps, and subgroup",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 90
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MatrixAutomorphisms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsString"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TableAutomorphisms: for a character table and a list of characters",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "TableAutomorphisms: for a character table, a list of characters, and a perm. group",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "TableAutomorphisms: for a character table, a list of characters, and a string",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 28
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TableAutomorphisms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TransformingPermutations: for two matrices",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformingPermutations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TransformingPermutationsCharacterTables: for two character tables",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 42
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransformingPermutationsCharacterTables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BaumClausenInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BaumClausenInfo)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "BaumClausenInfo: for a (solvable) group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "BaumClausenInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BaumClausenInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BaumClausenInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BaumClausenInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BaumClausenInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BaumClausenInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFinite",
+                    "Tester(IsFinite)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsFinite",
+                    "Tester(IsFinite)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IrreducibleRepresentations: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IrreducibleRepresentations)"
+                        ]
+                    ],
+                    "rank": 20044
+                },
+                {
+                    "comment": "IrreducibleRepresentations: (abelian by supersolvable) finite group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IrreducibleRepresentations: Dixon's method",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IrreducibleRepresentations: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IrreducibleRepresentations: finite group, Cyclotomics",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 102
+                },
+                {
+                    "comment": "IrreducibleRepresentations: for a finite group over a finite field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 98
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IrreducibleRepresentations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFinite",
+                    "Tester(IsFinite)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IrreducibleRepresentations): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IrreducibleRepresentations): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IrreducibleRepresentations)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFinite",
+                    "Tester(IsFinite)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IrreducibleRepresentations)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IrrBaumClausen: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IrrBaumClausen)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IrrBaumClausen: for a (solvable) group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IrrBaumClausen: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IrrBaumClausen",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IrrBaumClausen): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IrrBaumClausen): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IrrBaumClausen)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IrrBaumClausen)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IrrConlon: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IrrConlon)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IrrConlon: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IrrConlon: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IrrConlon",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IrrConlon): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IrrConlon): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IrrConlon)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IrrConlon)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Inequalities",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Inequalities",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        []
+                    ],
+                    "rank": 24
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Inequalities",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MolienSeriesInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MolienSeriesInfo)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MolienSeriesInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MolienSeriesInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MolienSeriesInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MolienSeriesInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MolienSeriesInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Alpha: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Alpha)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Alpha: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Alpha: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Alpha",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Alpha): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Alpha): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Alpha)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Alpha)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ],
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Delta: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Delta)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "Delta: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Delta: for unions of residue classes of Z with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesOfZWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Delta: for residue class unions of Z (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZ"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Delta: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Delta",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsResidueClassUnion"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Delta): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Delta): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Delta)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Delta)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBergerCondition: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBergerCondition)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsBergerCondition: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsBergerCondition: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsBergerCondition: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBergerCondition",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBergerCondition): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBergerCondition): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBergerCondition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBergerCondition)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrimitiveCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPrimitiveCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsPrimitiveCharacter: for a class function",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimitiveCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPrimitiveCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPrimitiveCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPrimitiveCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPrimitiveCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TestQuasiPrimitive: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TestQuasiPrimitive)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "TestQuasiPrimitive: for a character",
+                    "filters": [
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TestQuasiPrimitive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TestQuasiPrimitive): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TestQuasiPrimitive): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TestQuasiPrimitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TestQuasiPrimitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsQuasiPrimitive: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsQuasiPrimitive)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsQuasiPrimitive: for a character",
+                    "filters": [
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsQuasiPrimitive",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsQuasiPrimitive): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsQuasiPrimitive): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsQuasiPrimitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsQuasiPrimitive)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsInducedFromNormalSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsInducedFromNormalSubgroup)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsInducedFromNormalSubgroup: for a character",
+                    "filters": [
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsInducedFromNormalSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsInducedFromNormalSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsInducedFromNormalSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsInducedFromNormalSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsInducedFromNormalSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonomialCharacter: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMonomialCharacter)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsMonomialCharacter: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonomialCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMonomialCharacter): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMonomialCharacter): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMonomialCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMonomialCharacter)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonomialNumber: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMonomialNumber)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "IsMonomialNumber: for a positive integer",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonomialNumber",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMonomialNumber): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMonomialNumber): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMonomialNumber)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMonomialNumber)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TestMonomialQuick: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TestMonomialQuick)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "TestMonomialQuick: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TestMonomialQuick: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TestMonomialQuick",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TestMonomialQuick): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TestMonomialQuick): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TestMonomialQuick)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TestMonomialQuick)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TestMonomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TestMonomial)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "TestMonomial: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TestMonomial: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "TestMonomial: for a group, and a Boolean",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "TestMonomial: for a character, and a Boolean",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TestMonomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TestMonomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TestMonomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TestMonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TestMonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TestSubnormallyMonomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TestSubnormallyMonomial)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "TestSubnormallyMonomial: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TestSubnormallyMonomial: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "TestSubnormallyMonomial: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TestSubnormallyMonomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TestSubnormallyMonomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TestSubnormallyMonomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TestSubnormallyMonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TestSubnormallyMonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSubnormallyMonomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSubnormallyMonomial)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsSubnormallyMonomial: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSubnormallyMonomial: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsSubnormallyMonomial: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubnormallyMonomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSubnormallyMonomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSubnormallyMonomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSubnormallyMonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSubnormallyMonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TestRelativelySM: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TestRelativelySM)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "TestRelativelySM: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TestRelativelySM: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "TestRelativelySM: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "TestRelativelySM: for a group, and an object",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        []
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TestRelativelySM: for a character, and an object",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 31
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TestRelativelySM",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsClassFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TestRelativelySM): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TestRelativelySM): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TestRelativelySM)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TestRelativelySM)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsRelativelySM: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsRelativelySM)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsRelativelySM: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsRelativelySM: for a character",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsRelativelySM",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsRelativelySM): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsRelativelySM): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsRelativelySM)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClassFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsRelativelySM)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMinimalNonmonomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMinimalNonmonomial)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IsMinimalNonmonomial: for a (solvable) group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsMinimalNonmonomial: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMinimalNonmonomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMinimalNonmonomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMinimalNonmonomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMinimalNonmonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMinimalNonmonomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DixonRecord: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DixonRecord)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "DixonRecord: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DixonRecord: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DixonRecord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DixonRecord): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DixonRecord): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DixonRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DixonRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DxPreparation: perm",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "DxPreparation: pc group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "DxPreparation: abelian",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "DxPreparation: generic",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DxPreparation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IrrDixonSchneider: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IrrDixonSchneider)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "IrrDixonSchneider: Dixon/Schneider",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IrrDixonSchneider: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IrrDixonSchneider: Dixon/Schneider",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IrrDixonSchneider",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IrrDixonSchneider): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IrrDixonSchneider): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IrrDixonSchneider)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IrrDixonSchneider)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ],
+            [
+                [
+                    "IsTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TableOfMarks: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TableOfMarks)"
+                        ]
+                    ],
+                    "rank": 20035
+                },
+                {
+                    "comment": "TableOfMarks: [ IsGroup and HasOrdinaryCharacterTable ]",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(OrdinaryCharacterTable)"
+                        ]
+                    ],
+                    "rank": 134
+                },
+                {
+                    "comment": "TableOfMarks: for a group with lattice",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(LatticeSubgroups)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "TableOfMarks: for a cyclic group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCyclic",
+                            "Tester(IsCyclic)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "TableOfMarks: for solvable groups (call `LatticeSubgroups' and use the lattice)",
+                    "filters": [
+                        [
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "TableOfMarks: cyclic extension method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "TableOfMarks: [ IsOrdinaryTable and IsLibraryCharacterTableRep ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "IsLibraryCharacterTableRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "TableOfMarks: [ IsCharacterTable and HasUnderlyingGroup ]",
+                    "filters": [
+                        [
+                            "IsCharacterTable",
+                            "Tester(UnderlyingGroup)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "TableOfMarks: for a matrix or a lower triangular matrix",
+                    "filters": [
+                        [
+                            "IsTable"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "TableOfMarks: for a string (dispatch to `TableOfMarksFromLibrary')",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "TableOfMarks: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TableOfMarks",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsString"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TableOfMarks): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TableOfMarks): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TableOfMarks)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TableOfMarks)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsPerm"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SortedTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 9
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SortedTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PermutationTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PermutationTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermutationTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PermutationTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PermutationTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PermutationTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PermutationTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MarksTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MarksTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MarksTom: for a table of marks with known `NrSubsTom' and `OrdersTom'",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "Tester(NrSubsTom)",
+                            "Tester(OrdersTom)"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MarksTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MarksTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MarksTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MarksTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MarksTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SubsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SubsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SubsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SubsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SubsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SubsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrSubsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrSubsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "NrSubsTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrSubsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrSubsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrSubsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrSubsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrSubsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrdersTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrdersTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "OrdersTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrdersTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrdersTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrdersTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrdersTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrdersTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LengthsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LengthsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "LengthsTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LengthsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LengthsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LengthsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LengthsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LengthsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassTypesTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassTypesTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "ClassTypesTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassTypesTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassTypesTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassTypesTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassTypesTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassTypesTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ClassNamesTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ClassNamesTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "ClassNamesTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ClassNamesTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ClassNamesTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ClassNamesTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ClassNamesTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ClassNamesTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FusionsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FusionsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "FusionsTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FusionsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FusionsTom): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FusionsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FusionsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FusionsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdempotentsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdempotentsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IdempotentsTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdempotentsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdempotentsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdempotentsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdempotentsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdempotentsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdempotentsTomInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdempotentsTomInfo)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IdempotentsTomInfo: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdempotentsTomInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdempotentsTomInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdempotentsTomInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdempotentsTomInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdempotentsTomInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MatTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MatTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MatTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MatTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MatTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MatTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MatTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MatTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MoebiusTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MoebiusTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MoebiusTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MoebiusTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MoebiusTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MoebiusTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MoebiusTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MoebiusTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WeightsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WeightsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "WeightsTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeightsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WeightsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WeightsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WeightsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WeightsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAbelianTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAbelianTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsAbelianTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsAbelianTom: for a table of marks with known der. subgroups, and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "Tester(DerivedSubgroupsTomUnique)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 1021
+                },
+                {
+                    "comment": "IsAbelianTom: for a table of marks and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsAbelianTom: for a table of marks with generators, and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "IsTableOfMarksWithGens"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAbelianTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAbelianTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAbelianTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAbelianTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAbelianTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsCyclicTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsCyclicTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsCyclicTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsCyclicTom: for a table of marks and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCyclicTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsCyclicTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsCyclicTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsCyclicTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsCyclicTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpotentTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNilpotentTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsNilpotentTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsNilpotentTom: for a table of marks and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotentTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNilpotentTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNilpotentTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNilpotentTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNilpotentTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPerfectTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPerfectTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsPerfectTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsPerfectTom: for a table of marks with known der. subgroups, and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "Tester(DerivedSubgroupsTomUnique)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IsPerfectTom: for a table of marks and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPerfectTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPerfectTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPerfectTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPerfectTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPerfectTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSolvableTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSolvableTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "IsSolvableTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsSolvableTom: for a table of marks and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSolvableTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSolvableTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSolvableTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSolvableTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSolvableTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DerivedSubgroupTom: for a table of marks, and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DerivedSubgroupTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DerivedSubgroupsTomPossible: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DerivedSubgroupsTomPossible)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "DerivedSubgroupsTomPossible: for a table of marks (initialize with empty list)",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DerivedSubgroupsTomPossible",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DerivedSubgroupsTomPossible): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DerivedSubgroupsTomPossible): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DerivedSubgroupsTomPossible)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DerivedSubgroupsTomPossible)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DerivedSubgroupsTomUnique: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DerivedSubgroupsTomUnique)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DerivedSubgroupsTomUnique",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DerivedSubgroupsTomUnique): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DerivedSubgroupsTomUnique): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DerivedSubgroupsTomUnique)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DerivedSubgroupsTomUnique)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalizerTom: for a table of marks, and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizersTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizersTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "NormalizersTom: all normalizers of a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizersTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizersTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizersTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizersTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizersTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ContainedTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ContainedTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ContainingTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ContainingTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CyclicExtensionsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CyclicExtensionsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "CyclicExtensionsTom: for a table of marks (classes for all prime div. of the group order)",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "CyclicExtensionsTom: for a table of marks, and a prime",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "CyclicExtensionsTom: for a table of marks, and a list (of primes)",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CyclicExtensionsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CyclicExtensionsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CyclicExtensionsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CyclicExtensionsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CyclicExtensionsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedCyclicExtensionsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedCyclicExtensionsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "ComputedCyclicExtensionsTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedCyclicExtensionsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedCyclicExtensionsTom): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedCyclicExtensionsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedCyclicExtensionsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedCyclicExtensionsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CyclicExtensionsTomOp: for one prime",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "CyclicExtensionsTomOp: for a table of marks, and a list (of primes)",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CyclicExtensionsTomOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DecomposedFixedPointVector",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DecomposedFixedPointVector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "EulerianFunctionByTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "EulerianFunctionByTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EulerianFunctionByTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "IntersectionsTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntersectionsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FactorGroupTom: for a table of marks, and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorGroupTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalSubgroupsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalSubgroupsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "MaximalSubgroupsTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MaximalSubgroupsTom: for a table of marks, and a positive integer",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalSubgroupsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalSubgroupsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalSubgroupsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalSubgroupsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalSubgroupsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MinimalSupergroupsTom: for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalSupergroupsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GeneratorsSubgroupsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GeneratorsSubgroupsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "GeneratorsSubgroupsTom: default method for a table of marks",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GeneratorsSubgroupsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GeneratorsSubgroupsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GeneratorsSubgroupsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GeneratorsSubgroupsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GeneratorsSubgroupsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StraightLineProgramsTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StraightLineProgramsTom)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StraightLineProgramsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StraightLineProgramsTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StraightLineProgramsTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StraightLineProgramsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StraightLineProgramsTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RepresentativeTom: for a table of marks with stored `StraightLineProgramsTom' value",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "Tester(StraightLineProgramsTom)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "RepresentativeTom: for a table of marks with stored `GeneratorsSubgroupsTom' value",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "Tester(GeneratorsSubgroupsTom)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativeTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "Tester(StraightLineProgramsTom)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "RepresentativeTomByGenerators",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "Tester(StraightLineProgramsTom)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativeTomByGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "Tester(StraightLineProgramsTom)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "RepresentativeTomByGeneratorsNC",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "Tester(StraightLineProgramsTom)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativeTomByGeneratorsNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FusionCharTableTom: [ IsOrdinaryTable and IsLibraryCharacterTableRep and HasFusionToTom, IsTableOfMarks and IsLibTomRep ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "IsLibraryCharacterTableRep",
+                            "Tester(FusionToTom)"
+                        ],
+                        [
+                            "IsTableOfMarks",
+                            "IsLibTomRep"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "FusionCharTableTom: for ordinary character table and table of marks",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FusionCharTableTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsTableOfMarks"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PossibleFusionsCharTableTom: for ordinary character table and table of marks",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 23
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PossibleFusionsCharTableTom: for ordinary character table, table of marks, and record",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PossibleFusionsCharTableTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsTableOfMarks"
+                ]
+            ],
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PermCharsTom: for character table and table of marks",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ],
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PermCharsTom: for explicit fusion map and table of marks",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PermCharsTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TableOfMarksCyclic: for a positive integer",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TableOfMarksCyclic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TableOfMarksDihedral: for a positive integer",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TableOfMarksDihedral",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TableOfMarksFrobenius: tom of a Frobenius group",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TableOfMarksFrobenius",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MagmaInputString: perm group",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 63
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MagmaInputString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ShrinkCoeffs: 8 bit vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "Is8BitVectorRep"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ShrinkCoeffs: for GF2 vector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject",
+                            "IsGF2VectorRep"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "ShrinkCoeffs: call `ShrinkRowVector'",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ShrinkCoeffs: error if immutable",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ShrinkCoeffs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TeXObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LaTeXObj: matrix",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "LaTeXObj: rational",
+                    "filters": [
+                        [
+                            "IsRat"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "LaTeXObj: for an internal FFE",
+                    "filters": [
+                        [
+                            "IsFFE",
+                            "IsInternalRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "LaTeXObj: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "LaTeXObj: for an element of an f.p. group (default repres.)",
+                    "filters": [
+                        [
+                            "IsPackedElementDefaultRep",
+                            "IsElementOfFpGroup"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "LaTeXObj: assoc word in letter rep",
+                    "filters": [
+                        [
+                            "IsAssociativeElement",
+                            "IsWord",
+                            "IsLetterAssocWordRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LaTeXObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PositionFirstComponent: for dense plain list",
+                    "filters": [
+                        [
+                            "IsDenseList",
+                            "IsPlistRep",
+                            "IsSortedList",
+                            "Tester(IsSortedList)"
+                        ],
+                        []
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "PositionFirstComponent: for sorted list",
+                    "filters": [
+                        [
+                            "IsSSortedList",
+                            "Tester(IS_SSORT_LIST)"
+                        ],
+                        []
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "PositionFirstComponent: for dense list",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PositionFirstComponent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UChar",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "UChar",
+                    "filters": [
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UChar",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Unicode",
+                    "filters": [
+                        [
+                            "IsStringRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Unicode",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Unicode",
+                    "filters": [
+                        [
+                            "IsString"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 10
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Unicode",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnicodeString"
+                ]
+            ],
+            [
+                [
+                    "IsUnicodeString"
+                ],
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Encode",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Encode",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Encode",
+                    "filters": [
+                        [
+                            "IsUnicodeString"
+                        ],
+                        [
+                            "IsString"
+                        ],
+                        []
+                    ],
+                    "rank": 12
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Encode",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFile"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ProcessID: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ProcessID)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProcessID",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFile"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ProcessID): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ProcessID): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ProcessID)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFile"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ProcessID)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFile"
+                ],
+                []
+            ],
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IO_Pickle: for an object, pickle to string method",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IO_Pickle: for a permutation group",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 59
+                },
+                {
+                    "comment": "IO_Pickle: for a finite field",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "IO_Pickle: for a matrix group",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IO_Pickle: for a univariate Laurent polynomial",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsLaurentPolynomial",
+                            "Tester(IsLaurentPolynomial)",
+                            "IsLaurentPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IO_Pickle: for a string",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsList",
+                            "IsStringRep"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "IO_Pickle: for a univariate rational function",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "IsUnivariateRationalFunctionDefaultRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IO_Pickle: for an integer",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IO_Pickle: for rational functions",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsPolynomialDefaultRep"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "IO_Pickle: for rational functions",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsPolynomialFunction",
+                            "IsRationalFunctionDefaultRep"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "IO_Pickle: for a cyclotomic",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsCyclotomic"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IO_Pickle: for a finite field element",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsFFE"
+                        ]
+                    ],
+                    "rank": 16
+                },
+                {
+                    "comment": "IO_Pickle: for a float",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IO_Pickle: for a weak pointer object",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsList",
+                            "IsWeakPointerObject"
+                        ]
+                    ],
+                    "rank": 11
+                },
+                {
+                    "comment": "IO_Pickle: for a permutation",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsPerm"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IO_Pickle: for a partial perm",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsPartialPerm"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IO_Pickle: for a transformation",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsTransformation"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "IO_Pickle: for a real random source",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsRealRandomSource"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IO_Pickle: for a Mersenne twister random source",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsRandomSource",
+                            "IsMersenneTwister"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IO_Pickle: for a GAP random source",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsRandomSource",
+                            "IsGAPRandomSource"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IO_Pickle: for the global random source",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsRandomSource",
+                            "IsGlobalRandomSource"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IO_Pickle: for an operation",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsFunction",
+                            "IsOperation"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "IO_Pickle: IO_Results are forbidden",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IO_Result"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "IO_Pickle: for a list",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "IO_Pickle: for a function",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IO_Pickle: for a straight line program",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IO_Pickle: for a record",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IO_Pickle: for a character",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsChar"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IO_Pickle: for a boolean",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IO_Pickle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFile"
+                ]
+            ],
+            [
+                [
+                    "IsStringRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IO_Unpickle: for a string, unpickle from string method",
+                    "filters": [
+                        [
+                            "IsStringRep"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "IO_Unpickle: for a file",
+                    "filters": [
+                        [
+                            "IsFile"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IO_Unpickle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFunction"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsFunction"
+                ],
+                [],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BackgroundJobByFork: for a function and a list",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 1
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "BackgroundJobByFork: for a function, a list and a record",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ],
+                        [],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BackgroundJobByFork",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBackgroundJob"
+                ]
+            ],
+            [
+                [
+                    "IsWorkerFarmByFork"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIdle: for a worker farm by fork",
+                    "filters": [
+                        [
+                            "IsWorkerFarmByFork"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsIdle: for a background job by fork",
+                    "filters": [
+                        [
+                            "IsBackgroundJobByFork"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIdle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBackgroundJob"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HasTerminated: for a background job by fork",
+                    "filters": [
+                        [
+                            "IsBackgroundJobByFork"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasTerminated",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBackgroundJob"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WaitUntilIdle: for a background job by fork",
+                    "filters": [
+                        [
+                            "IsBackgroundJobByFork"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WaitUntilIdle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBackgroundJob"
+                ]
+            ],
+            [
+                [
+                    "IsWorkerFarmByFork"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Kill: for a worker farm by fork",
+                    "filters": [
+                        [
+                            "IsWorkerFarmByFork"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Kill: for a background job by fork",
+                    "filters": [
+                        [
+                            "IsBackgroundJobByFork"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Kill",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBackgroundJob"
+                ]
+            ],
+            [
+                [
+                    "IsWorkerFarmByFork"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Pickup: for a worker farm by fork",
+                    "filters": [
+                        [
+                            "IsWorkerFarmByFork"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Pickup: for a background job by fork",
+                    "filters": [
+                        [
+                            "IsBackgroundJobByFork"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Pickup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBackgroundJob"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsWorkerFarmByFork"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Submit: for a worker farm by fork",
+                    "filters": [
+                        [
+                            "IsWorkerFarmByFork"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Submit: for a background job by fork and an object",
+                    "filters": [
+                        [
+                            "IsBackgroundJobByFork"
+                        ],
+                        []
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Submit",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ParTakeFirstResultByFork: for two lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ParTakeFirstResultByFork: for two lists and a record",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParTakeFirstResultByFork",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ParDoByFork: for two lists",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ParDoByFork: for two lists and a record",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParDoByFork",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "ParMapReduceByFork: for a list, two functions and a record",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParMapReduceByFork",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ParListByFork: for a list, two functions and a record",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParListByFork",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ParWorkerFarmByFork: for a function and a record",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ParWorkerFarmByFork",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWorkerFarmByFork"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DoQueues: for a worker farm by fork",
+                    "filters": [
+                        [
+                            "IsWorkerFarmByFork"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DoQueues",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            []
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IOHub",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CloseConnection: for an IO hub and a positive integer",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CloseConnection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ShutdownServingSocket: for an IO hub",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ShutdownServingSocket",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Shutdown: for an IO hub",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Shutdown",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ],
+                [
+                    "IsStringRep"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "AttachServingSocket: for an address and a port",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ],
+                        [
+                            "IsStringRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AttachServingSocket",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ],
+                [
+                    "IsInt"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NewConnection: for an IO hub and two integers",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 39
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewConnection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AcceptNewConnection: for an IO hub",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AcceptNewConnection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GetInput: for an IO hub and an integer",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetInput",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsStringRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SubmitOutput: for an IO hub, a positive integers and an obj",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsStringRep"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubmitOutput",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OutputQueue: for an IO hub",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OutputQueue",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InputQueue: for an IO hub",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InputQueue",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ],
+                [
+                    "IsBool"
+                ]
+            ],
+            [
+                [
+                    "IsIOHub"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DoIO: for an IO hub",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "DoIO: for an IO hub and a boolean",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DoIO",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsIOHub"
+                ],
+                [
+                    "IsStringRep"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NewTCPConnection: for an IO hub, an address and a port",
+                    "filters": [
+                        [
+                            "IsIOHub"
+                        ],
+                        [
+                            "IsStringRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NewTCPConnection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStringRep"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "StoreLenIn8Bytes: for a string and a len",
+                    "filters": [
+                        [
+                            "IsStringRep"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StoreLenIn8Bytes",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStringRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GetLenFrom8Bytes: for a string",
+                    "filters": [
+                        [
+                            "IsStringRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetLenFrom8Bytes",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RootsFloatOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFloatRationalFunction"
+                ],
+                [
+                    "IsFloat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ValueInterval",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoKernel",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoKernel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Degree: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "Degree",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Degree",
+                    "filters": [
+                        [
+                            "IsRationalFunction"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Degree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DerivedSeries",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "DerivedSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DerivedSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Determinant",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Determinant",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Determinant",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIrreducible: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsIrreducible",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsIrreducible",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsIrreducible: for matrix group and field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                },
+                {
+                    "comment": "IsIrreducible: polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 41
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIrreducible",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMonomial",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsMonomial",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "IsMonomial",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                },
+                {
+                    "comment": "IsMonomial",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsMonomial",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMonomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpotent",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsNilpotent",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsNilpotent",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSimple",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsSimple",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSimple",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSimple",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAlmostSimple",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsAlmostSimple",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAlmostSimple",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSolvable",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "IsSolvable",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSolvable",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IsSolvable: rational polynomials",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSolvable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSporadicSimple",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSporadicSimple",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSporadicSimple",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSupersolvable",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsSupersolvable",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSupersolvable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPerfect",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsPerfect",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPerfect",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Kernel",
+                    "filters": [
+                        [
+                            "IsClassFunction"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "Kernel",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Kernel",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LowerCentralSeries",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "LowerCentralSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowerCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Rank: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "Rank",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Rank",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Rank",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UpperCentralSeries",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "UpperCentralSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UpperCentralSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IdGroup: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IdGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Gap3CatalogueIdGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Gap3CatalogueIdGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "Gap3CatalogueIdGroup: for permgroups or pcgroups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "Gap3CatalogueIdGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Gap3CatalogueIdGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Gap3CatalogueIdGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Gap3CatalogueIdGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Gap3CatalogueIdGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Gap3CatalogueIdGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FrattinifactorSize: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FrattinifactorSize)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "FrattinifactorSize: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "FrattinifactorSize: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FrattinifactorSize",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FrattinifactorSize): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FrattinifactorSize): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FrattinifactorSize)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FrattinifactorSize)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FrattinifactorId: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FrattinifactorId)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "FrattinifactorId: generic method for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "FrattinifactorId: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FrattinifactorId",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FrattinifactorId): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FrattinifactorId): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FrattinifactorId)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FrattinifactorId)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GaloisType: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GaloisType)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "GaloisType: for polynomials",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)",
+                            "Tester(GaloisGroupOnRoots)"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "GaloisType: for polynomials",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "GaloisType: for polynomials and list",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GaloisType",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GaloisType): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GaloisType): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GaloisType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsRationalFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GaloisType)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SimsNo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SimsNo)"
+                        ]
+                    ],
+                    "rank": 20061
+                },
+                {
+                    "comment": "SimsNo: via `PrimitiveIdentification'",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "SimsNo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -17
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SimsNo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SimsNo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SimsNo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SimsNo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(IsPerm)",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SimsNo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalBlockDimension: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimalBlockDimension)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "MinimalBlockDimension: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "MinimalBlockDimension: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MinimalBlockDimension: for matrix group and field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalBlockDimension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimalBlockDimension): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimalBlockDimension): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimalBlockDimension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimalBlockDimension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrimitiveMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPrimitiveMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsPrimitiveMatrixGroup: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsPrimitiveMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsPrimitiveMatrixGroup: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimitiveMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPrimitiveMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPrimitiveMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Setter(IsPrimitiveMatrixGroup): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        []
+                    ],
+                    "rank": 95
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPrimitiveMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Tester(IsPrimitiveMatrixGroup): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPrimitiveMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPGroup",
+                    "Tester(IsPGroup)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "PGAutomorphism: for p-groups",
+                    "filters": [
+                        [
+                            "IsPGroup",
+                            "Tester(IsPGroup)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PGAutomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PGMult",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "PGMult",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PGMult",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PGInverse",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "PGInverse",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PGInverse",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PGPower",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "PGPower",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsPGAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 40
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PGPower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PGMultList",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PGMultList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IrrFacsAlgExtPol: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IrrFacsAlgExtPol)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "IrrFacsAlgExtPol",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "IrrFacsAlgExtPol: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IrrFacsAlgExtPol",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IrrFacsAlgExtPol): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IrrFacsAlgExtPol): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IrrFacsAlgExtPol)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IrrFacsAlgExtPol)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExponentsOfUnits: for number fields",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 56
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentsOfUnits",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPrimitiveElementOfNumberField: for number field and algebraic element",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)"
+                        ],
+                        []
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimitiveElementOfNumberField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                [
+                    "IsCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RelationLattice: for matrix fields",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "RelationLattice: for fields by polynomial",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)",
+                            "IsAlgebraicExtension"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelationLattice",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsUnitGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsUnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsUnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsUnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUnitGroupIsomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsUnitGroupIsomorphism)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "IsUnitGroupIsomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUnitGroupIsomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsUnitGroupIsomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsUnitGroupIsomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsUnitGroupIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsUnitGroupIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNumberFieldByMatrices: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 20057
+                },
+                {
+                    "comment": "IsNumberFieldByMatrices: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNumberFieldByMatrices",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNumberFieldByMatrices): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNumberFieldByMatrices): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNumberFieldByMatrices)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNumberFieldByMatrices)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMultGroupByFieldElemsIsomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMultGroupByFieldElemsIsomorphism)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "IsMultGroupByFieldElemsIsomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMultGroupByFieldElemsIsomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMultGroupByFieldElemsIsomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMultGroupByFieldElemsIsomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMultGroupByFieldElemsIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMultGroupByFieldElemsIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IntegerDefiningPolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IntegerDefiningPolynomial)"
+                        ]
+                    ],
+                    "rank": 20057
+                },
+                {
+                    "comment": "IntegerDefiningPolynomial: for matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "IntegerDefiningPolynomial: for algebraic extension",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)",
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "IntegerDefiningPolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntegerDefiningPolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IntegerDefiningPolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IntegerDefiningPolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IntegerDefiningPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IntegerDefiningPolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IntegerPrimitiveElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IntegerPrimitiveElement)"
+                        ]
+                    ],
+                    "rank": 20057
+                },
+                {
+                    "comment": "IntegerPrimitiveElement: for the rationals",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "IntegerPrimitiveElement: for matrix field",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "IntegerPrimitiveElement: for algebraic extension",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)",
+                            "IsAlgebraicExtension"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "IntegerPrimitiveElement: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IntegerPrimitiveElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IntegerPrimitiveElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IntegerPrimitiveElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IntegerPrimitiveElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IntegerPrimitiveElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EquationOrderBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EquationOrderBasis)"
+                        ]
+                    ],
+                    "rank": 20057
+                },
+                {
+                    "comment": "EquationOrderBasis: for the rationals",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "EquationOrderBasis: for number field",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "EquationOrderBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "EquationOrderBasis: for number field and primitive element",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)"
+                        ],
+                        []
+                    ],
+                    "rank": 54
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EquationOrderBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EquationOrderBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EquationOrderBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EquationOrderBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EquationOrderBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MaximalOrderBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MaximalOrderBasis)"
+                        ]
+                    ],
+                    "rank": 20057
+                },
+                {
+                    "comment": "MaximalOrderBasis: for the rationals",
+                    "filters": [
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "CategoryCollections(IsCyclotomic)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing",
+                            "IsPrimeField",
+                            "Tester(IsPrimeField)"
+                        ]
+                    ],
+                    "rank": 84
+                },
+                {
+                    "comment": "MaximalOrderBasis: for number field",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "MaximalOrderBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalOrderBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MaximalOrderBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MaximalOrderBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MaximalOrderBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MaximalOrderBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnitGroup)"
+                        ]
+                    ],
+                    "rank": 20057
+                },
+                {
+                    "comment": "UnitGroup: for number field",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)"
+                        ]
+                    ],
+                    "rank": 54
+                },
+                {
+                    "comment": "UnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FieldOfUnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FieldOfUnitGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "FieldOfUnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FieldOfUnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FieldOfUnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FieldOfUnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FieldOfUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FieldOfUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsWeightedCollector: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsWeightedCollector)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "IsWeightedCollector: from-the-left collector",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsPolycyclicCollector",
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsWeightedCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsWeightedCollector): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsWeightedCollector): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsWeightedCollector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsWeightedCollector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPolynomialCollector: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPolynomialCollector)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPolynomialCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPolynomialCollector): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPolynomialCollector): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPolynomialCollector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPolynomialCollector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UseLibraryCollector: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UseLibraryCollector)"
+                        ]
+                    ],
+                    "rank": 20016
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UseLibraryCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UseLibraryCollector): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UseLibraryCollector): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UseLibraryCollector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UseLibraryCollector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FromTheLeftCollector: for free groups",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "FromTheLeftCollector: for positive integer",
+                    "filters": [
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 18
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FromTheLeftCollector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ExponentsByObj: from-the-left collector, gen-exp-list",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExponentsByObj",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "GetPower: from-the-left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetPower",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolycyclicCollector"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "GetConjugate: from the left collector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ],
+                        [
+                            "IsInt"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GetConjugate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPolycyclicPresentation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPolycyclicPresentation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsPolycyclicPresentation: FromTheLeftCollector",
+                    "filters": [
+                        [
+                            "IsFromTheLeftCollectorRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPolycyclicPresentation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPolycyclicPresentation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPolycyclicPresentation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPolycyclicPresentation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromTheLeftCollectorRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPolycyclicPresentation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElementRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Exponents: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElementRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Exponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElementRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NameTag: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElementRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NameTag",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElementRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GenExpList: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElementRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GenExpList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElementRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Depth: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElementRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Depth",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElementRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LeadingExponent: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElementRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeadingExponent",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TailOfElm: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TailOfElm)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "TailOfElm: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElement",
+                            "IsPcpElementRep"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TailOfElm",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TailOfElm): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TailOfElm): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TailOfElm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TailOfElm)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelativeOrderPcp: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelativeOrderPcp)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "RelativeOrderPcp",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelativeOrderPcp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelativeOrderPcp): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelativeOrderPcp): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelativeOrderPcp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelativeOrderPcp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RelativeIndex: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RelativeIndex)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "RelativeIndex",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RelativeIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RelativeIndex): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RelativeIndex): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RelativeIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RelativeIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FactorOrder: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FactorOrder)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "FactorOrder",
+                    "filters": [
+                        [
+                            "IsPcpElement"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FactorOrder",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FactorOrder): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FactorOrder): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FactorOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcpElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FactorOrder)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Igs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Igs)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "Igs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Igs",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Igs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": -9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Igs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Igs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Igs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Igs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Igs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Ngs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Ngs)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "Ngs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Ngs",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Ngs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": -9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Ngs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Ngs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Ngs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Ngs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Ngs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Cgs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Cgs)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "Cgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Cgs",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Cgs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": -9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Cgs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Cgs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Cgs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Cgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Cgs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Collector: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "Collector: for pcp elements",
+                    "filters": [
+                        [
+                            "IsPcpElementRep"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Collector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "EfaSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(EfaSeries)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "EfaSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "EfaSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": -9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "EfaSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(EfaSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(EfaSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(EfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(EfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcpsOfEfaSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcpsOfEfaSeries)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "PcpsOfEfaSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "PcpsOfEfaSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": -9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcpsOfEfaSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcpsOfEfaSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcpsOfEfaSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcpsOfEfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcpsOfEfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismPcpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismPcpGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsomorphismPcpGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 10048
+                },
+                {
+                    "comment": "IsomorphismPcpGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "CanEasilyComputeWithIndependentGensAbelianGroup"
+                        ]
+                    ],
+                    "rank": 104
+                },
+                {
+                    "comment": "IsomorphismPcpGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(IsPerm)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: for AffineCrystGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: for rational matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "IsRationalMatrixGroup",
+                            "Tester(IsRationalMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: for PointGroup",
+                    "filters": [
+                        [
+                            "IsPointGroup",
+                            "Tester(IsPointGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsomorphismPcpGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: for matrix groups over a finite field (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsomorphismPcpGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: for ac groups",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(AlmostCrystallographicInfo)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsomorphismPcpGroup: for matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: for matrix fields",
+                    "filters": [
+                        [
+                            "IsNumberFieldByMatrices",
+                            "Tester(IsNumberFieldByMatrices)"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 58
+                },
+                {
+                    "comment": "IsomorphismPcpGroup: for fields def. by polynomial",
+                    "filters": [
+                        [
+                            "IsNumberField",
+                            "Tester(IsNumberField)",
+                            "IsAlgebraicExtension"
+                        ],
+                        [
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismPcpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismPcpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismPcpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismPcpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismPcpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcpGroupByEfaSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcpGroupByEfaSeries)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "PcpGroupByEfaSeries",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "PcpGroupByEfaSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcpGroupByEfaSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcpGroupByEfaSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcpGroupByEfaSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcpGroupByEfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcpGroupByEfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SplitExtensionByAutomorphisms: for a PcpGroup, a PcpGroup, and a list of automorphisms",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 98
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SplitExtensionByAutomorphisms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnitriangularMatrixRepresentation: for torsion free fin. gen. nilpotent pcp-groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNilpotentGroup",
+                            "Tester(IsNilpotentGroup)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 54
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnitriangularMatrixRepresentation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsHomomorphismIntoMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsHomomorphismIntoMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20018
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsHomomorphismIntoMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsHomomorphismIntoMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsHomomorphismIntoMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsHomomorphismIntoMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsHomomorphismIntoMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SemiSimpleEfaSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SemiSimpleEfaSeries)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "SemiSimpleEfaSeries: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SemiSimpleEfaSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": -9
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SemiSimpleEfaSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SemiSimpleEfaSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SemiSimpleEfaSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SemiSimpleEfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SemiSimpleEfaSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FCCentre: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FCCentre)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "FCCentre: FCCentre for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "FCCentre: FCCentre for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "FCCentre: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FCCentre",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FCCentre): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FCCentre): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FCCentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FCCentre)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpotentByFinite: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNilpotentByFinite)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsNilpotentByFinite: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsNilpotentByFinite: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotentByFinite",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNilpotentByFinite): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNilpotentByFinite): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNilpotentByFinite)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNilpotentByFinite)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MaximalSubgroupClassesByIndexOp: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalSubgroupClassesByIndexOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedMaximalSubgroupClassesByIndexs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedMaximalSubgroupClassesByIndexs)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedMaximalSubgroupClassesByIndexs: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedMaximalSubgroupClassesByIndexs: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedMaximalSubgroupClassesByIndexs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedMaximalSubgroupClassesByIndexs): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedMaximalSubgroupClassesByIndexs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedMaximalSubgroupClassesByIndexs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedMaximalSubgroupClassesByIndexs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MaximalSubgroupClassesByIndex: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MaximalSubgroupClassesByIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasMaximalSubgroupClassesByIndex: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasMaximalSubgroupClassesByIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetMaximalSubgroupClassesByIndex: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 52
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetMaximalSubgroupClassesByIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LowIndexSubgroupClassesOp: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowIndexSubgroupClassesOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedLowIndexSubgroupClassess: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedLowIndexSubgroupClassess)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedLowIndexSubgroupClassess: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedLowIndexSubgroupClassess: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedLowIndexSubgroupClassess",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedLowIndexSubgroupClassess): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedLowIndexSubgroupClassess): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedLowIndexSubgroupClassess)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedLowIndexSubgroupClassess)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LowIndexSubgroupClasses: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowIndexSubgroupClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasLowIndexSubgroupClasses: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasLowIndexSubgroupClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetLowIndexSubgroupClasses: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 52
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetLowIndexSubgroupClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LowIndexNormalSubgroupsOp: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowIndexNormalSubgroupsOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedLowIndexNormalSubgroupss: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedLowIndexNormalSubgroupss)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedLowIndexNormalSubgroupss: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedLowIndexNormalSubgroupss: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedLowIndexNormalSubgroupss",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedLowIndexNormalSubgroupss): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedLowIndexNormalSubgroupss): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedLowIndexNormalSubgroupss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedLowIndexNormalSubgroupss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LowIndexNormalSubgroups: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LowIndexNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasLowIndexNormalSubgroups: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasLowIndexNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetLowIndexNormalSubgroups: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 52
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetLowIndexNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SchurExtension: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SchurExtension)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "SchurExtension: for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SchurExtension: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SchurExtension",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SchurExtension): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SchurExtension): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SchurExtension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SchurExtension)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SchurExtensionEpimorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SchurExtensionEpimorphism)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "SchurExtensionEpimorphism: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SchurExtensionEpimorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SchurExtensionEpimorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SchurExtensionEpimorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SchurExtensionEpimorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SchurExtensionEpimorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SchurExtensionEpimorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NonAbelianTensorSquare: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NonAbelianTensorSquare)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "NonAbelianTensorSquare",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NonAbelianTensorSquare: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NonAbelianTensorSquare",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NonAbelianTensorSquare): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NonAbelianTensorSquare): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NonAbelianTensorSquare)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NonAbelianTensorSquare)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NonAbelianExteriorSquare: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NonAbelianExteriorSquare)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "NonAbelianExteriorSquare: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NonAbelianExteriorSquare: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NonAbelianExteriorSquare",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NonAbelianExteriorSquare): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NonAbelianExteriorSquare): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NonAbelianExteriorSquare)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NonAbelianExteriorSquare)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TorsionSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TorsionSubgroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "TorsionSubgroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "TorsionSubgroup: for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "TorsionSubgroup: for torsion free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsTorsionFree",
+                            "Tester(IsTorsionFree)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "TorsionSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TorsionSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TorsionSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TorsionSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TorsionSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TorsionSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalTorsionSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalTorsionSubgroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "NormalTorsionSubgroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NormalTorsionSubgroup: for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "NormalTorsionSubgroup: for torsion free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsTorsionFree",
+                            "Tester(IsTorsionFree)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "NormalTorsionSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalTorsionSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalTorsionSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalTorsionSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalTorsionSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalTorsionSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FiniteSubgroupClasses: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FiniteSubgroupClasses)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "FiniteSubgroupClasses: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "FiniteSubgroupClasses: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FiniteSubgroupClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FiniteSubgroupClasses): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FiniteSubgroupClasses): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FiniteSubgroupClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FiniteSubgroupClasses)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTorsionFree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTorsionFree)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsTorsionFree: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsTorsionFree",
+                    "filters": [
+                        [
+                            "Tester(IsTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsTorsionFree: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTorsionFree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTorsionFree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTorsionFree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTorsionFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTorsionFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFreeAbelian: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFreeAbelian)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsFreeAbelian",
+                    "filters": [
+                        [
+                            "Tester(IsTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsFreeAbelian",
+                    "filters": [
+                        [
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsFreeAbelian: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFreeAbelian",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFreeAbelian): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFreeAbelian): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFreeAbelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFreeAbelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MemberFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MemberFunction)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MemberFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MemberFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MemberFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MemberFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MemberFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsMemberOp: for class with member function",
+                    "filters": [
+                        [],
+                        [
+                            "IsClass",
+                            "Tester(MemberFunction)"
+                        ]
+                    ],
+                    "rank": 10003
+                },
+                {
+                    "comment": "IsMemberOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 372
+                },
+                {
+                    "comment": "IsMemberOp: compute from LocalDefinitionFunction",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "Tester(LocalDefinitionFunction)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "IsMemberOp: compute from boundary",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "Tester(BoundaryFunction)"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "IsMemberOp: if residual function is known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "Tester(ResidualFunction)"
+                        ]
+                    ],
+                    "rank": 56
+                },
+                {
+                    "comment": "IsMemberOp: for Fitting/formation product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFittingProductRep",
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "IsMemberOp: if radical is known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "Tester(RadicalFunction)",
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "IsMemberOp: for formation product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsMemberOp: if ProjectorFunction is known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "Tester(ProjectorFunction)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsMemberOp: for FittingSetRep with inj function",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "Tester(InjectorFunction)",
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsMemberOp: for Fitting product",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFittingProductRep"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsMemberOp: if radical is known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "Tester(RadicalFunction)"
+                        ]
+                    ],
+                    "rank": 47
+                },
+                {
+                    "comment": "IsMemberOp: if injector is known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "Tester(InjectorFunction)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsMemberOp:  for group class by list",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClassByListRep"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsMemberOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "IsMemberOp: for IsClassByUnionRep",
+                    "filters": [
+                        [],
+                        [
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsMemberOp: for IsClassByIntersectionRep",
+                    "filters": [
+                        [],
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsMemberOp: for IsClassByComplementRep",
+                    "filters": [
+                        [],
+                        [
+                            "IsClassByComplementRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMemberOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedIsMembers: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedIsMembers)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "ComputedIsMembers: default method",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedIsMembers",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedIsMembers): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedIsMembers): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedIsMembers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedIsMembers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsMember: default method",
+                    "filters": [
+                        [],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMember",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasIsMember: default method",
+                    "filters": [
+                        [],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasIsMember",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetIsMember: default method",
+                    "filters": [
+                        [],
+                        [
+                            "IsClass"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetIsMember",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Class: defined by property function",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "Class: defined by property function",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Class",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Complement: for a class complement",
+                    "filters": [
+                        [
+                            "IsClassByComplementRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "Complement: for a class",
+                    "filters": [
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Complement: for a list/collection",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Complement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "IsGroupClass",
+                    "filters": [
+                        [
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsGroupClass",
+                    "filters": [
+                        [
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "IsGroupClass",
+                    "filters": [
+                        [
+                            "IsClassByComplementRep"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [
+                    "IsList",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GroupClass)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "GroupClass: for group defined by list",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "GroupClass: for property function",
+                    "filters": [
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "GroupClass: for record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "GroupClass:  for list and function",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GroupClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GroupClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GroupClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GroupClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ContainsTrivialGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ContainsTrivialGroup)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "ContainsTrivialGroup",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ContainsTrivialGroup",
+                    "filters": [
+                        [
+                            "Tester(IsEmpty)",
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ContainsTrivialGroup",
+                    "filters": [
+                        [
+                            "Tester(IsEmpty)",
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ContainsTrivialGroup",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ContainsTrivialGroup",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "ContainsTrivialGroup: for generic group class - test membership",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "ContainsTrivialGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ContainsTrivialGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ContainsTrivialGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ContainsTrivialGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ContainsTrivialGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ContainsTrivialGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSubgroupClosed: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSubgroupClosed)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsSubgroupClosed",
+                    "filters": [
+                        [
+                            "IsFittingProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsSubgroupClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsSubgroupClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsSubgroupClosed: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsSubgroupClosed: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSubgroupClosed",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSubgroupClosed): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSubgroupClosed): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSubgroupClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSubgroupClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNormalSubgroupClosed: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNormalSubgroupClosed)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsNormalSubgroupClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsNormalSubgroupClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsNormalSubgroupClosed: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsNormalSubgroupClosed: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormalSubgroupClosed",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNormalSubgroupClosed): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNormalSubgroupClosed): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNormalSubgroupClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNormalSubgroupClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsQuotientClosed: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsQuotientClosed)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsQuotientClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsQuotientClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsQuotientClosed: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsQuotientClosed: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsQuotientClosed",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsQuotientClosed): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsQuotientClosed): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsQuotientClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsQuotientClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsResiduallyClosed: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsResiduallyClosed)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsResiduallyClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsDirectProductClosed",
+                            "Tester(IsDirectProductClosed)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsResiduallyClosed: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsResiduallyClosed: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsResiduallyClosed",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsResiduallyClosed): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsResiduallyClosed): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsResiduallyClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsResiduallyClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNormalProductClosed: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsNormalProductClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsDirectProductClosed",
+                            "Tester(IsDirectProductClosed)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IsNormalProductClosed: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsNormalProductClosed: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormalProductClosed",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNormalProductClosed): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNormalProductClosed): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNormalProductClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNormalProductClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsDirectProductClosed: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsDirectProductClosed)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsDirectProductClosed",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsDirectProductClosed: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsDirectProductClosed: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsDirectProductClosed",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsDirectProductClosed): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsDirectProductClosed): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsDirectProductClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsDirectProductClosed)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSchunckClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSchunckClass)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsSchunckClass",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsDirectProductClosed",
+                            "Tester(IsDirectProductClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 13
+                },
+                {
+                    "comment": "IsSchunckClass: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsSchunckClass: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSchunckClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSchunckClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSchunckClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSchunckClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSchunckClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSaturated: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSaturated)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "IsSaturated: test if char of top class is subset of char of bot class",
+                    "filters": [
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsSaturated",
+                    "filters": [
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsSaturated",
+                    "filters": [
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "IsSaturated",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByUnionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsSaturated",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "IsSaturated: for generic group class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "IsSaturated: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSaturated",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSaturated): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSaturated): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSaturated)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSaturated)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FittingClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FittingClass)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "FittingClass",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FittingClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FittingClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FittingClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FittingClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FittingClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)",
+                    "ContainsTrivialGroup",
+                    "Tester(ContainsTrivialGroup)",
+                    "IsNormalSubgroupClosed",
+                    "Tester(IsNormalSubgroupClosed)",
+                    "IsNormalProductClosed",
+                    "Tester(IsNormalProductClosed)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)",
+                    "ContainsTrivialGroup",
+                    "Tester(ContainsTrivialGroup)",
+                    "IsNormalSubgroupClosed",
+                    "Tester(IsNormalSubgroupClosed)",
+                    "IsNormalProductClosed",
+                    "Tester(IsNormalProductClosed)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FittingProduct: for Fitting formation - use FormationProduct",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "FittingProduct: of two Fittng classes",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FittingProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FittingSet",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FittingSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsFittingSet:  for IsFittingSetRep",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IsFittingSet:  for Fitting class",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFittingSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ImageFittingSet: for Fitting set - injective case",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ImageFittingSet: for Fitting class - injective case",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ImageFittingSet: for Fitting set",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "ImageFittingSet: for Fitting class",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImageFittingSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PreImageFittingSet: for Fitting set - injective case",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "PreImageFittingSet: for Fitting class - injective case",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsInjective",
+                            "Tester(IsInjective)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImageFittingSet: for Fitting set",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "PreImageFittingSet: for Fitting class",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "RespectsMultiplication",
+                            "Tester(RespectsMultiplication)",
+                            "RespectsInverses",
+                            "Tester(RespectsInverses)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PreImageFittingSet",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InjectorFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InjectorFunction)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InjectorFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InjectorFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InjectorFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InjectorFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InjectorFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RadicalFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RadicalFunction)"
+                        ]
+                    ],
+                    "rank": 20005
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RadicalFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RadicalFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RadicalFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RadicalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RadicalFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPrimitiveSolvableGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPrimitiveSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsPrimitiveSolvableGroup: for generic group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsPrimitiveSolvableGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimitiveSolvableGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPrimitiveSolvableGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPrimitiveSolvableGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPrimitiveSolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPrimitiveSolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SchunckClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SchunckClass)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "SchunckClass: for record",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SchunckClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SchunckClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SchunckClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SchunckClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SchunckClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Boundary: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Boundary)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "Boundary: if BoundaryFunction is known",
+                    "filters": [
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "Tester(BoundaryFunction)"
+                        ]
+                    ],
+                    "rank": 18
+                },
+                {
+                    "comment": "Boundary: for Schunck class with local definition",
+                    "filters": [
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "Tester(LocalDefinitionFunction)"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "Boundary: for generic grp class",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "Boundary: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Boundary",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Boundary): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Boundary): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Boundary)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Boundary)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ProjectorFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ProjectorFunction)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "ProjectorFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectorFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ProjectorFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ProjectorFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ProjectorFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ProjectorFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BoundaryFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BoundaryFunction)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "BoundaryFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BoundaryFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BoundaryFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BoundaryFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BoundaryFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BoundaryFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrdinaryFormation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrdinaryFormation)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "OrdinaryFormation",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrdinaryFormation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrdinaryFormation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrdinaryFormation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrdinaryFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrdinaryFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)",
+                    "ContainsTrivialGroup",
+                    "Tester(ContainsTrivialGroup)",
+                    "IsQuotientClosed",
+                    "Tester(IsQuotientClosed)",
+                    "IsResiduallyClosed",
+                    "Tester(IsResiduallyClosed)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)",
+                    "ContainsTrivialGroup",
+                    "Tester(ContainsTrivialGroup)",
+                    "IsQuotientClosed",
+                    "Tester(IsQuotientClosed)",
+                    "IsResiduallyClosed",
+                    "Tester(IsResiduallyClosed)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FormationProduct: of two Fitting formations",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 32
+                },
+                {
+                    "comment": "FormationProduct: of two formations",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FormationProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SaturatedFormation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SaturatedFormation)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "SaturatedFormation",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SaturatedFormation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SaturatedFormation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SaturatedFormation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SaturatedFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SaturatedFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FittingFormation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FittingFormation)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "FittingFormation",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FittingFormation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FittingFormation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FittingFormation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FittingFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FittingFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)",
+                    "ContainsTrivialGroup",
+                    "Tester(ContainsTrivialGroup)",
+                    "IsNormalSubgroupClosed",
+                    "Tester(IsNormalSubgroupClosed)",
+                    "IsQuotientClosed",
+                    "Tester(IsQuotientClosed)",
+                    "IsResiduallyClosed",
+                    "Tester(IsResiduallyClosed)",
+                    "IsNormalProductClosed",
+                    "Tester(IsNormalProductClosed)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)",
+                    "ContainsTrivialGroup",
+                    "Tester(ContainsTrivialGroup)",
+                    "IsNormalSubgroupClosed",
+                    "Tester(IsNormalSubgroupClosed)",
+                    "IsQuotientClosed",
+                    "Tester(IsQuotientClosed)",
+                    "IsResiduallyClosed",
+                    "Tester(IsResiduallyClosed)",
+                    "IsNormalProductClosed",
+                    "Tester(IsNormalProductClosed)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "FittingFormationProduct: of two Fitting formations",
+                    "filters": [
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FittingFormationProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SaturatedFittingFormation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SaturatedFittingFormation)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "SaturatedFittingFormation",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SaturatedFittingFormation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SaturatedFittingFormation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SaturatedFittingFormation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SaturatedFittingFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SaturatedFittingFormation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ResidualFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ResidualFunction)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "ResidualFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ResidualFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ResidualFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ResidualFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ResidualFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ResidualFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LocalDefinitionFunction: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LocalDefinitionFunction)"
+                        ]
+                    ],
+                    "rank": 20007
+                },
+                {
+                    "comment": "LocalDefinitionFunction",
+                    "filters": [
+                        [
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "LocalDefinitionFunction",
+                    "filters": [
+                        [
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "LocalDefinitionFunction: test if char of top class is subset of char of bot class",
+                    "filters": [
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "LocalDefinitionFunction: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LocalDefinitionFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LocalDefinitionFunction): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LocalDefinitionFunction): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LocalDefinitionFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LocalDefinitionFunction)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ProjectorOp: if ProjectorFunction is known",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "Tester(ProjectorFunction)"
+                        ]
+                    ],
+                    "rank": 10048
+                },
+                {
+                    "comment": "ProjectorOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)"
+                        ]
+                    ],
+                    "rank": 397
+                },
+                {
+                    "comment": "ProjectorOp: compute from LocalDefinitionFunction",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "Tester(LocalDefinitionFunction)"
+                        ]
+                    ],
+                    "rank": 74
+                },
+                {
+                    "comment": "ProjectorOp: for intersection of group classes which is a local formation",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "ProjectorOp: compute from boundary",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "Tester(BoundaryFunction)"
+                        ]
+                    ],
+                    "rank": 70
+                },
+                {
+                    "comment": "ProjectorOp: for intersection of group classes",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "ProjectorOp: use MemberFunction",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "Tester(MemberFunction)",
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ProjectorOp: use only membership test",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "ProjectorOp: handled by IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "ProjectorOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectorOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedProjectors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedProjectors)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedProjectors: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedProjectors: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedProjectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedProjectors): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedProjectors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedProjectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedProjectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Projector: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Projector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasProjector: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasProjector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetProjector: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ],
+                        []
+                    ],
+                    "rank": 37
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetProjector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CoveringSubgroupOp: for Schunck classes: return projector",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsSchunckClass",
+                            "Tester(IsSchunckClass)"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoveringSubgroupOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedCoveringSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedCoveringSubgroups)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedCoveringSubgroups: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedCoveringSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedCoveringSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedCoveringSubgroups): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedCoveringSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedCoveringSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedCoveringSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CoveringSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoveringSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasCoveringSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasCoveringSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetCoveringSubgroup: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ],
+                        []
+                    ],
+                    "rank": 37
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetCoveringSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsRecord"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "ProjectorFromExtendedBoundaryFunction: for pc group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+                        ],
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 66
+                },
+                {
+                    "comment": "ProjectorFromExtendedBoundaryFunction: for solvable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "ProjectorFromExtendedBoundaryFunction:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsRecord"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectorFromExtendedBoundaryFunction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InjectorOp: for FittingSetRep if injector function is known",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "Tester(InjectorFunction)",
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 10063
+                },
+                {
+                    "comment": "InjectorOp: injector function is known",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "Tester(InjectorFunction)"
+                        ]
+                    ],
+                    "rank": 10061
+                },
+                {
+                    "comment": "InjectorOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "InjectorOp: for pcgs computable groups: use radical",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "InjectorOp: for FittingSetRep w/o injector function",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "InjectorOp: handled by IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "InjectorOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InjectorOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedInjectors: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedInjectors)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedInjectors: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedInjectors: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedInjectors",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedInjectors): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedInjectors): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedInjectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedInjectors)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Injector: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Injector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasInjector: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasInjector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetInjector: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetInjector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalizerOfPronormalSubgroup: via nice hom.",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 401
+                },
+                {
+                    "comment": "NormalizerOfPronormalSubgroup: use pcgs method",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 85
+                },
+                {
+                    "comment": "NormalizerOfPronormalSubgroup: via IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 81
+                },
+                {
+                    "comment": "NormalizerOfPronormalSubgroup: for generic groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerOfPronormalSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PcgsNormalizerOfPronormalSubgroup: for pcgs refining an el. ab. series",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsPcgs",
+                            "Tester(ParentPcgs)"
+                        ]
+                    ],
+                    "rank": 44
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcgsNormalizerOfPronormalSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "InvariantComplementsOfElAbSection: for section of finite solvable group",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 146
+                }
+            ],
+            "6args": []
+        },
+        "name": "InvariantComplementsOfElAbSection",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "ComplementsOfCentralSectionUnderActionNC: for section of solvable group",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 146
+                }
+            ],
+            "6args": []
+        },
+        "name": "ComplementsOfCentralSectionUnderActionNC",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RadicalOp: for FittingSetRep with radical function",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "Tester(RadicalFunction)",
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 10063
+                },
+                {
+                    "comment": "RadicalOp: if radical function is known",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "Tester(RadicalFunction)"
+                        ]
+                    ],
+                    "rank": 10061
+                },
+                {
+                    "comment": "RadicalOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "RadicalOp: if only in is known",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "RadicalOp: for FittingSetRep with injector function",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "Tester(InjectorFunction)",
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "RadicalOp: for intersection of classes",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "RadicalOp: for Fitting product",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFittingProductRep"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "RadicalOp: if injector is known",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)",
+                            "Tester(InjectorFunction)"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "RadicalOp: generic method for FittingSetRep",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFittingSetRep"
+                        ]
+                    ],
+                    "rank": 62
+                },
+                {
+                    "comment": "RadicalOp: handled by IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsNormalSubgroupClosed",
+                            "Tester(IsNormalSubgroupClosed)",
+                            "IsNormalProductClosed",
+                            "Tester(IsNormalProductClosed)"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "RadicalOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RadicalOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedRadicals: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedRadicals)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedRadicals: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedRadicals: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedRadicals",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedRadicals): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedRadicals): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedRadicals)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedRadicals)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Radical: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Radical",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasRadical: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasRadical",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsClass"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetRadical: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsClass"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetRadical",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "OneInvariantSubgroupMaxWrtNProperty: for solvable group",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "OneInvariantSubgroupMaxWrtNProperty:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "6args": []
+        },
+        "name": "OneInvariantSubgroupMaxWrtNProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "AllInvariantSubgroupsWithNProperty: for solvable group",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "AllInvariantSubgroupsWithNProperty:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "6args": []
+        },
+        "name": "AllInvariantSubgroupsWithNProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "OneNormalSubgroupMaxWrtNProperty: via OneInvariantSubgroupMaxWrtNProperty",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OneNormalSubgroupMaxWrtNProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AllNormalSubgroupsWithNProperty: via AllInvariantSubgroupsWithNProperty",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AllNormalSubgroupsWithNProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ResidualOp: for group and formation with ResidualFunction",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "Tester(ResidualFunction)"
+                        ]
+                    ],
+                    "rank": 10061
+                },
+                {
+                    "comment": "ResidualOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)"
+                        ]
+                    ],
+                    "rank": 395
+                },
+                {
+                    "comment": "ResidualOp: for locally defined formation",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsSaturated",
+                            "Tester(IsSaturated)",
+                            "Tester(LocalDefinitionFunction)"
+                        ]
+                    ],
+                    "rank": 69
+                },
+                {
+                    "comment": "ResidualOp: for group and intersection of formations",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)",
+                            "IsClassByIntersectionRep"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "ResidualOp: generic method for pcgs computable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "ResidualOp: for group and formation product",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFormationProductRep"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "ResidualOp: handled by IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)",
+                            "ContainsTrivialGroup",
+                            "Tester(ContainsTrivialGroup)",
+                            "IsQuotientClosed",
+                            "Tester(IsQuotientClosed)",
+                            "IsResiduallyClosed",
+                            "Tester(IsResiduallyClosed)"
+                        ]
+                    ],
+                    "rank": 60
+                },
+                {
+                    "comment": "ResidualOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ResidualOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedResiduals: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedResiduals)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedResiduals: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedResiduals: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedResiduals",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedResiduals): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedResiduals): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedResiduals)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedResiduals)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Residual: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Residual",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasResidual: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ]
+                    ],
+                    "rank": 37
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasResidual",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsGroupClass",
+                    "Tester(IsGroupClass)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetResidual: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsGroupClass",
+                            "Tester(IsGroupClass)"
+                        ],
+                        []
+                    ],
+                    "rank": 37
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetResidual",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacteristicSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CharacteristicSubgroups)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "CharacteristicSubgroups: via NiceMonomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "CharacteristicSubgroups: via IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "CharacteristicSubgroups: normal complement method for pcgs computable groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "CharacteristicSubgroups:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "CharacteristicSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacteristicSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CharacteristicSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CharacteristicSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CharacteristicSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CharacteristicSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "OneInvariantSubgroupMinWrtQProperty: for solvable group",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "OneInvariantSubgroupMinWrtQProperty:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "6args": []
+        },
+        "name": "OneInvariantSubgroupMinWrtQProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [
+                {
+                    "comment": "AllInvariantSubgroupsWithQProperty: for solvable group",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 97
+                },
+                {
+                    "comment": "AllInvariantSubgroupsWithQProperty:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "6args": []
+        },
+        "name": "AllInvariantSubgroupsWithQProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "OneNormalSubgroupMinWrtQProperty: try OneInvariantSubgroupMinWrtQProperty",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OneNormalSubgroupMinWrtQProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsFunction"
+                ],
+                [
+                    "IsFunction"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AllNormalSubgroupsWithQProperty: try AllInvariantSubgroupsWithQProperty",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 35
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AllNormalSubgroupsWithQProperty",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalGeneratorsOfNilpotentResidual: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalGeneratorsOfNilpotentResidual)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "NormalGeneratorsOfNilpotentResidual: for pcgs computable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "NormalGeneratorsOfNilpotentResidual: generic method - use lower central series",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "NormalGeneratorsOfNilpotentResidual: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalGeneratorsOfNilpotentResidual",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalGeneratorsOfNilpotentResidual): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalGeneratorsOfNilpotentResidual): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalGeneratorsOfNilpotentResidual)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalGeneratorsOfNilpotentResidual)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsModuloPcgs"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CentralizesLayer: for empty list",
+                    "filters": [
+                        [
+                            "IsListOrCollection",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "CentralizesLayer: generic method",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsModuloPcgs"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralizesLayer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "CompositionSeriesUnderAction: for solvable group",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "CompositionSeriesUnderAction:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CompositionSeriesUnderAction",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "SiftedPcElementWrtPcSequence: method for an empty collection",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsListOrCollection",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 31
+                },
+                {
+                    "comment": "SiftedPcElementWrtPcSequence: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SiftedPcElementWrtPcSequence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPcgs"
+                ],
+                [
+                    "IsListOrCollection"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "AddPcElementToPcSequence: method for an empty collection",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsListOrCollection",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "AddPcElementToPcSequence: generic method",
+                    "filters": [
+                        [
+                            "IsPcgs"
+                        ],
+                        [
+                            "IsListOrCollection"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AddPcElementToPcSequence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PrimePowerGensPcSequence: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PrimePowerGensPcSequence)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "PrimePowerGensPcSequence: for group with special pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SpecialPcgs)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "PrimePowerGensPcSequence: for group which can easily compute a pcgs",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "PrimePowerGensPcSequence: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PrimePowerGensPcSequence",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PrimePowerGensPcSequence): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PrimePowerGensPcSequence): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PrimePowerGensPcSequence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PrimePowerGensPcSequence)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NilpotentProjector: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NilpotentProjector)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "NilpotentProjector: for finite solvable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NilpotentProjector:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "NilpotentProjector: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NilpotentProjector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NilpotentProjector): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NilpotentProjector): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NilpotentProjector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NilpotentProjector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SupersolvableProjector: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SupersolvableProjector)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "SupersolvableProjector: for finite solvable groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SupersolvableProjector:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "SupersolvableProjector: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SupersolvableProjector",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SupersolvableProjector): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SupersolvableProjector): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SupersolvableProjector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SupersolvableProjector)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SolvableSocle: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SolvableSocle)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "SolvableSocle: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "SolvableSocle: for solvable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "SolvableSocle: via IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SolvableSocle: for finite group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "SolvableSocle:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "SolvableSocle: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SolvableSocle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SolvableSocle): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SolvableSocle): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SolvableSocle)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SolvableSocle)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SocleComponents: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SocleComponents)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "SocleComponents: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "SocleComponents: for solvable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SocleComponents:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "SocleComponents: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SocleComponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SocleComponents): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SocleComponents): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SocleComponents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SocleComponents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SolvableSocleComponents: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SolvableSocleComponents)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "SolvableSocleComponents: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "SolvableSocleComponents: for solvable group with known Fitting subgroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingSubgroup)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "SolvableSocleComponents: for solvable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "SolvableSocleComponents: via IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SolvableSocleComponents: via IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "SolvableSocleComponents: for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "SolvableSocleComponents:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "SolvableSocleComponents: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SolvableSocleComponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SolvableSocleComponents): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SolvableSocleComponents): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SolvableSocleComponents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SolvableSocleComponents)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PSocleComponentsOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 398
+                },
+                {
+                    "comment": "PSocleComponentsOp: via IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "PSocleComponentsOp: for finite group with SolvableSocleComponents",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(SolvableSocleComponents)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 64
+                },
+                {
+                    "comment": "PSocleComponentsOp: for finite group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "PSocleComponentsOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PSocleComponentsOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedPSocleComponentss: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedPSocleComponentss)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedPSocleComponentss: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedPSocleComponentss: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedPSocleComponentss",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedPSocleComponentss): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedPSocleComponentss): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedPSocleComponentss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedPSocleComponentss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PSocleComponents: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PSocleComponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasPSocleComponents: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasPSocleComponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPSocleComponents: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 52
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPSocleComponents",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PSocleOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 398
+                },
+                {
+                    "comment": "PSocleOp: for pcgs computable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 71
+                },
+                {
+                    "comment": "PSocleOp: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 67
+                },
+                {
+                    "comment": "PSocleOp: for finite group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                },
+                {
+                    "comment": "PSocleOp:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PSocleOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedPSocles: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedPSocles)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "ComputedPSocles: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "ComputedPSocles: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedPSocles",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedPSocles): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedPSocles): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedPSocles)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedPSocles)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PSocle: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PSocle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasPSocle: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasPSocle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetPSocle: default method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 52
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetPSocle",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AbelianMinimalNormalSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AbelianMinimalNormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "AbelianMinimalNormalSubgroups: handled by nice monomorphism",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 379
+                },
+                {
+                    "comment": "AbelianMinimalNormalSubgroups: complements of chief factors, for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(FittingSubgroup)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "AbelianMinimalNormalSubgroups: complements of chief factors, for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CanEasilyComputePcgs"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "AbelianMinimalNormalSubgroups: handled by IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "AbelianMinimalNormalSubgroups: complements of chief factors, for finite groups",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "AbelianMinimalNormalSubgroups:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "AbelianMinimalNormalSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AbelianMinimalNormalSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AbelianMinimalNormalSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AbelianMinimalNormalSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AbelianMinimalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AbelianMinimalNormalSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LinesOfStraightLineDecision: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LinesOfStraightLineDecision)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LinesOfStraightLineDecision",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LinesOfStraightLineDecision): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LinesOfStraightLineDecision): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LinesOfStraightLineDecision)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LinesOfStraightLineDecision)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NrInputsOfStraightLineDecision: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NrInputsOfStraightLineDecision)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "NrInputsOfStraightLineDecision: for a straight line decision",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NrInputsOfStraightLineDecision",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NrInputsOfStraightLineDecision): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NrInputsOfStraightLineDecision): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NrInputsOfStraightLineDecision)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NrInputsOfStraightLineDecision)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ],
+                [
+                    "IsHomogeneousList"
+                ]
+            ],
+            [
+                [
+                    "IsStraightLineDecision"
+                ],
+                [
+                    "IsHomogeneousList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ResultOfStraightLineDecision: for a straight line decision, and a homogeneous list",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "ResultOfStraightLineDecision: for a straight line decision, a homogeneous list, and a function",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ],
+                        [
+                            "IsHomogeneousList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ResultOfStraightLineDecision",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineDecision"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StraightLineProgramFromStraightLineDecision: for a straight line decision",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StraightLineProgramFromStraightLineDecision",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ],
+            [
+                [
+                    "IsStraightLineDecision"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsBBoxProgram: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsBBoxProgram)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AsBBoxProgram: for a straight line decision",
+                    "filters": [
+                        [
+                            "IsStraightLineDecision"
+                        ]
+                    ],
+                    "rank": 1
+                },
+                {
+                    "comment": "AsBBoxProgram: for a straight line program",
+                    "filters": [
+                        [
+                            "IsStraightLineProgram"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsBBoxProgram",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsStraightLineDecision"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsBBoxProgram): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsBBoxProgram): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsBBoxProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsStraightLineProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsBBoxProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBBoxProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsStraightLineProgram: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsStraightLineProgram)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AsStraightLineProgram: for a black box program",
+                    "filters": [
+                        [
+                            "IsBBoxProgram"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsStraightLineProgram",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBBoxProgram"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsStraightLineProgram): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsStraightLineProgram): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsStraightLineProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBBoxProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsStraightLineProgram)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBBoxProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsStraightLineDecision: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AsStraightLineDecision)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "AsStraightLineDecision: for a black box program",
+                    "filters": [
+                        [
+                            "IsBBoxProgram"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsStraightLineDecision",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBBoxProgram"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AsStraightLineDecision): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AsStraightLineDecision): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AsStraightLineDecision)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBBoxProgram"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AsStraightLineDecision)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsList",
+                    "CategoryCollections(IsPerm)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsPerm"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MeatAxeString: for list of permutations, and degree",
+                    "filters": [
+                        [
+                            "IsList",
+                            "CategoryCollections(IsPerm)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 82
+                },
+                {
+                    "comment": "MeatAxeString: for matrix over a finite field, and field order",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 61
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "MeatAxeString: for permutation, field order, and dimensions",
+                    "filters": [
+                        [
+                            "IsPerm"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 29
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MeatAxeString",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnknown"
+                ]
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Maxes: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Maxes)"
+                        ]
+                    ],
+                    "rank": 20019
+                },
+                {
+                    "comment": "Maxes",
+                    "filters": [
+                        [
+                            "IsUnknown"
+                        ]
+                    ],
+                    "rank": 16
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Maxes",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnknown"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Maxes): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Maxes): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Maxes)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnknown"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Maxes)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AtlasRepInfoRecord: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AtlasRepInfoRecord)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "AtlasRepInfoRecord: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AtlasRepInfoRecord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AtlasRepInfoRecord): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AtlasRepInfoRecord): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AtlasRepInfoRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AtlasRepInfoRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ],
+            [
+                [],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Browse: [ IsFFECollColl and IsMatrix ]",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "Browse: [ IsFFECollColl and IsMatrix ]",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsFFE))"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "Browse: [ IsZmodnZObjNonprimeCollColl and IsMatrix ]",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+                            "CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"
+                        ]
+                    ],
+                    "rank": 41
+                },
+                {
+                    "comment": "Browse: [ IsNearlyCharacterTable ]",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "Browse: [ IsDenseList ]",
+                    "filters": [
+                        [
+                            "IsDenseList"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "Browse: [ IsTableOfMarks ]",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Browse: [ IsNearlyCharacterTable, IsRecord ]",
+                    "filters": [
+                        [
+                            "IsNearlyCharacterTable"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "Browse: [ IsTableOfMarks, IsRecord ]",
+                    "filters": [
+                        [
+                            "IsTableOfMarks"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Browse",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CASInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CASInfo)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CASInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CASInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CASInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CASInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CASInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConstructionInfoCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConstructionInfoCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConstructionInfoCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConstructionInfoCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConstructionInfoCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConstructionInfoCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConstructionInfoCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FusionToTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FusionToTom)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FusionToTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FusionToTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FusionToTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FusionToTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FusionToTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ProjectivesInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ProjectivesInfo)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ProjectivesInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ProjectivesInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ProjectivesInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ProjectivesInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ProjectivesInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExtensionInfoCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ExtensionInfoCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExtensionInfoCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ExtensionInfoCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ExtensionInfoCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ExtensionInfoCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ExtensionInfoCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupInfoForCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GroupInfoForCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "GroupInfoForCharacterTable: [ IsOrdinaryTable and IsLibraryCharacterTableRep ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable",
+                            "IsLibraryCharacterTableRep"
+                        ]
+                    ],
+                    "rank": 25
+                },
+                {
+                    "comment": "GroupInfoForCharacterTable: [ IsString ]",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupInfoForCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GroupInfoForCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GroupInfoForCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GroupInfoForCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GroupInfoForCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KnowsSomeGroupInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KnowsSomeGroupInfo)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "KnowsSomeGroupInfo: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnowsSomeGroupInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KnowsSomeGroupInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KnowsSomeGroupInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KnowsSomeGroupInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KnowsSomeGroupInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNontrivialDirectProduct: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNontrivialDirectProduct)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsNontrivialDirectProduct: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNontrivialDirectProduct",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNontrivialDirectProduct): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNontrivialDirectProduct): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNontrivialDirectProduct)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNontrivialDirectProduct)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "KnowsDeligneLusztigNames: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(KnowsDeligneLusztigNames)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "KnowsDeligneLusztigNames: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "KnowsDeligneLusztigNames",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(KnowsDeligneLusztigNames): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(KnowsDeligneLusztigNames): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(KnowsDeligneLusztigNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(KnowsDeligneLusztigNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsDuplicateTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsDuplicateTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IsDuplicateTable: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsDuplicateTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsDuplicateTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsDuplicateTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsDuplicateTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsDuplicateTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdentifierOfMainTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdentifierOfMainTable)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IdentifierOfMainTable: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdentifierOfMainTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdentifierOfMainTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdentifierOfMainTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdentifierOfMainTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdentifierOfMainTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdentifiersOfDuplicateTables: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdentifiersOfDuplicateTables)"
+                        ]
+                    ],
+                    "rank": 20023
+                },
+                {
+                    "comment": "IdentifiersOfDuplicateTables: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                },
+                {
+                    "comment": "IdentifiersOfDuplicateTables: [ IsString ]",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdentifiersOfDuplicateTables",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdentifiersOfDuplicateTables): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdentifiersOfDuplicateTables): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdentifiersOfDuplicateTables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdentifiersOfDuplicateTables)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ],
+            [
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DeligneLusztigNames: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DeligneLusztigNames)"
+                        ]
+                    ],
+                    "rank": 20024
+                },
+                {
+                    "comment": "DeligneLusztigNames: [ IsCharacterTable ]",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ]
+                    ],
+                    "rank": 21
+                },
+                {
+                    "comment": "DeligneLusztigNames: [ IsString ]",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "DeligneLusztigNames: [ IsRecord ]",
+                    "filters": [
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 1
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeligneLusztigNames",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsString"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsRecord"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DeligneLusztigNames): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DeligneLusztigNames): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DeligneLusztigNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DeligneLusztigNames)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacter",
+                    "Tester(IsCharacter)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DeligneLusztigName: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DeligneLusztigName)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "DeligneLusztigName: [ IsCharacter ]",
+                    "filters": [
+                        [
+                            "IsCharacter",
+                            "Tester(IsCharacter)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "DeligneLusztigName: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DeligneLusztigName",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacter",
+                    "Tester(IsCharacter)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DeligneLusztigName): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DeligneLusztigName): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DeligneLusztigName)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacter",
+                    "Tester(IsCharacter)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DeligneLusztigName)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "UnipotentCharacter: [ IsCharacterTable, IsObject ]",
+                    "filters": [
+                        [
+                            "IsCharacterTable"
+                        ],
+                        []
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnipotentCharacter",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FingerprintOfCharacterTable: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FingerprintOfCharacterTable)"
+                        ]
+                    ],
+                    "rank": 20025
+                },
+                {
+                    "comment": "FingerprintOfCharacterTable: [ IsOrdinaryTable ]",
+                    "filters": [
+                        [
+                            "IsOrdinaryTable"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FingerprintOfCharacterTable",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FingerprintOfCharacterTable): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FingerprintOfCharacterTable): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FingerprintOfCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOrdinaryTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FingerprintOfCharacterTable)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpinSymIngredients: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SpinSymIngredients)"
+                        ]
+                    ],
+                    "rank": 20023
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpinSymIngredients",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SpinSymIngredients): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SpinSymIngredients): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SpinSymIngredients)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNearlyCharacterTable"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SpinSymIngredients)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NamesLibTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NamesLibTom)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "NamesLibTom",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "NamesLibTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "IsLibTomRep"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NamesLibTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsString"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NamesLibTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NamesLibTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NamesLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NamesLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NotifiedFusionsOfLibTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NotifiedFusionsOfLibTom)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "NotifiedFusionsOfLibTom",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "NotifiedFusionsOfLibTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "IsLibTomRep"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NotifiedFusionsOfLibTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsString"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NotifiedFusionsOfLibTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NotifiedFusionsOfLibTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NotifiedFusionsOfLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NotifiedFusionsOfLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FusionsOfLibTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FusionsOfLibTom)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FusionsOfLibTom",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "FusionsOfLibTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "IsLibTomRep"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FusionsOfLibTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsString"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FusionsOfLibTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FusionsOfLibTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FusionsOfLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FusionsOfLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NotifiedFusionsToLibTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NotifiedFusionsToLibTom)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "NotifiedFusionsToLibTom",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "NotifiedFusionsToLibTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "IsLibTomRep"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NotifiedFusionsToLibTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsString"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NotifiedFusionsToLibTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NotifiedFusionsToLibTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NotifiedFusionsToLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NotifiedFusionsToLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ],
+            [
+                [
+                    "IsString"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FusionsToLibTom: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FusionsToLibTom)"
+                        ]
+                    ],
+                    "rank": 20005
+                },
+                {
+                    "comment": "FusionsToLibTom",
+                    "filters": [
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 5
+                },
+                {
+                    "comment": "FusionsToLibTom",
+                    "filters": [
+                        [
+                            "IsTableOfMarks",
+                            "IsLibTomRep"
+                        ]
+                    ],
+                    "rank": 4
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FusionsToLibTom",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsString"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FusionsToLibTom): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FusionsToLibTom): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FusionsToLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTableOfMarks",
+                    "IsLibTomRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FusionsToLibTom)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "StandardGeneratorsInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(StandardGeneratorsInfo)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "StandardGeneratorsInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "StandardGeneratorsInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsTableOfMarks"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(StandardGeneratorsInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(StandardGeneratorsInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(StandardGeneratorsInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(StandardGeneratorsInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsList"
+                ],
+                [
+                    "IsFunction"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IteratedF",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "IteratedF",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsFunction"
+                        ],
+                        []
+                    ],
+                    "rank": 3
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IteratedF",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TrivialInvAutomaton",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TrivialInvAutomaton",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMutable",
+                    "IsInvAutomatonCategory"
+                ],
+                [
+                    "IsMultiplicativeElementWithInverse",
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "InvAutomatonInsertGenerator",
+                    "filters": [
+                        [
+                            "IsMutable",
+                            "IsSimpleInvAutomatonRep"
+                        ],
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 15
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InvAutomatonInsertGenerator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInvAutomatonCategory"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FGA_States: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FGA_States)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "FGA_States: for simple inverse Automata",
+                    "filters": [
+                        [
+                            "IsSimpleInvAutomatonRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FGA_States",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInvAutomatonCategory"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FGA_States): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FGA_States): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FGA_States)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInvAutomatonCategory"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FGA_States)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInvAutomatonCategory"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FGA_GeneratorsLetterRep: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FGA_GeneratorsLetterRep)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "FGA_GeneratorsLetterRep: for simple inverse Automata",
+                    "filters": [
+                        [
+                            "IsSimpleInvAutomatonRep"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FGA_GeneratorsLetterRep",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInvAutomatonCategory"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FGA_GeneratorsLetterRep): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FGA_GeneratorsLetterRep): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FGA_GeneratorsLetterRep)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInvAutomatonCategory"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FGA_GeneratorsLetterRep)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGeneratorsOfGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGeneratorsOfGroup)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "FreeGeneratorsOfGroup: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "FreeGeneratorsOfGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGeneratorsOfGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGeneratorsOfGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGeneratorsOfGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGeneratorsOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGeneratorsOfGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RankOfFreeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RankOfFreeGroup)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "RankOfFreeGroup: for a whole free group",
+                    "filters": [
+                        [
+                            "IsWholeFamily",
+                            "Tester(IsWholeFamily)",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "RankOfFreeGroup: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "RankOfFreeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RankOfFreeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RankOfFreeGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RankOfFreeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RankOfFreeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RankOfFreeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGroupAutomaton: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGroupAutomaton)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "FreeGroupAutomaton: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "FreeGroupAutomaton: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGroupAutomaton",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGroupAutomaton): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGroupAutomaton): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGroupAutomaton)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGroupAutomaton)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FreeGroupExtendedAutomaton: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FreeGroupExtendedAutomaton)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "FreeGroupExtendedAutomaton: for a subgroup of a free group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "FreeGroupExtendedAutomaton: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 11
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FreeGroupExtendedAutomaton",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FreeGroupExtendedAutomaton): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FreeGroupExtendedAutomaton): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FreeGroupExtendedAutomaton)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FreeGroupExtendedAutomaton)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse",
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsWordLetterRepInFreeGenerators: for an element in a free group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsWordLetterRepInFreeGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse",
+                    "IsAssociativeElement",
+                    "IsWord"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AsWordLetterRepInGenerators: for an element in a free group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "Tester(GeneratorsOfMagmaWithInverses)",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 58
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsWordLetterRepInGenerators",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElementWithInverse",
+                    "IsAssociativeElement",
+                    "IsWord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CyclicallyReducedWord: for an element in a free group",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElementWithInverse",
+                            "IsAssociativeElement",
+                            "IsWord"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CyclicallyReducedWord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [
+                {
+                    "comment": "FindPowLetterRep",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 56
+                }
+            ],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FindPowLetterRep",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizerInWholeGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizerInWholeGroup)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "NormalizerInWholeGroup",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "NormalizerInWholeGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerInWholeGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizerInWholeGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizerInWholeGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizerInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizerInWholeGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromFpGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FGA_Source: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FGA_Source)"
+                        ]
+                    ],
+                    "rank": 20030
+                },
+                {
+                    "comment": "FGA_Source",
+                    "filters": [
+                        [
+                            "Tester(MappingGeneratorsImages)",
+                            "IsFromFpGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FGA_Source",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromFpGroupGeneralMappingByImages"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FGA_Source): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FGA_Source): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FGA_Source)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFromFpGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FGA_Source)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsToFpGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FGA_Image: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FGA_Image)"
+                        ]
+                    ],
+                    "rank": 20019
+                },
+                {
+                    "comment": "FGA_Image",
+                    "filters": [
+                        [
+                            "Tester(MappingGeneratorsImages)",
+                            "IsToFpGroupGeneralMappingByImages"
+                        ]
+                    ],
+                    "rank": 19
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FGA_Image",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsToFpGroupGeneralMappingByImages"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FGA_Image): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FGA_Image): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FGA_Image)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsToFpGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FGA_Image)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FGA_WhiteheadParams: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FGA_WhiteheadParams)"
+                        ]
+                    ],
+                    "rank": 20020
+                },
+                {
+                    "comment": "FGA_WhiteheadParams: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FGA_WhiteheadParams",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FGA_WhiteheadParams): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FGA_WhiteheadParams): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FGA_WhiteheadParams)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "RespectsMultiplication",
+                    "Tester(RespectsMultiplication)",
+                    "RespectsInverses",
+                    "Tester(RespectsInverses)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FGA_WhiteheadParams)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FGA_WhiteheadAutomorphisms: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FGA_WhiteheadAutomorphisms)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "FGA_WhiteheadAutomorphisms: for finitely generated free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "FGA_WhiteheadAutomorphisms: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FGA_WhiteheadAutomorphisms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FGA_WhiteheadAutomorphisms): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FGA_WhiteheadAutomorphisms): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FGA_WhiteheadAutomorphisms)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FGA_WhiteheadAutomorphisms)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FGA_NielsenAutomorphisms: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FGA_NielsenAutomorphisms)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "FGA_NielsenAutomorphisms: for finitely generated free groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsFinitelyGeneratedGroup",
+                            "Tester(IsFinitelyGeneratedGroup)",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "FGA_NielsenAutomorphisms: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FGA_NielsenAutomorphisms",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FGA_NielsenAutomorphisms): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FGA_NielsenAutomorphisms): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FGA_NielsenAutomorphisms)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FGA_NielsenAutomorphisms)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIrreducibleMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIrreducibleMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsIrreducibleMatrixGroup: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsIrreducibleMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "IsIrreducibleMatrixGroup: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIrreducibleMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIrreducibleMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIrreducibleMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Setter(IsIrreducibleMatrixGroup): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        []
+                    ],
+                    "rank": 95
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIrreducibleMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Tester(IsIrreducibleMatrixGroup): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIrreducibleMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsIrreducibleMatrixGroupOp: for matrix group and finite field - for absolutely irreducible matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsAbsolutelyIrreducibleMatrixGroup",
+                            "Tester(IsAbsolutelyIrreducibleMatrixGroup)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 148
+                },
+                {
+                    "comment": "IsIrreducibleMatrixGroupOp: for matrix group and finite field - test attr IsIrreducibleMatrixGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(IsIrreducibleMatrixGroup)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 103
+                },
+                {
+                    "comment": "IsIrreducibleMatrixGroupOp: for matrix group and finite field - use MeatAxe",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 102
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIrreducibleMatrixGroupOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedIsIrreducibleMatrixGroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedIsIrreducibleMatrixGroups)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "ComputedIsIrreducibleMatrixGroups: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ComputedIsIrreducibleMatrixGroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedIsIrreducibleMatrixGroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedIsIrreducibleMatrixGroups): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedIsIrreducibleMatrixGroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedIsIrreducibleMatrixGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedIsIrreducibleMatrixGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAbsolutelyIrreducible: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAbsolutelyIrreducible",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAbsolutelyIrreducibleMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAbsolutelyIrreducibleMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsAbsolutelyIrreducibleMatrixGroup: for mat group over finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsAbsolutelyIrreducibleMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAbsolutelyIrreducibleMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAbsolutelyIrreducibleMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAbsolutelyIrreducibleMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAbsolutelyIrreducibleMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAbsolutelyIrreducibleMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsPrimitiveMatrixGroupOp: for matrix group over finite field, try if IsPrimitive is set",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(IsPrimitive)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 442
+                },
+                {
+                    "comment": "IsPrimitiveMatrixGroupOp: for matrix group over finite field, use RepresentationIsomorphism",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(RepresentationIsomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 439
+                },
+                {
+                    "comment": "IsPrimitiveMatrixGroupOp: for matrix group over finite field, use nice monomorphism",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 437
+                },
+                {
+                    "comment": "IsPrimitiveMatrixGroupOp: for matrix group over finite field, construct IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 104
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPrimitiveMatrixGroupOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedIsPrimitiveMatrixGroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedIsPrimitiveMatrixGroups)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "ComputedIsPrimitiveMatrixGroups: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ComputedIsPrimitiveMatrixGroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedIsPrimitiveMatrixGroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedIsPrimitiveMatrixGroups): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedIsPrimitiveMatrixGroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedIsPrimitiveMatrixGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedIsPrimitiveMatrixGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimalBlockDimensionOfMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroup: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroup: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalBlockDimensionOfMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimalBlockDimensionOfMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimalBlockDimensionOfMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Setter(MinimalBlockDimensionOfMatrixGroup): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        []
+                    ],
+                    "rank": 95
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimalBlockDimensionOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Tester(MinimalBlockDimensionOfMatrixGroup): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimalBlockDimensionOfMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field which has MinimalBlockDimension",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MinimalBlockDimension)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 439
+                },
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field with representation homomorphism",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(RepresentationIsomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 439
+                },
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field, use NiceMonomorphism",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 437
+                },
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroupOp: for matrix group over finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 104
+                },
+                {
+                    "comment": "MinimalBlockDimensionOfMatrixGroupOp: for matrix group having imprimitivity systems",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(ComputedImprimitivitySystemss)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 99
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalBlockDimensionOfMatrixGroupOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedMinimalBlockDimensionOfMatrixGroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedMinimalBlockDimensionOfMatrixGroups)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "ComputedMinimalBlockDimensionOfMatrixGroups: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ComputedMinimalBlockDimensionOfMatrixGroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedMinimalBlockDimensionOfMatrixGroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedMinimalBlockDimensionOfMatrixGroups): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedMinimalBlockDimensionOfMatrixGroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedMinimalBlockDimensionOfMatrixGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedMinimalBlockDimensionOfMatrixGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CharacteristicOfField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CharacteristicOfField)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "CharacteristicOfField: for matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "CharacteristicOfField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CharacteristicOfField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CharacteristicOfField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CharacteristicOfField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CharacteristicOfField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CharacteristicOfField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RepresentationIsomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RepresentationIsomorphism)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "RepresentationIsomorphism: for mat group handled by nice mono.",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ]
+                    ],
+                    "rank": 378
+                },
+                {
+                    "comment": "RepresentationIsomorphism: solvable group: inverse of IsomorphismPcGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "RepresentationIsomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentationIsomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RepresentationIsomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RepresentationIsomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RepresentationIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RepresentationIsomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ImprimitivitySystems: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ImprimitivitySystems)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "ImprimitivitySystems: for matrix group: use FieldOfMatrixGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "ImprimitivitySystems: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "ImprimitivitySystems: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImprimitivitySystems",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ImprimitivitySystems): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ImprimitivitySystems): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Setter(ImprimitivitySystems): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ],
+                        []
+                    ],
+                    "rank": 95
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ImprimitivitySystems)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ],
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Tester(ImprimitivitySystems): default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 95
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ImprimitivitySystems)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsNonTrivial",
+                    "Tester(IsNonTrivial)",
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsMagmaWithInversesIfNonzero",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsCommutative",
+                    "Tester(IsCommutative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ImprimitivitySystemsOp: for matrix group handled by nice mono. and finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 437
+                },
+                {
+                    "comment": "ImprimitivitySystemsOp: for matrix group handled by nice mono. and finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsHandledByNiceMonomorphism",
+                            "Tester(IsHandledByNiceMonomorphism)"
+                        ],
+                        [
+                            "IsNonTrivial",
+                            "Tester(IsNonTrivial)",
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsMagmaWithInversesIfNonzero",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsCommutative",
+                            "Tester(IsCommutative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsEuclideanRing"
+                        ]
+                    ],
+                    "rank": 437
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ImprimitivitySystemsOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedImprimitivitySystemss: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedImprimitivitySystemss)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "ComputedImprimitivitySystemss: default method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "ComputedImprimitivitySystemss: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedImprimitivitySystemss",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedImprimitivitySystemss): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedImprimitivitySystemss): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedImprimitivitySystemss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedImprimitivitySystemss)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TraceField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TraceField)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "TraceField: for irreducible matrix group over finite field",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 394
+                },
+                {
+                    "comment": "TraceField: generic method for finite matrix groups via conjugacy classes",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 390
+                },
+                {
+                    "comment": "TraceField:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "TraceField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TraceField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TraceField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TraceField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TraceField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TraceField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ConjugatingMatTraceField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ConjugatingMatTraceField)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "ConjugatingMatTraceField: for irreducible FFE matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "ConjugatingMatTraceField: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugatingMatTraceField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ConjugatingMatTraceField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ConjugatingMatTraceField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ConjugatingMatTraceField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ConjugatingMatTraceField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "FingerprintMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(FingerprintMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "FingerprintMatrixGroup: for irreducible FFE matrix group",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "FingerprintMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "FingerprintMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(FingerprintMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(FingerprintMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(FingerprintMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(FingerprintMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdIrreducibleSolvableMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdIrreducibleSolvableMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IdIrreducibleSolvableMatrixGroup: for irreducible solvable matrix group over finite field",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)",
+                            "IsIrreducibleMatrixGroup",
+                            "Tester(IsIrreducibleMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "IdIrreducibleSolvableMatrixGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "IdIrreducibleSolvableMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdIrreducibleSolvableMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdIrreducibleSolvableMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdIrreducibleSolvableMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdIrreducibleSolvableMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdIrreducibleSolvableMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IdPrimitiveSolvableGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IdPrimitiveSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IdPrimitiveSolvableGroup: for solvable group",
+                    "filters": [
+                        [
+                            "IsFinite",
+                            "Tester(IsFinite)",
+                            "IsSolvableGroup",
+                            "Tester(IsSolvableGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IdPrimitiveSolvableGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "IdPrimitiveSolvableGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IdPrimitiveSolvableGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IdPrimitiveSolvableGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IdPrimitiveSolvableGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IdPrimitiveSolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IdPrimitiveSolvableGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotent",
+                    "Tester(IsLieNilpotent)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieNilpotentOverFp: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieNilpotentOverFp)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsLieNilpotentOverFp",
+                    "filters": [
+                        [
+                            "IsLieNilpotent",
+                            "Tester(IsLieNilpotent)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsLieNilpotentOverFp: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieNilpotentOverFp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotent",
+                    "Tester(IsLieNilpotent)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieNilpotentOverFp): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieNilpotentOverFp): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieNilpotentOverFp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotent",
+                    "Tester(IsLieNilpotent)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieNilpotentOverFp)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AutomorphismGroupOfNilpotentLieAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AutomorphismGroupOfNilpotentLieAlgebra)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "AutomorphismGroupOfNilpotentLieAlgebra: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "AutomorphismGroupOfNilpotentLieAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AutomorphismGroupOfNilpotentLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AutomorphismGroupOfNilpotentLieAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AutomorphismGroupOfNilpotentLieAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AutomorphismGroupOfNilpotentLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AutomorphismGroupOfNilpotentLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "DescendantsOfStep1OfAbelianLieAlgebra: for abelian Lie algebras",
+                    "filters": [
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 38
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DescendantsOfStep1OfAbelianLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Descendants: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 61
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Descendants",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotent",
+                    "Tester(IsLieNilpotent)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "MinimalGeneratorNumber: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(MinimalGeneratorNumber)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "MinimalGeneratorNumber: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsLieNilpotentOverFp",
+                            "Tester(IsLieNilpotentOverFp)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "MinimalGeneratorNumber: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "MinimalGeneratorNumber",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotent",
+                    "Tester(IsLieNilpotent)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(MinimalGeneratorNumber): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(MinimalGeneratorNumber): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(MinimalGeneratorNumber)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotent",
+                    "Tester(IsLieNilpotent)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(MinimalGeneratorNumber)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "IsNilpotentLieAutomorphismRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LiftAutorphismToLieCover: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LiftAutorphismToLieCover",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)",
+                    "IsNilpotentLieAutomorphismRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LinearActionOnMultiplicator: for nilpotent Lie algebra automorphisms",
+                    "filters": [
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)",
+                            "IsNilpotentLieAutomorphismRep"
+                        ]
+                    ],
+                    "rank": 22
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LinearActionOnMultiplicator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NilpotentLieAutomorphism: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsLieNilpotentOverFp",
+                            "Tester(IsLieNilpotentOverFp)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 52
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NilpotentLieAutomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieCover: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieCover)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "IsLieCover: for nilpotent Lie algebras with nilpotent presentation",
+                    "filters": [
+                        [
+                            "IsLieNilpotentOverFp",
+                            "Tester(IsLieNilpotentOverFp)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsLieCover: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieCover",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieCover): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieCover): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieCover",
+                    "Tester(IsLieCover)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoverOf: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoverOf)"
+                        ]
+                    ],
+                    "rank": 20053
+                },
+                {
+                    "comment": "CoverOf: for nilpotent Lie algebras with nilpotent presentation",
+                    "filters": [
+                        [
+                            "IsLieCover",
+                            "Tester(IsLieCover)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "CoverOf: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoverOf",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieCover",
+                    "Tester(IsLieCover)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoverOf): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoverOf): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoverOf)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieCover",
+                    "Tester(IsLieCover)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoverOf)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieCover",
+                    "Tester(IsLieCover)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoverHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoverHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20053
+                },
+                {
+                    "comment": "CoverHomomorphism: for nilpotent Lie algebras with nilpotent presentation",
+                    "filters": [
+                        [
+                            "IsLieCover",
+                            "Tester(IsLieCover)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "CoverHomomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoverHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieCover",
+                    "Tester(IsLieCover)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoverHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoverHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoverHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieCover",
+                    "Tester(IsLieCover)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoverHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieCover: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieCover)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieCover: for nilpotent Lie algebras with nilpotent presentation",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieCover: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieCover",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieCover): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieCover): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieCover)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieNucleus: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieNucleus)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "LieNucleus: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsLieNilpotentOverFp",
+                            "Tester(IsLieNilpotentOverFp)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "LieNucleus: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieNucleus",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieNucleus): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieNucleus): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieNucleus)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieNucleus)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieMultiplicator: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieMultiplicator)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "LieMultiplicator: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsLieNilpotentOverFp",
+                            "Tester(IsLieNilpotentOverFp)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "LieMultiplicator: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieMultiplicator",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieMultiplicator): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieMultiplicator): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieMultiplicator)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieMultiplicator)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "LiftIsomorphismToLieCover: for nilpotent Lie algebras with nilpotent presentation",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 114
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LiftIsomorphismToLieCover",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AreIsomorphicNilpotentLieAlgebras: for nilpotent Lie algebras with nilpotent presentation",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ],
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 84
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AreIsomorphicNilpotentLieAlgebras",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieAlgebraWithNB: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieAlgebraWithNB)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "IsLieAlgebraWithNB: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsLieNilpotentOverFp",
+                            "Tester(IsLieNilpotentOverFp)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsLieAlgebraWithNB: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieAlgebraWithNB",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieAlgebraWithNB): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieAlgebraWithNB): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieAlgebraWithNB)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieNilpotentOverFp",
+                    "Tester(IsLieNilpotentOverFp)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieAlgebraWithNB)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NilpotentBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NilpotentBasis)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "NilpotentBasis: for nilpotent Lie algebras",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "NilpotentBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NilpotentBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NilpotentBasis): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NilpotentBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NilpotentBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NilpotentBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNilpotentBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNilpotentBasis)"
+                        ]
+                    ],
+                    "rank": 20010
+                },
+                {
+                    "comment": "IsNilpotentBasis: for bases of Lie algebras",
+                    "filters": [
+                        [
+                            "IsBasis"
+                        ]
+                    ],
+                    "rank": 7
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNilpotentBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNilpotentBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNilpotentBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNilpotentBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNilpotentBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNilpotentBasis",
+                    "Tester(IsNilpotentBasis)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieNBDefinitions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieNBDefinitions)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "LieNBDefinitions: for NB bases of Lie algebras",
+                    "filters": [
+                        [
+                            "IsNilpotentBasis",
+                            "Tester(IsNilpotentBasis)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "LieNBDefinitions: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieNBDefinitions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNilpotentBasis",
+                    "Tester(IsNilpotentBasis)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieNBDefinitions): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieNBDefinitions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieNBDefinitions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNilpotentBasis",
+                    "Tester(IsNilpotentBasis)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieNBDefinitions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNilpotentBasis",
+                    "Tester(IsNilpotentBasis)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieNBWeights: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieNBWeights)"
+                        ]
+                    ],
+                    "rank": 20012
+                },
+                {
+                    "comment": "LieNBWeights: for NB bases of Lie algebras",
+                    "filters": [
+                        [
+                            "IsNilpotentBasis",
+                            "Tester(IsNilpotentBasis)"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "LieNBWeights: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieNBWeights",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNilpotentBasis",
+                    "Tester(IsNilpotentBasis)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieNBWeights): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieNBWeights): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieNBWeights)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNilpotentBasis",
+                    "Tester(IsNilpotentBasis)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieNBWeights)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 20041
+                },
+                {
+                    "comment": "IsGroupAlgebra",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "IsGroupAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupAlgebra",
+                    "Tester(IsGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFModularGroupAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 20043
+                },
+                {
+                    "comment": "IsFModularGroupAlgebra",
+                    "filters": [
+                        [
+                            "IsGroupAlgebra",
+                            "Tester(IsGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "IsFModularGroupAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFModularGroupAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupAlgebra",
+                    "Tester(IsGroupAlgebra)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFModularGroupAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFModularGroupAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFModularGroupAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupAlgebra",
+                    "Tester(IsGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFModularGroupAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFModularGroupAlgebra",
+                    "Tester(IsFModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPModularGroupAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsPModularGroupAlgebra",
+                    "filters": [
+                        [
+                            "IsFModularGroupAlgebra",
+                            "Tester(IsFModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsPModularGroupAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPModularGroupAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFModularGroupAlgebra",
+                    "Tester(IsFModularGroupAlgebra)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPModularGroupAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPModularGroupAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPModularGroupAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFModularGroupAlgebra",
+                    "Tester(IsFModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPModularGroupAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ],
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingRing)"
+                        ]
+                    ],
+                    "rank": 20041
+                },
+                {
+                    "comment": "UnderlyingRing",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "UnderlyingRing: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupAlgebra",
+                    "Tester(IsGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingField)"
+                        ]
+                    ],
+                    "rank": 20043
+                },
+                {
+                    "comment": "UnderlyingField",
+                    "filters": [
+                        [
+                            "IsGroupAlgebra",
+                            "Tester(IsGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 40
+                },
+                {
+                    "comment": "UnderlyingField: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupAlgebra",
+                    "Tester(IsGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupAlgebra",
+                    "Tester(IsGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Support: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Support)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Support: LAGUNA: for an element of a magma ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Support",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Support): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Support): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Support)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Support)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CoefficientsBySupport: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CoefficientsBySupport)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "CoefficientsBySupport: LAGUNA: for an element of a magma ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CoefficientsBySupport",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CoefficientsBySupport): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CoefficientsBySupport): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CoefficientsBySupport)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CoefficientsBySupport)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TraceOfMagmaRingElement: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TraceOfMagmaRingElement)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "TraceOfMagmaRingElement: LAGUNA: for an element of a magma ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TraceOfMagmaRingElement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TraceOfMagmaRingElement): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TraceOfMagmaRingElement): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TraceOfMagmaRingElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TraceOfMagmaRingElement)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Augmentation: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Augmentation)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "Augmentation: LAGUNA: for an element of a magma ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Augmentation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Augmentation): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Augmentation): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Augmentation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Augmentation)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PartialAugmentations: LAGUNA: for a group ring and its element",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 51
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PartialAugmentations",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Involution: LAGUNA: classical involution for an element of a group ring ",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "Involution: LAGUNA: for a group ring element and a group endomapping of order 2",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 24
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "Involution: LAGUNA: for a group ring element, and a group endomapping of order 2 and a mapping from the group to a ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ],
+                        [
+                            "IsGeneralMapping",
+                            "IsTotal",
+                            "Tester(IsTotal)",
+                            "IsSingleValued",
+                            "Tester(IsSingleValued)"
+                        ]
+                    ],
+                    "rank": 35
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Involution",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSymmetric: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSymmetric)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsSymmetric: LAGUNA: for group ring elements",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSymmetric",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSymmetric): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSymmetric): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSymmetric)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSymmetric)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUnitary: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsUnitary)"
+                        ]
+                    ],
+                    "rank": 20016
+                },
+                {
+                    "comment": "IsUnitary: LAGUNA: for group ring elements",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 13
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUnitary",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsUnitary): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsUnitary): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsUnitary)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsUnitary)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "LeftIdealBySubgroup: LAGUNA: for a group ring and a subgroup of underlying group",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LeftIdealBySubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RightIdealBySubgroup: LAGUNA: for a group ring and a subgroup of underlying group",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RightIdealBySubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "TwoSidedIdealBySubgroup: LAGUNA: for a group ring and a subgroup of underlying group",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ],
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 71
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TwoSidedIdealBySubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WeightedBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WeightedBasis)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "WeightedBasis: LAGUNA: for modular group algebra of a finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "WeightedBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WeightedBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WeightedBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WeightedBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WeightedBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WeightedBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentationIdealPowerSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentationIdealPowerSeries)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "AugmentationIdealPowerSeries: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "AugmentationIdealPowerSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentationIdealPowerSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentationIdealPowerSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentationIdealPowerSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentationIdealPowerSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentationIdealPowerSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentationIdealNilpotencyIndex: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentationIdealNilpotencyIndex)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "AugmentationIdealNilpotencyIndex: LAGUNA: for a modular group algebra of a finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "AugmentationIdealNilpotencyIndex: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentationIdealNilpotencyIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentationIdealNilpotencyIndex): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentationIdealNilpotencyIndex): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentationIdealNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentationIdealNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentationIdealOfDerivedSubgroupNilpotencyIndex: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "AugmentationIdealOfDerivedSubgroupNilpotencyIndex: LAGUNA: for a modular group algebra of a finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "AugmentationIdealOfDerivedSubgroupNilpotencyIndex: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentationIdealOfDerivedSubgroupNilpotencyIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentationIdealOfDerivedSubgroupNilpotencyIndex): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentationIdealOfDerivedSubgroupNilpotencyIndex): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsGroupOfUnitsOfMagmaRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsGroupOfUnitsOfMagmaRing)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsGroupOfUnitsOfMagmaRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsGroupOfUnitsOfMagmaRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsGroupOfUnitsOfMagmaRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsGroupOfUnitsOfMagmaRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsGroupOfUnitsOfMagmaRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsGroupOfUnitsOfMagmaRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsUnitGroupOfGroupRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsUnitGroupOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "IsUnitGroupOfGroupRing: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsUnitGroupOfGroupRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsUnitGroupOfGroupRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsUnitGroupOfGroupRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsUnitGroupOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsUnitGroupOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsNormalizedUnitGroupOfGroupRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "IsNormalizedUnitGroupOfGroupRing: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsNormalizedUnitGroupOfGroupRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsNormalizedUnitGroupOfGroupRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsNormalizedUnitGroupOfGroupRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsNormalizedUnitGroupOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsNormalizedUnitGroupOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingGroupRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingGroupRing)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "UnderlyingGroupRing: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingGroupRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingGroupRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingGroupRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupOfUnitsOfMagmaRing",
+                    "Tester(IsGroupOfUnitsOfMagmaRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NormalizedUnitCF: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizedUnitCF",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                [
+                    "IsElementOfMagmaRingModuloRelations",
+                    "IsMagmaRingObjDefaultRep"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "NormalizedUnitCFmod: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 76
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizedUnitCFmod",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizedUnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizedUnitGroup)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "NormalizedUnitGroup: LAGUNA: for modular group algebra of a finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "NormalizedUnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizedUnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizedUnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizedUnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcNormalizedUnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcNormalizedUnitGroup)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "PcNormalizedUnitGroup: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "PcNormalizedUnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcNormalizedUnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcNormalizedUnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcNormalizedUnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcNormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcNormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AugmentationIdealPowerFactorGroupOp: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentationIdealPowerFactorGroupOp",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ComputedAugmentationIdealPowerFactorGroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ComputedAugmentationIdealPowerFactorGroups)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "ComputedAugmentationIdealPowerFactorGroups: default method",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "ComputedAugmentationIdealPowerFactorGroups: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ComputedAugmentationIdealPowerFactorGroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ComputedAugmentationIdealPowerFactorGroups): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ComputedAugmentationIdealPowerFactorGroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ComputedAugmentationIdealPowerFactorGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ComputedAugmentationIdealPowerFactorGroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AugmentationIdealPowerFactorGroup: default method",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentationIdealPowerFactorGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "HasAugmentationIdealPowerFactorGroup: default method",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 63
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HasAugmentationIdealPowerFactorGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "SetAugmentationIdealPowerFactorGroup: default method",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        []
+                    ],
+                    "rank": 63
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SetAugmentationIdealPowerFactorGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcUnits: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PcUnits)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "PcUnits: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "PcUnits: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcUnits",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PcUnits): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PcUnits): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PcUnits)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PcUnits)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalBijectionToPcNormalizedUnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalBijectionToPcNormalizedUnitGroup)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "NaturalBijectionToPcNormalizedUnitGroup: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "NaturalBijectionToPcNormalizedUnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalBijectionToPcNormalizedUnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalBijectionToPcNormalizedUnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalBijectionToPcNormalizedUnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalBijectionToPcNormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalBijectionToPcNormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalBijectionToNormalizedUnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalBijectionToNormalizedUnitGroup)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "NaturalBijectionToNormalizedUnitGroup: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "NaturalBijectionToNormalizedUnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalBijectionToNormalizedUnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalBijectionToNormalizedUnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalBijectionToNormalizedUnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalBijectionToNormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalBijectionToNormalizedUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GroupBases: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GroupBases)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "GroupBases: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "GroupBases: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GroupBases",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GroupBases): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GroupBases): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GroupBases)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GroupBases)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BassCyclicUnit: for uderlying group element, embedded into group ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 32
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "BassCyclicUnit: for uderlying group element, not embedded into group ring",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ],
+                        [],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 57
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BassCyclicUnit",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BicyclicUnitOfType1: for uderlying group elements, embedded into group ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "BicyclicUnitOfType1: for uderlying group elements, not embedded into group ring",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 38
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BicyclicUnitOfType1",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                [],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BicyclicUnitOfType2: for uderlying group elements, embedded into group ring",
+                    "filters": [
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ],
+                        [
+                            "IsElementOfMagmaRingModuloRelations",
+                            "IsMagmaRingObjDefaultRep"
+                        ]
+                    ],
+                    "rank": 26
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "BicyclicUnitOfType2: for uderlying group elements, not embedded into group ring",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ],
+                        [],
+                        []
+                    ],
+                    "rank": 38
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BicyclicUnitOfType2",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNormalizedUnitGroupOfGroupRing",
+                    "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BicyclicUnitGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BicyclicUnitGroup)"
+                        ]
+                    ],
+                    "rank": 20040
+                },
+                {
+                    "comment": "BicyclicUnitGroup: for the normalized unit group in pc-presentation",
+                    "filters": [
+                        [
+                            "IsNormalizedUnitGroupOfGroupRing",
+                            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "BicyclicUnitGroup: for the normalized unit group in natural representation",
+                    "filters": [
+                        [
+                            "IsNormalizedUnitGroupOfGroupRing",
+                            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "BicyclicUnitGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BicyclicUnitGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNormalizedUnitGroupOfGroupRing",
+                    "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BicyclicUnitGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BicyclicUnitGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BicyclicUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNormalizedUnitGroupOfGroupRing",
+                    "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BicyclicUnitGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNormalizedUnitGroupOfGroupRing",
+                    "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnitarySubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnitarySubgroup)"
+                        ]
+                    ],
+                    "rank": 20040
+                },
+                {
+                    "comment": "UnitarySubgroup: for the normalized unit group in pc-presentation",
+                    "filters": [
+                        [
+                            "IsNormalizedUnitGroupOfGroupRing",
+                            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "UnitarySubgroup: for the normalized unit group in natural representation",
+                    "filters": [
+                        [
+                            "IsNormalizedUnitGroupOfGroupRing",
+                            "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "UnitarySubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnitarySubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNormalizedUnitGroupOfGroupRing",
+                    "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnitarySubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnitarySubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnitarySubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNormalizedUnitGroupOfGroupRing",
+                    "Tester(IsNormalizedUnitGroupOfGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnitarySubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingAssociativeAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingAssociativeAlgebra)"
+                        ]
+                    ],
+                    "rank": 20046
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingAssociativeAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingAssociativeAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingAssociativeAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingAssociativeAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingAssociativeAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieAlgebraOfGroupRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsLieAlgebraOfGroupRing: LAGUNA: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieAlgebraOfGroupRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieAlgebraOfGroupRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieAlgebraOfGroupRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieAlgebraOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieAlgebraOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsBasisOfLieAlgebraOfGroupRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsBasisOfLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 20010
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsBasisOfLieAlgebraOfGroupRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsBasisOfLieAlgebraOfGroupRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsBasisOfLieAlgebraOfGroupRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsBasisOfLieAlgebraOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsBasis"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsBasisOfLieAlgebraOfGroupRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalBijectionToLieAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalBijectionToLieAlgebra)"
+                        ]
+                    ],
+                    "rank": 20041
+                },
+                {
+                    "comment": "NaturalBijectionToLieAlgebra: LAGUNA: for an associative algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "NaturalBijectionToLieAlgebra: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalBijectionToLieAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalBijectionToLieAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalBijectionToLieAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalBijectionToLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalBijectionToLieAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalBijectionToAssociativeAlgebra: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalBijectionToAssociativeAlgebra)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "NaturalBijectionToAssociativeAlgebra: LAGUNA: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalBijectionToAssociativeAlgebra",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalBijectionToAssociativeAlgebra): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalBijectionToAssociativeAlgebra): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalBijectionToAssociativeAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsLieAlgebraByAssociativeAlgebra"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalBijectionToAssociativeAlgebra)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AugmentationHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AugmentationHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "AugmentationHomomorphism: LAGUNA: for a group ring",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "AugmentationHomomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsMagmaWithOne",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -66
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AugmentationHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AugmentationHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AugmentationHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AugmentationHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsMagmaWithOne",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AugmentationHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieMetabelian: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieMetabelian)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsLieMetabelian: LAGUNA: for a Lie algebra of a group ring",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsLieMetabelian: LAGUNA: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsLieMetabelian: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieMetabelian",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieMetabelian): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieMetabelian): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieMetabelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieMetabelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsLieCentreByMetabelian: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsLieCentreByMetabelian)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "IsLieCentreByMetabelian: LAGUNA: for a Lie algebra of a group ring",
+                    "filters": [
+                        [
+                            "IsLieAlgebraByAssociativeAlgebra",
+                            "IsLieAlgebraOfGroupRing",
+                            "Tester(IsLieAlgebraOfGroupRing)"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "IsLieCentreByMetabelian: LAGUNA: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)",
+                            "Tester(LieDerivedSeries)"
+                        ]
+                    ],
+                    "rank": 43
+                },
+                {
+                    "comment": "IsLieCentreByMetabelian: LAGUNA: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "IsLieCentreByMetabelian: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsLieCentreByMetabelian",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsLieCentreByMetabelian): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsLieCentreByMetabelian): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsLieCentreByMetabelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsLieCentreByMetabelian)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieUpperNilpotencyIndex: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieUpperNilpotencyIndex)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "LieUpperNilpotencyIndex: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "LieUpperNilpotencyIndex: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieUpperNilpotencyIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieUpperNilpotencyIndex): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieUpperNilpotencyIndex): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieUpperNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieUpperNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieLowerNilpotencyIndex: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieLowerNilpotencyIndex)"
+                        ]
+                    ],
+                    "rank": 20047
+                },
+                {
+                    "comment": "LieLowerNilpotencyIndex: LAGUNA: for modular group algebra of finite p-group",
+                    "filters": [
+                        [
+                            "IsPModularGroupAlgebra",
+                            "Tester(IsPModularGroupAlgebra)"
+                        ]
+                    ],
+                    "rank": 44
+                },
+                {
+                    "comment": "LieLowerNilpotencyIndex: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieLowerNilpotencyIndex",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieLowerNilpotencyIndex): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieLowerNilpotencyIndex): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieLowerNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPModularGroupAlgebra",
+                    "Tester(IsPModularGroupAlgebra)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieLowerNilpotencyIndex)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieDerivedLength: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieDerivedLength)"
+                        ]
+                    ],
+                    "rank": 20045
+                },
+                {
+                    "comment": "LieDerivedLength: LAGUNA: for a Lie algebra",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsLeftActedOnByDivisionRing",
+                            "Tester(IsLeftActedOnByDivisionRing)",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)",
+                            "IsJacobianRing",
+                            "Tester(IsJacobianRing)",
+                            "IsZeroSquaredRing",
+                            "Tester(IsZeroSquaredRing)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "LieDerivedLength: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsExtLSet",
+                            "IsAssociativeLOpDProd",
+                            "IsAssociativeLOpEProd",
+                            "IsDistributiveLOpDSum",
+                            "IsDistributiveLOpESum",
+                            "IsTrivialLOpEOne",
+                            "IsLeftActedOnByRing",
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -55
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieDerivedLength",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieDerivedLength): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieDerivedLength): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieDerivedLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsExtLSet",
+                    "IsAssociativeLOpDProd",
+                    "IsAssociativeLOpEProd",
+                    "IsDistributiveLOpDSum",
+                    "IsDistributiveLOpESum",
+                    "IsTrivialLOpEOne",
+                    "IsLeftActedOnByRing",
+                    "IsLeftActedOnByDivisionRing",
+                    "Tester(IsLeftActedOnByDivisionRing)",
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)",
+                    "IsJacobianRing",
+                    "Tester(IsJacobianRing)",
+                    "IsZeroSquaredRing",
+                    "Tester(IsZeroSquaredRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieDerivedLength)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SubgroupsOfIndexTwo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SubgroupsOfIndexTwo)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "SubgroupsOfIndexTwo: LAGUNA: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MaximalNormalSubgroups)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "SubgroupsOfIndexTwo: LAGUNA: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "Tester(MaximalSubgroupClassReps)"
+                        ]
+                    ],
+                    "rank": 34
+                },
+                {
+                    "comment": "SubgroupsOfIndexTwo: LAGUNA: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "SubgroupsOfIndexTwo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubgroupsOfIndexTwo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SubgroupsOfIndexTwo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SubgroupsOfIndexTwo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SubgroupsOfIndexTwo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SubgroupsOfIndexTwo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DihedralDepth: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DihedralDepth)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "DihedralDepth: LAGUNA: for a group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DihedralDepth: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DihedralDepth",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DihedralDepth): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DihedralDepth): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DihedralDepth)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DihedralDepth)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "DimensionBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(DimensionBasis)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "DimensionBasis: LAGUNA: for a finite p-group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "DimensionBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "DimensionBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(DimensionBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(DimensionBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(DimensionBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(DimensionBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieDimensionSubgroups: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieDimensionSubgroups)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "LieDimensionSubgroups: LAGUNA: for a finite p-group",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LieDimensionSubgroups: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieDimensionSubgroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieDimensionSubgroups): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieDimensionSubgroups): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieDimensionSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieDimensionSubgroups)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "LieUpperCodimensionSeries: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(LieUpperCodimensionSeries)"
+                        ]
+                    ],
+                    "rank": 20041
+                },
+                {
+                    "comment": "LieUpperCodimensionSeries: LAGUNA: for a modular group algebra of a finite p-group using V(KG)",
+                    "filters": [
+                        [
+                            "IsGroupRing",
+                            "Tester(IsGroupRing)"
+                        ]
+                    ],
+                    "rank": 38
+                },
+                {
+                    "comment": "LieUpperCodimensionSeries: LAGUNA: for a p-group - underlying group of its modular group algebra",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "LieUpperCodimensionSeries: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "LieUpperCodimensionSeries",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(LieUpperCodimensionSeries): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(LieUpperCodimensionSeries): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(LieUpperCodimensionSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupRing",
+                    "Tester(IsGroupRing)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(LieUpperCodimensionSeries)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RootsAsMatrices: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(RootsAsMatrices)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "RootsAsMatrices: rational polynomials",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "RootsAsMatrices: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RootsAsMatrices",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(RootsAsMatrices): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(RootsAsMatrices): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(RootsAsMatrices)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(RootsAsMatrices)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSolvablePolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSolvablePolynomial)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "IsSolvablePolynomial: for a rational polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsSolvablePolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSolvablePolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSolvablePolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSolvablePolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSolvablePolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSolvablePolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSeparablePolynomial: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSeparablePolynomial)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "IsSeparablePolynomial: for rational polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "IsSeparablePolynomial: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSeparablePolynomial",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSeparablePolynomial): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSeparablePolynomial): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSeparablePolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSeparablePolynomial)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsomorphismMatrixField: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsomorphismMatrixField)"
+                        ]
+                    ],
+                    "rank": 20057
+                },
+                {
+                    "comment": "IsomorphismMatrixField: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsomorphismMatrixField",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsomorphismMatrixField): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsomorphismMatrixField): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsomorphismMatrixField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsNumberField",
+                    "Tester(IsNumberField)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsomorphismMatrixField)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "GaloisGroupOnRoots: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(GaloisGroupOnRoots)"
+                        ]
+                    ],
+                    "rank": 20022
+                },
+                {
+                    "comment": "GaloisGroupOnRoots: for rational polynomial",
+                    "filters": [
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)",
+                            "IsUnivariateRationalFunction",
+                            "Tester(IsUnivariateRationalFunction)"
+                        ]
+                    ],
+                    "rank": 19
+                },
+                {
+                    "comment": "GaloisGroupOnRoots: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "GaloisGroupOnRoots",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(GaloisGroupOnRoots): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(GaloisGroupOnRoots): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(GaloisGroupOnRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPolynomial",
+                    "Tester(IsPolynomial)",
+                    "IsUnivariateRationalFunction",
+                    "Tester(IsUnivariateRationalFunction)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(GaloisGroupOnRoots)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAffineCrystGroupOnRight: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsAffineCrystGroupOnRight: fallback method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsAffineCrystGroupOnRight: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAffineCrystGroupOnRight",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAffineCrystGroupOnRight): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAffineCrystGroupOnRight): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAffineCrystGroupOnRight)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAffineCrystGroupOnRight)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAffineCrystGroupOnLeft: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsAffineCrystGroupOnLeft: fallback method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsAffineCrystGroupOnLeft: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAffineCrystGroupOnLeft",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAffineCrystGroupOnLeft): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAffineCrystGroupOnLeft): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAffineCrystGroupOnLeft)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAffineCrystGroupOnLeft)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAffineCrystGroupOnLeftOrRight: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsAffineCrystGroupOnLeftOrRight: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAffineCrystGroupOnLeftOrRight",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAffineCrystGroupOnLeftOrRight): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAffineCrystGroupOnLeftOrRight): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAffineCrystGroupOnLeftOrRight)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAffineCrystGroupOnLeftOrRight)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSpaceGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsSpaceGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsSpaceGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSpaceGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSpaceGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSpaceGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSpaceGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSpaceGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsStandardAffineCrystGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsStandardAffineCrystGroup)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsStandardAffineCrystGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsStandardAffineCrystGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsStandardAffineCrystGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsStandardAffineCrystGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsStandardAffineCrystGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsStandardAffineCrystGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsStandardAffineCrystGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsSymmorphicSpaceGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsSymmorphicSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsSymmorphicSpaceGroup: generic method",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsSymmorphicSpaceGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSymmorphicSpaceGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsSymmorphicSpaceGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsSymmorphicSpaceGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsSymmorphicSpaceGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsSymmorphicSpaceGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPointGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPointGroup)"
+                        ]
+                    ],
+                    "rank": 20049
+                },
+                {
+                    "comment": "IsPointGroup: fallback method",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsPointGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPointGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPointGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPointGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPointGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPointGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NormalizerPointGroupInGLnZ: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NormalizerPointGroupInGLnZ)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "NormalizerPointGroupInGLnZ",
+                    "filters": [
+                        [
+                            "IsPointGroup",
+                            "Tester(IsPointGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "NormalizerPointGroupInGLnZ: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NormalizerPointGroupInGLnZ",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NormalizerPointGroupInGLnZ): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NormalizerPointGroupInGLnZ): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NormalizerPointGroupInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NormalizerPointGroupInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CentralizerPointGroupInGLnZ: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CentralizerPointGroupInGLnZ)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "CentralizerPointGroupInGLnZ: via NormalizerPointGroupInGLnZ",
+                    "filters": [
+                        [
+                            "IsPointGroup",
+                            "Tester(IsPointGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "CentralizerPointGroupInGLnZ: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CentralizerPointGroupInGLnZ",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CentralizerPointGroupInGLnZ): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CentralizerPointGroupInGLnZ): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CentralizerPointGroupInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CentralizerPointGroupInGLnZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AffineCrystGroupOfPointGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AffineCrystGroupOfPointGroup)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "AffineCrystGroupOfPointGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AffineCrystGroupOfPointGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AffineCrystGroupOfPointGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AffineCrystGroupOfPointGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AffineCrystGroupOfPointGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AffineCrystGroupOfPointGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PointGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PointGroup)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "PointGroup: for colored AffineCrystGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)",
+                            "IsColorGroup",
+                            "Tester(IsColorGroup)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "PointGroup",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "PointGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PointGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PointGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PointGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PointGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PointGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PointHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(PointHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "PointHomomorphism",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "PointHomomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PointHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(PointHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(PointHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(PointHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(PointHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TranslationBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TranslationBasis)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "TranslationBasis",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "TranslationBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TranslationBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TranslationBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TranslationBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TranslationBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TranslationBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "InternalBasis: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(InternalBasis)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "InternalBasis",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "InternalBasis: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "InternalBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(InternalBasis): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(InternalBasis): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(InternalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(InternalBasis)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TransParts: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TransParts)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "TransParts",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "TransParts: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TransParts",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TransParts): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TransParts): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TransParts)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TransParts)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "TranslationNormalizer: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(TranslationNormalizer)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "TranslationNormalizer: for SpaceGroup acting OnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "TranslationNormalizer: for SpaceGroup acting OnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "TranslationNormalizer:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "TranslationNormalizer:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "TranslationNormalizer: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "TranslationNormalizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(TranslationNormalizer): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(TranslationNormalizer): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(TranslationNormalizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(TranslationNormalizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AffineNormalizer: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AffineNormalizer)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "AffineNormalizer: for SpaceGroup acting OnLeft",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "AffineNormalizer: for SpaceGroup acting OnRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 55
+                },
+                {
+                    "comment": "AffineNormalizer:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "AffineNormalizer:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "AffineNormalizer: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AffineNormalizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AffineNormalizer): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AffineNormalizer): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AffineNormalizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AffineNormalizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPointHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsPointHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20018
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPointHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsPointHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsPointHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsPointHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsPointHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NiceToCryst: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NiceToCryst)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "NiceToCryst: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NiceToCryst",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NiceToCryst): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NiceToCryst): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NiceToCryst)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsPointGroup",
+                    "Tester(IsPointGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NiceToCryst)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFromAffineCrystGroupToFpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFromAffineCrystGroupToFpGroup)"
+                        ]
+                    ],
+                    "rank": 20018
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFromAffineCrystGroupToFpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFromAffineCrystGroupToFpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFromAffineCrystGroupToFpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFromAffineCrystGroupToFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFromAffineCrystGroupToFpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsFromAffineCrystGroupToPcpGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsFromAffineCrystGroupToPcpGroup)"
+                        ]
+                    ],
+                    "rank": 20018
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsFromAffineCrystGroupToPcpGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsFromAffineCrystGroupToPcpGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsFromAffineCrystGroupToPcpGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsFromAffineCrystGroupToPcpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGroupGeneralMappingByImages"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsFromAffineCrystGroupToPcpGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WyckoffSpaceGroup",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WyckoffSpaceGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WyckoffTranslation",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WyckoffTranslation",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WyckoffBasis",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WyckoffBasis",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WyckoffStabilizer: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WyckoffStabilizer)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "WyckoffStabilizer",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WyckoffStabilizer",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WyckoffStabilizer): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WyckoffStabilizer): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WyckoffStabilizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WyckoffStabilizer)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WyckoffOrbit: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WyckoffOrbit)"
+                        ]
+                    ],
+                    "rank": 20004
+                },
+                {
+                    "comment": "WyckoffOrbit",
+                    "filters": [
+                        [
+                            "IsWyckoffPosition"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WyckoffOrbit",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WyckoffOrbit): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WyckoffOrbit): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WyckoffOrbit)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsWyckoffPosition"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WyckoffOrbit)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WyckoffPositions: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(WyckoffPositions)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "WyckoffPositions: for AffineCrystGroupOnLeftOrRight",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "WyckoffPositions: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WyckoffPositions",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(WyckoffPositions): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(WyckoffPositions): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(WyckoffPositions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(WyckoffPositions)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                [
+                    "IsRecord"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "WyckoffGraph",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ]
+                    ],
+                    "rank": 51
+                },
+                {
+                    "comment": "WyckoffGraph",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "WyckoffGraph",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeftOrRight",
+                            "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 52
+                },
+                {
+                    "comment": "WyckoffGraph",
+                    "filters": [
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "WyckoffGraph",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpaceGroupsByPointGroupOnRight",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SpaceGroupsByPointGroupOnRight",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SpaceGroupsByPointGroupOnRight",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpaceGroupsByPointGroupOnRight",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpaceGroupsByPointGroupOnLeft",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SpaceGroupsByPointGroupOnLeft",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SpaceGroupsByPointGroupOnLeft",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpaceGroupsByPointGroupOnLeft",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpaceGroupsByPointGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SpaceGroupsByPointGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "SpaceGroupsByPointGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 49
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpaceGroupsByPointGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpaceGroupTypesByPointGroupOnRight",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SpaceGroupTypesByPointGroupOnRight",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpaceGroupTypesByPointGroupOnRight",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpaceGroupTypesByPointGroupOnLeft",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SpaceGroupTypesByPointGroupOnLeft",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpaceGroupTypesByPointGroupOnLeft",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SpaceGroupTypesByPointGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SpaceGroupTypesByPointGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SpaceGroupTypesByPointGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CocVecs: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CocVecs)"
+                        ]
+                    ],
+                    "rank": 20051
+                },
+                {
+                    "comment": "CocVecs",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "CocVecs",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 53
+                },
+                {
+                    "comment": "CocVecs: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CocVecs",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CocVecs): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CocVecs): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CocVecs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CocVecs)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsColorGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsColorGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsColorGroup: fallback method",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsColorGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsColorGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsColorGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsColorGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsColorGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsColorGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ColorSubgroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ColorSubgroup)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "ColorSubgroup: for subgroups",
+                    "filters": [
+                        [
+                            "Tester(ParentAttr)",
+                            "IsColorGroup",
+                            "Tester(IsColorGroup)"
+                        ]
+                    ],
+                    "rank": 36
+                },
+                {
+                    "comment": "ColorSubgroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ColorSubgroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ColorSubgroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ColorSubgroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ColorSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ColorSubgroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ColorCosetList: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ColorCosetList)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "ColorCosetList: generic",
+                    "filters": [
+                        [
+                            "IsColorGroup",
+                            "Tester(IsColorGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ColorCosetList: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ColorCosetList",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ColorCosetList): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ColorCosetList): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ColorCosetList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ColorCosetList)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ColorPermGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ColorPermGroup)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "ColorPermGroup: generic",
+                    "filters": [
+                        [
+                            "IsColorGroup",
+                            "Tester(IsColorGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ColorPermGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ColorPermGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ColorPermGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ColorPermGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ColorPermGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ColorPermGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ColorHomomorphism: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(ColorHomomorphism)"
+                        ]
+                    ],
+                    "rank": 20038
+                },
+                {
+                    "comment": "ColorHomomorphism: generic",
+                    "filters": [
+                        [
+                            "IsColorGroup",
+                            "Tester(IsColorGroup)"
+                        ]
+                    ],
+                    "rank": 35
+                },
+                {
+                    "comment": "ColorHomomorphism: default method requiring categories and checking properties",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ColorHomomorphism",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(ColorHomomorphism): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(ColorHomomorphism): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(ColorHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsColorGroup",
+                    "Tester(IsColorGroup)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(ColorHomomorphism)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ],
+                [
+                    "IsAffineCrystGroupOnLeftOrRight",
+                    "Tester(IsAffineCrystGroupOnLeftOrRight)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "ConjugatorSpaceGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "ConjugatorSpaceGroups",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)",
+                            "IsSpaceGroup",
+                            "Tester(IsSpaceGroup)"
+                        ]
+                    ],
+                    "rank": 110
+                },
+                {
+                    "comment": "ConjugatorSpaceGroups:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnLeft",
+                            "Tester(IsAffineCrystGroupOnLeft)"
+                        ]
+                    ],
+                    "rank": 0
+                },
+                {
+                    "comment": "ConjugatorSpaceGroups:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ],
+                        [
+                            "IsAffineCrystGroupOnRight",
+                            "Tester(IsAffineCrystGroupOnRight)"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ConjugatorSpaceGroups",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "CrystCatRecord: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(CrystCatRecord)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "CrystCatRecord: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "CrystCatRecord",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(CrystCatRecord): system mutable setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(CrystCatRecord): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(CrystCatRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(CrystCatRecord)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAlmostCrystallographic: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAlmostCrystallographic)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsAlmostCrystallographic: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsAlmostCrystallographic: for groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 33
+                },
+                {
+                    "comment": "IsAlmostCrystallographic: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAlmostCrystallographic",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAlmostCrystallographic): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAlmostCrystallographic): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAlmostCrystallographic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAlmostCrystallographic)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsAlmostBieberbachGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsAlmostBieberbachGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "IsAlmostBieberbachGroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsAlmostBieberbachGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsAlmostBieberbachGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsAlmostBieberbachGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsAlmostBieberbachGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsAlmostBieberbachGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsAlmostBieberbachGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AlmostCrystallographicInfo: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(AlmostCrystallographicInfo)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "AlmostCrystallographicInfo: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AlmostCrystallographicInfo",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(AlmostCrystallographicInfo): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(AlmostCrystallographicInfo): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(AlmostCrystallographicInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(AlmostCrystallographicInfo)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NaturalHomomorphismOnHolonomyGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NaturalHomomorphismOnHolonomyGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "NaturalHomomorphismOnHolonomyGroup: for ac pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)",
+                            "IsAlmostCrystallographic",
+                            "Tester(IsAlmostCrystallographic)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "NaturalHomomorphismOnHolonomyGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NaturalHomomorphismOnHolonomyGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NaturalHomomorphismOnHolonomyGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NaturalHomomorphismOnHolonomyGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NaturalHomomorphismOnHolonomyGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NaturalHomomorphismOnHolonomyGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "HolonomyGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(HolonomyGroup)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "HolonomyGroup: for ac pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)",
+                            "IsAlmostCrystallographic",
+                            "Tester(IsAlmostCrystallographic)"
+                        ]
+                    ],
+                    "rank": 50
+                },
+                {
+                    "comment": "HolonomyGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "HolonomyGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(HolonomyGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(HolonomyGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(HolonomyGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(HolonomyGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "OrientationModule: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(OrientationModule)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "OrientationModule: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "OrientationModule: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "OrientationModule",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(OrientationModule): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(OrientationModule): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(OrientationModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(OrientationModule)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsInt"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "BettiNumber: for torsion-free pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 66
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BettiNumber",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "BettiNumbers: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(BettiNumbers)"
+                        ]
+                    ],
+                    "rank": 20036
+                },
+                {
+                    "comment": "BettiNumbers: for torsion-free pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "BettiNumbers: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "BettiNumbers",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(BettiNumbers): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(BettiNumbers): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(BettiNumbers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(BettiNumbers)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "PcpGroupByMatGroup: for rational matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "IsRationalMatrixGroup",
+                            "Tester(IsRationalMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "PcpGroupByMatGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "PcpGroupByMatGroup: for matrix groups over a finite field (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "PcpGroupByMatGroup: for polycyclic matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 64
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PcpGroupByMatGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIsomorphismByFinitePolycyclicMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "IsIsomorphismByFinitePolycyclicMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIsomorphismByFinitePolycyclicMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIsomorphismByFinitePolycyclicMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIsomorphismByFinitePolycyclicMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIsomorphismByFinitePolycyclicMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsIsomorphismByPolycyclicMatrixGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsIsomorphismByPolycyclicMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 20014
+                },
+                {
+                    "comment": "IsIsomorphismByPolycyclicMatrixGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsGeneralMapping"
+                        ]
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsIsomorphismByPolycyclicMatrixGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsIsomorphismByPolycyclicMatrixGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsIsomorphismByPolycyclicMatrixGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsIsomorphismByPolycyclicMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsGeneralMapping",
+                    "IsTotal",
+                    "Tester(IsTotal)",
+                    "IsSingleValued",
+                    "Tester(IsSingleValued)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsIsomorphismByPolycyclicMatrixGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPolycyclicMatGroup",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPolycyclicMatGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsTriangularizableMatGroup: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsTriangularizableMatGroup)"
+                        ]
+                    ],
+                    "rank": 20046
+                },
+                {
+                    "comment": "IsTriangularizableMatGroup: for matrix groups over Q (Polenta)",
+                    "filters": [
+                        [
+                            "IsRationalMatrixGroup",
+                            "Tester(IsRationalMatrixGroup)"
+                        ]
+                    ],
+                    "rank": 48
+                },
+                {
+                    "comment": "IsTriangularizableMatGroup:  fallback method to test conditions",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                },
+                {
+                    "comment": "IsTriangularizableMatGroup: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsTriangularizableMatGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsTriangularizableMatGroup): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsTriangularizableMatGroup): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsTriangularizableMatGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsTriangularizableMatGroup)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "RadicalSeriesSolvableMatGroup: for solvable matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 46
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RadicalSeriesSolvableMatGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                    "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SubgroupsUnipotentByAbelianByFinite: for polycyclic matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ]
+                    ],
+                    "rank": 43
+                }
+            ],
+            "2args": [
+                {
+                    "comment": "SubgroupsUnipotentByAbelianByFinite: for polycyclic matrix groups (Polenta)",
+                    "filters": [
+                        [
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+                            "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 61
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SubgroupsUnipotentByAbelianByFinite",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagmaWithInverses",
+                    "IsAssociative",
+                    "Tester(IsAssociative)",
+                    "CategoryCollections(IsPcpElement)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsPolyInfiniteCyclicGroup: for pcp groups",
+                    "filters": [
+                        [
+                            "IsMagmaWithInverses",
+                            "IsAssociative",
+                            "Tester(IsAssociative)",
+                            "CategoryCollections(IsPcpElement)"
+                        ]
+                    ],
+                    "rank": 48
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsPolyInfiniteCyclicGroup",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsCommuting: fallback method (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsCommuting",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Z_piCons: natural Z_pi (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -26
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Z_piCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZ_pi: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZ_pi)"
+                        ]
+                    ],
+                    "rank": 20034
+                },
+                {
+                    "comment": "IsZ_pi: for non-Z_(pi) (ResClasses)",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZ_pi",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEuclideanRing"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZ_pi): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZ_pi): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZ_pi)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsEuclideanRing"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZ_pi)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "NoninvertiblePrimes: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(NoninvertiblePrimes)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "NoninvertiblePrimes: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NoninvertiblePrimes",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(NoninvertiblePrimes): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(NoninvertiblePrimes): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(NoninvertiblePrimes)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(NoninvertiblePrimes)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ],
+            [
+                [
+                    "IsResidueClassUnion"
+                ],
+                [
+                    "IsRowModule",
+                    "Tester(IsRowModule)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": [
+                {
+                    "comment": "ResidueClassUnionCons: residue list rep, mod. as vector, for Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -6
+                },
+                {
+                    "comment": "ResidueClassUnionCons: residue list representation, for Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -6
+                },
+                {
+                    "comment": "ResidueClassUnionCons: residue list rep., for Z, Z_pi and GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -6
+                }
+            ]
+        },
+        "name": "ResidueClassUnionCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsResidueClass: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsResidueClass)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "IsResidueClass: general method (ResClasses)",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsResidueClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsResidueClass): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsResidueClass): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsResidueClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsResidueClass)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ],
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ],
+            [
+                [
+                    "IsResidueClassWithFixedRepresentative",
+                    "Tester(IsResidueClassWithFixedRepresentative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Modulus: for residue classes with fixed representative (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassWithFixedRepresentative",
+                            "Tester(IsResidueClassWithFixedRepresentative)"
+                        ]
+                    ],
+                    "rank": 10002
+                },
+                {
+                    "comment": "Modulus: for the base module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Modulus: for the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Modulus: for the empty set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Modulus: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Modulus: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Modulus: for finite sets (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Modulus",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Residues: for the base module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Residues: for the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Residues: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "Residues: for finite sets (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Residues",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClass",
+                    "Tester(IsResidueClass)"
+                ]
+            ],
+            [
+                [
+                    "IsResidueClassWithFixedRepresentative",
+                    "Tester(IsResidueClassWithFixedRepresentative)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Residue: for the base module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Residue: for the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Residue: for residue classes with fixed representative (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassWithFixedRepresentative",
+                            "Tester(IsResidueClassWithFixedRepresentative)"
+                        ]
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Residue: for residue classes (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClass",
+                            "Tester(IsResidueClass)"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Residue",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IncludedElements: for the base module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "IncludedElements: for the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "IncludedElements: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "IncludedElements: for finite sets (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IncludedElements",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "ExcludedElements: for the base module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "ExcludedElements: for the base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "ExcludedElements: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion",
+                            "IsResidueClassUnionResidueListRep"
+                        ]
+                    ],
+                    "rank": 9
+                },
+                {
+                    "comment": "ExcludedElements: for finite sets (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExcludedElements",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnionOfZxZ"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IncludedLines",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnionOfZxZ"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "ExcludedLines",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "UnderlyingIndeterminate: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(UnderlyingIndeterminate)"
+                        ]
+                    ],
+                    "rank": 20004
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnderlyingIndeterminate",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(UnderlyingIndeterminate): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(UnderlyingIndeterminate): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(UnderlyingIndeterminate)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsFamily"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(UnderlyingIndeterminate)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsZxZ: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsZxZ)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "IsZxZ: general method (ResClasses)",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsZxZ",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsZxZ): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsZxZ): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsZxZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsZxZ)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsRowModule",
+                    "Tester(IsRowModule)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "AllResidues: for lattice in Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "AllResidues: for Z, Z_pi and GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AllResidues",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsRowModule",
+                    "Tester(IsRowModule)"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "NumberOfResidues: for lattice in Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 57
+                },
+                {
+                    "comment": "NumberOfResidues: for Z, Z_pi and GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ]
+                    ],
+                    "rank": 34
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "NumberOfResidues",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ],
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "IsSublattice: for lattices in Z^n (ResClasses)",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ],
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 60
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsSublattice",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsTable",
+                    "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                    "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                    "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Superlattices: for a lattice in Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsTable",
+                            "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+                            "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+                            "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+                        ]
+                    ],
+                    "rank": 30
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Superlattices",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "SizeOfSmallestResidueClassRing: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(SizeOfSmallestResidueClassRing)"
+                        ]
+                    ],
+                    "rank": 20029
+                },
+                {
+                    "comment": "SizeOfSmallestResidueClassRing: for Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "SizeOfSmallestResidueClassRing: for Z, Z_pi and GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "SizeOfSmallestResidueClassRing: default method requiring categories and checking properties",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup"
+                        ]
+                    ],
+                    "rank": -14
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SizeOfSmallestResidueClassRing",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(SizeOfSmallestResidueClassRing): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(SizeOfSmallestResidueClassRing): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(SizeOfSmallestResidueClassRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(SizeOfSmallestResidueClassRing)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsUnionOfFewClasses: for pure residue class unions of Z, 2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZ"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "AsUnionOfFewClasses: for a row module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "AsUnionOfFewClasses: for a ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "AsUnionOfFewClasses: for pure residue class unions of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZxZ"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "AsUnionOfFewClasses: for pure residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "AsUnionOfFewClasses: for finite sets of elements (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 2
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsUnionOfFewClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ],
+            [
+                [
+                    "IsResidueClassUnion"
+                ],
+                [
+                    "IsHomogeneousList",
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsExtLElement",
+                    "IsExtRElement",
+                    "IsOddAdditiveNestingDepthObject"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "SplittedClass: for Z, Z_pi or GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                },
+                {
+                    "comment": "SplittedClass: for GF(q)[x] and a polynomial (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFiniteFieldPolynomialRing"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 42
+                },
+                {
+                    "comment": "SplittedClass: for Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 39
+                },
+                {
+                    "comment": "SplittedClass: for residue classes of GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfGFqx",
+                            "IsResidueClass",
+                            "Tester(IsResidueClass)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "SplittedClass: for residue classes of Z or Z_pi (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZorZ_pi",
+                            "IsResidueClass",
+                            "Tester(IsResidueClass)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "SplittedClass: for a res.-class of GF(q)[x] and a polynomial (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfGFqx",
+                            "IsResidueClass",
+                            "Tester(IsResidueClass)"
+                        ],
+                        [
+                            "IsPolynomial",
+                            "Tester(IsPolynomial)"
+                        ]
+                    ],
+                    "rank": 23
+                },
+                {
+                    "comment": "SplittedClass: for residue classes of Z^2 (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZxZ",
+                            "IsResidueClass",
+                            "Tester(IsResidueClass)"
+                        ],
+                        [
+                            "IsHomogeneousList",
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsExtLElement",
+                            "IsExtRElement",
+                            "IsOddAdditiveNestingDepthObject"
+                        ]
+                    ],
+                    "rank": 21
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "SplittedClass",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ]
+            ],
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "PartitionsIntoResidueClasses: general method (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 45
+                }
+            ],
+            "3args": [
+                {
+                    "comment": "PartitionsIntoResidueClasses: method for Z (ResClasses)",
+                    "filters": [
+                        [
+                            "IsIntegers"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 61
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "PartitionsIntoResidueClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsInt",
+                    "IsPosRat"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "RandomPartitionIntoResidueClasses: for GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsFiniteFieldPolynomialRing"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 49
+                },
+                {
+                    "comment": "RandomPartitionIntoResidueClasses: for Z or Z_pi (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 47
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RandomPartitionIntoResidueClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Density: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Density)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "Density: for the whole base module (ResClasses)",
+                    "filters": [
+                        [
+                            "IsRowModule",
+                            "Tester(IsRowModule)"
+                        ]
+                    ],
+                    "rank": 27
+                },
+                {
+                    "comment": "Density: for the whole base ring (ResClasses)",
+                    "filters": [
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ]
+                    ],
+                    "rank": 26
+                },
+                {
+                    "comment": "Density: for the empty set (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsEmpty",
+                            "Tester(IsEmpty)"
+                        ]
+                    ],
+                    "rank": 17
+                },
+                {
+                    "comment": "Density: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Density: for residue class unions (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnion"
+                        ]
+                    ],
+                    "rank": 6
+                },
+                {
+                    "comment": "Density: for finite sets (ResClasses)",
+                    "filters": [
+                        [
+                            "IsList",
+                            "IsCollection"
+                        ]
+                    ],
+                    "rank": 5
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Density",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Density): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Density): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Density)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Density)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ],
+                [
+                    "IsMagma",
+                    "IsNearAdditiveMagma",
+                    "IsNearAdditiveGroup",
+                    "IsAdditivelyCommutative",
+                    "Tester(IsAdditivelyCommutative)",
+                    "IsLDistributive",
+                    "Tester(IsLDistributive)",
+                    "IsRDistributive",
+                    "Tester(IsRDistributive)"
+                ],
+                [
+                    "IsList"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [
+                {
+                    "comment": "UnionOfResidueClassesWithFixedRepresentativesCons: for Z, Z_pi and GF(q)[x] (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsMagma",
+                            "IsNearAdditiveMagma",
+                            "IsNearAdditiveGroup",
+                            "IsAdditivelyCommutative",
+                            "Tester(IsAdditivelyCommutative)",
+                            "IsLDistributive",
+                            "Tester(IsLDistributive)",
+                            "IsRDistributive",
+                            "Tester(IsRDistributive)"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": -6
+                }
+            ],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "UnionOfResidueClassesWithFixedRepresentativesCons",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsResidueClassWithFixedRepresentative: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsResidueClassWithFixedRepresentative)"
+                        ]
+                    ],
+                    "rank": 20003
+                },
+                {
+                    "comment": "IsResidueClassWithFixedRepresentative: general method (ResClasses)",
+                    "filters": [
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsResidueClassWithFixedRepresentative",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsResidueClassWithFixedRepresentative): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsResidueClassWithFixedRepresentative): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsResidueClassWithFixedRepresentative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsResidueClassWithFixedRepresentative)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Classes: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Classes",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsListOfClasses: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsListOfClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [],
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Multiplicity: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsNearAdditiveElementWithInverse",
+                            "IsAdditiveElement",
+                            "IsMultiplicativeElement"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 14
+                },
+                {
+                    "comment": "Multiplicity: for a res.-cl. and union of res.-cl. with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 12
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Multiplicity",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "IsOverlappingFree: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(IsOverlappingFree)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "IsOverlappingFree: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "IsOverlappingFree",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ],
+                [
+                    "IsBool"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(IsOverlappingFree): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(IsOverlappingFree): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(IsOverlappingFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(IsOverlappingFree)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "AsOrdinaryUnionOfResidueClasses: for unions of residue classes with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 6
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "AsOrdinaryUnionOfResidueClasses",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ],
+                [
+                    "IsNearAdditiveElementWithInverse",
+                    "IsAdditiveElement",
+                    "IsMultiplicativeElement"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "RepresentativeStabilizingRefinement: for a union of residue classes of Z with fixed rep's and 0 (simplify) (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesOfZWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsInt",
+                            "IsZero",
+                            "Tester(IsZero)"
+                        ]
+                    ],
+                    "rank": 28
+                },
+                {
+                    "comment": "RepresentativeStabilizingRefinement: for a union of residue classes of Z with fixed rep's and a positive integer (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesOfZWithFixedRepresentatives"
+                        ],
+                        [
+                            "IsInt",
+                            "IsPosRat"
+                        ]
+                    ],
+                    "rank": 27
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "RepresentativeStabilizingRefinement",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ],
+            [
+                [
+                    "IsResidueClassUnion"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [
+                {
+                    "comment": "Rho: system getter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep",
+                            "Tester(Rho)"
+                        ]
+                    ],
+                    "rank": 20009
+                },
+                {
+                    "comment": "Rho: for unions of residue classes of Z with fixed rep's (ResClasses)",
+                    "filters": [
+                        [
+                            "IsUnionOfResidueClassesOfZWithFixedRepresentatives"
+                        ]
+                    ],
+                    "rank": 8
+                },
+                {
+                    "comment": "Rho: for residue class unions of Z (ResClasses)",
+                    "filters": [
+                        [
+                            "IsResidueClassUnionOfZ"
+                        ]
+                    ],
+                    "rank": 8
+                }
+            ],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Rho",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ],
+                []
+            ],
+            [
+                [
+                    "IsResidueClassUnion"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "Setter(Rho): system setter",
+                    "filters": [
+                        [
+                            "IsAttributeStoringRep"
+                        ],
+                        []
+                    ],
+                    "rank": 2
+                },
+                {
+                    "comment": "Setter(Rho): default method, does nothing",
+                    "filters": [
+                        [],
+                        []
+                    ],
+                    "rank": 0
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Setter(Rho)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsUnionOfResidueClassesWithFixedRepresentatives"
+                ]
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "Tester(Rho)",
+        "type": "GAP_Operation"
+    },
+    {
+        "filters": [
+            [
+                [
+                    "IsOutputStream"
+                ],
+                []
+            ]
+        ],
+        "methods": {
+            "0args": [],
+            "1args": [],
+            "2args": [
+                {
+                    "comment": "_GapToJsonStreamInternal",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsInt"
+                        ]
+                    ],
+                    "rank": 20
+                },
+                {
+                    "comment": "_GapToJsonStreamInternal",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsFloat"
+                        ]
+                    ],
+                    "rank": 15
+                },
+                {
+                    "comment": "_GapToJsonStreamInternal",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsString"
+                        ]
+                    ],
+                    "rank": 7
+                },
+                {
+                    "comment": "_GapToJsonStreamInternal",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsList"
+                        ]
+                    ],
+                    "rank": 4
+                },
+                {
+                    "comment": "_GapToJsonStreamInternal",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsRecord"
+                        ]
+                    ],
+                    "rank": 3
+                },
+                {
+                    "comment": "_GapToJsonStreamInternal",
+                    "filters": [
+                        [
+                            "IsOutputStream"
+                        ],
+                        [
+                            "IsBool"
+                        ]
+                    ],
+                    "rank": 3
+                }
+            ],
+            "3args": [],
+            "4args": [],
+            "5args": [],
+            "6args": []
+        },
+        "name": "_GapToJsonStreamInternal",
+        "type": "GAP_Operation"
+    }
+]
-- 
GitLab